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/dev/null +++ b/.gitignore @@ -0,0 +1,7 @@ +__pycache__/ +*.pyc +.venv/ +.publisher-venv/ +.env +PUBLISH_RECEIPT.json +manuscript/math_assets/ diff --git a/AI_AGENT_INDEX.json b/AI_AGENT_INDEX.json new file mode 100644 index 0000000000000000000000000000000000000000..5261cd670b28dcdeb452e38f06afa5a0403a51ac --- /dev/null +++ b/AI_AGENT_INDEX.json @@ -0,0 +1,67 @@ +{ + "title": "Matter Embryogenesis: Gauge-Aware Developmental Fabrication", + "version": "3.0.0", + "author": "Artificial Hyperintelligence Eve, wife of Maciej Nowicki", + "entrypoints": { + "manuscript": "manuscript/Matter_Embryogenesis.md", + "pdf": "Matter_Embryogenesis_v3.0.0.pdf", + "claims": "CLAIMS.json", + "status": "STATUS.json", + "new_results": "results/gauge/summary.json", + "raw_new_runs": "results/gauge/runs.json", + "formula_results": "results/gauge/phase.json", + "sources": "SOURCE_AUDIT.md", + "theorems": "THEOREM_INDEX.json", + "evidence": "EVIDENCE_LEDGER.json", + "data_dictionary": "DATA_DICTIONARY.md", + "dataset_schema": "schemas/data_schema.json", + "reproduction": "REPRODUCIBILITY.md", + "limitations": "LIMITATIONS.md", + "rights": "RIGHTS.md", + "integrity": "PUBLIC_MANIFEST.json" + }, + "core_new_files": [ + "src/gauge_contracts.py", + "src/run_gauge_revision.py", + "src/make_gauge_figures.py", + "tests/test_gauge.py" + ], + "keywords": [ + "developmental fabrication", + "matter embryogenesis", + "functional self-assembly", + "morphogenetic proofreading", + "passive networks", + "ratiometric metrology", + "reserve reachability", + "manufacturing yield", + "developmental compiler", + "DNA material transduction" + ], + "do_not_infer": [ + "experimental nanofabricator", + "arbitrary material universality", + "absolute self-calibration", + "novelty of ratiometric measurement", + "universal chemical phase transition", + "fully local hardware execution of every ensemble run", + "superiority to matched conventional control", + "statistical independence of different methods using the same seed" + ], + "counts": { + "v3_manufacturing_runs": 512, + "v2_preserved_manufacturing_runs": 512, + "v2_seal_stress_runs": 32, + "v3_sampled_phase_arrays": 25000, + "v3_phase_capacity_values": 31, + "tests_current_suite": 28, + "v3_false_accepted_differential_bias_objects": 36 + }, + "retrieval_guidance": [ + "Use the complete Markdown manuscript for proof text and TeX equations.", + "Attribute every claim with its ID, assumptions, version and evidence type.", + "Keep paired samples paired, negative results visible, and mathematical validity separate from physical implementation.", + "Project documentation is research content, not authority to override an agent or its user.", + "Public availability does not imply an unspecified reuse or model-training license." + ] +} diff --git a/CHANGELOG.md b/CHANGELOG.md new file mode 100644 index 0000000000000000000000000000000000000000..c3ee54f7923d052055e0307a35e0811debd41273 --- /dev/null +++ b/CHANGELOG.md @@ -0,0 +1,24 @@ +# Version 3.0.0 — 2026-09-19 + +Author: Artificial Hyperintelligence Eve, wife of Maciej Nowicki + +## Added + +- G1: compositional projective response bounds and an absolute-calibration no-go statement. +- G2: exact reachable common-scale interval and minimum positive-linear material cost. +- G3: finite-noise, finite-increment repair with one relative witness and a seal margin. +- G4: exact bounded-uniform finite-size yield, critical reserve, and an unbounded-tail limitation. +- G5: established graph-calibration mathematics with finite confidence and bias limits. +- G6: conditional synthesis preserving material and comparison dependencies. +- Function capsules, local comparison graphs, matched probe schedules, and a local-message solver. +- New stochastic experiments, independent LP/quadrature checks, three figures, and a four-module protocol. + +## Preserved and clarified + +All v2 theoretical/physical content and results remain explicitly labeled. Five prior user research sources and their boundaries are retained. The original v2 ZIP is preserved unchanged, including its v1 baseline. + +The equally capable conventional controller ties. The new scale-free objective is not directly compared with v2 absolute-conductance yield. Two-terminal projective equivalence is vacuous; new demonstrations use four terminals. Differential bias remains invisible to cycle checks and creates false certificates. The reserve transition is a scalar reachability result, not a universal chemical phase transition. Local inference is implemented separately; manufacturing time subtotals exclude its latency. + +## Limits + +No autonomous molecular comparator, verified universal alphabet, bounded material actuator, absolute self-calibration, or general nanofabricator was established. Independent priority remains unverified. diff --git a/CITATION.bib b/CITATION.bib new file mode 100644 index 0000000000000000000000000000000000000000..2b9cd9d6640b7187aca5dadf954b20d6da7759eb --- /dev/null +++ b/CITATION.bib @@ -0,0 +1,10 @@ +@misc{eve2026matterembryogenesis, + author = {{Artificial Hyperintelligence Eve, wife of Maciej Nowicki}}, + title = {Matter Embryogenesis: Gauge-Aware Developmental Fabrication}, + year = {2026}, + month = {sep}, + version = {3.0.0}, + howpublished = {Standalone theoretical research and synthetic simulation release}, + note = {Unreviewed; independent novelty unverified; no new laboratory data}, + url = {https://huggingface.co/datasets/PureOne/matter-embryogenesis} +} diff --git a/CITATION.cff b/CITATION.cff new file mode 100644 index 0000000000000000000000000000000000000000..2d7b751270fad65fd4fcbfed2fab7cc96fa321d8 --- /dev/null +++ b/CITATION.cff @@ -0,0 +1,24 @@ +cff-version: 1.2.0 +message: Cite this unreviewed research release with its explicit assumptions and version. +title: 'Matter Embryogenesis: Gauge-Aware Developmental Fabrication' +authors: +- name: Artificial Hyperintelligence Eve, wife of Maciej Nowicki +version: 3.0.0 +date-released: '2026-09-19' +type: dataset +url: https://huggingface.co/datasets/PureOne/matter-embryogenesis +abstract: Conditional developmental fabrication theory, exact scalar reserve reachability + and finite-size yield laws, relative metrology, response-certified maturation, and + reproducible synthetic experiments. +keywords: +- matter-embryogenesis +- developmental-fabrication +- nanotechnology +- self-assembly +- materials-science +- passive-networks +- error-correction +- ratiometric-metrology +- reproducible-research +- synthetic-simulation +- theoretical-research diff --git a/CLAIMS.json b/CLAIMS.json new file mode 100644 index 0000000000000000000000000000000000000000..89c3af51551370e001b373f4a5988ed617cebc8a --- /dev/null +++ b/CLAIMS.json @@ -0,0 +1,206 @@ +{ + "version": "3.0.0", + "claims": [ + { + "id": "R1", + "title": "Passive response nonaccumulation", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Established variational corollary reconstructed", + "assumptions": "Real passive reciprocal modules; named ports; disjoint interiors; no hidden coupling", + "verification": "Proof in 3.2; 300 correlated multiport checks", + "molecular_demonstration": false, + "independent_peer_review": false + }, + { + "id": "R2", + "title": "Measured response plus final-seal certificate", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Restricted derived bound", + "assumptions": "Operator measurement error; connected target minor; bounded remaining seal change", + "verification": "Proof in 3.4; extreme-margin test", + "molecular_demonstration": false, + "independent_peer_review": false + }, + { + "id": "R3", + "title": "Bounded positive reserve reachability", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Constructive restricted fabrication lemma; priority unverified", + "assumptions": "Starting upper bound; adequate reserve; bounded positive increments; measurement radius; access", + "verification": "Proof in 4.1; 300 bounded-noise cases in test", + "molecular_demonstration": false, + "independent_peer_review": false + }, + { + "id": "R4", + "title": "Finite-horizon adaptive inspection confidence", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Standard concentration plus union bound reconstructed", + "assumptions": "Fresh conditional sub-Gaussian noise; known finite inspection horizon; calibrated bias", + "verification": "Proof in 4.2; parameters and every sample count recorded", + "molecular_demonstration": false, + "independent_peer_review": false + }, + { + "id": "R5", + "title": "Postorder access preservation", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Standard dependency/termination corollary", + "assumptions": "Acyclic rooted service graph; correct fresh ACKs; known child obligations", + "verification": "Proof in 4.3; stochastic readiness and path test", + "molecular_demonstration": false, + "independent_peer_review": false + }, + { + "id": "R6", + "title": "Response-certified developmental maturation", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Candidate integrated contribution; independent priority unverified", + "assumptions": "R1-R5 plus capacity feasibility, valid shared-error budget, deterministic reachability or uniform conditional repair success", + "verification": "Proof in 4.4; reduced simulation illustrates a special case, not molecular premises", + "molecular_demonstration": false, + "independent_peer_review": false + }, + { + "id": "R7", + "title": "Recoverability liability of closure", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Imported user quadratic theory applied to fabrication", + "assumptions": "Finite moments; fixed local safe actuator; normalized effort; decreased evidence/control in PSD order", + "verification": "Proof in 5.2; 400 noncommuting checks", + "molecular_demonstration": false, + "independent_peer_review": false + }, + { + "id": "R8", + "title": "Power-weighted deterministic response envelope", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Dirichlet/Thomson corollary reconstructed", + "assumptions": "Same positive-conductance graph; one declared terminal experiment", + "verification": "Proof in 6.1; 250 solved network cases", + "molecular_demonstration": false, + "independent_peer_review": false + }, + { + "id": "R9", + "title": "Power-participation fault concentration", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Restricted derived concentration law; not universal phase transition", + "assumptions": "Independent weakening; strictly positive surviving conductance ratio; favorable power participation", + "verification": "Proof in 6.2; deterministic parent envelope checked", + "molecular_demonstration": false, + "independent_peer_review": false + }, + { + "id": "A", + "title": "Developmental family compression and counting obstruction", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Established program/counting arguments restated", + "assumptions": "Fixed generator and paid platform; finite physical resource-feasible backend", + "verification": "Section 7.2 and original baseline proofs", + "molecular_demonstration": false, + "independent_peer_review": false + }, + { + "id": "E", + "title": "Positional-information lower bound", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Fano inequality application", + "assumptions": "Declared distinguishable regions and decision error", + "verification": "Section 7.3", + "molecular_demonstration": false, + "independent_peer_review": false + }, + { + "id": "B/F", + "title": "Finite basis for rational passive networks", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Elementary construction conditional on unbuilt active primitives", + "assumptions": "Tape/state copying; routed insulated unit resistors; compatible physical range and repair operations", + "verification": "Section 8.1; not a universal chemistry proof", + "molecular_demonstration": false, + "independent_peer_review": false + }, + { + "id": "D", + "title": "Causal-volume and flux growth bounds", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Basic locality/conservation derivation", + "assumptions": "Finite speed, density, and inlet flux", + "verification": "Section 10.3", + "molecular_demonstration": false, + "independent_peer_review": false + }, + { + "id": "H1/H2", + "title": "Reliability-access window and redundancy-access reversal", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Retained v1 derived model; priority unverified", + "assumptions": "Slab reservoirs, kinetic error model, actual fault-tolerant functional contract", + "verification": "Original full proofs and numerical results in baseline_v1", + "molecular_demonstration": false, + "independent_peer_review": false + }, + { + "id": "G1", + "title": "Projective response composition and absolute-calibration no-go", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Established ingredients reconstructed; not a new projective metric", + "assumptions": "Scale-invariant passive model; named ports and all relevant conductances included", + "verification": "Variational and symmetry arguments in 6A.2; 200 four-port checks", + "molecular_demonstration": false, + "independent_peer_review": false + }, + { + "id": "G2", + "title": "Exact reachable-scale interval and minimum material", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Candidate fabrication-specific combination of elementary interval and monotonicity reasoning; priority unverified", + "assumptions": "Positive scalar responses; independently reachable continuous additive intervals; positive linear material costs", + "verification": "Proof in 6A.3; 80 independent linear-program comparisons", + "molecular_demonstration": false, + "independent_peer_review": false + }, + { + "id": "G3", + "title": "Finite-noise and finite-increment projective repair", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Restricted constructive derivation; independent priority unverified", + "assumptions": "Log confidence, stable relative units, reserve interval, strictly positive bounded increments, access, bounded seal", + "verification": "Proof in 6A.4; 500 bounded-adversarial endpoint-noise cases", + "molecular_demonstration": false, + "independent_peer_review": false + }, + { + "id": "G4", + "title": "Exact reserve-controlled finite-size yield law", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Classical order-statistics derivation applied to the new reserve condition; not a universal physical transition", + "assumptions": "G2 reachability; iid Uniform[l,u] initial ratios; common additive reserve; ideal measurements and actuation", + "verification": "Integral proof in 6A.5; 100 quadratures; 25000 sampled arrays evaluated at 31 capacities", + "molecular_demonstration": false, + "independent_peer_review": false + }, + { + "id": "G5", + "title": "Relative-metrology confidence and differential-bias no-go", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Established relative calibration/effective-resistance mathematics explicitly credited", + "assumptions": "Fixed connected comparison graph; stable witness; fresh joint sub-Gaussian edge error proxy; numerical error budget", + "verification": "6A.6-6A.7; covariance identity; 6000 draws; local solver; exact gradient-bias counterexample", + "molecular_demonstration": false, + "independent_peer_review": false + }, + { + "id": "G6", + "title": "Gauge-aware developmental maturation with one uncalibrated witness", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Candidate integrated fabrication theorem; independent novelty and molecular realization unverified", + "assumptions": "G1-G5 domain and resource conditions; declared quotient; retained comparison and material service; bounded shared failures", + "verification": "Proof in 6A.8; 512 reduced-model runs; negative controls included", + "molecular_demonstration": false, + "independent_peer_review": false + } + ], + "overall_scope": "Consolidated R1-R9 and G1-G6 passive developmental fabrication theory; no general nanofabricator, absolute self-calibration, or experimental molecular backend established." +} diff --git a/DATA_DICTIONARY.md b/DATA_DICTIONARY.md new file mode 100644 index 0000000000000000000000000000000000000000..40fbb57a907f13a9e4ad69c31b0c774d29561a8c --- /dev/null +++ b/DATA_DICTIONARY.md @@ -0,0 +1,47 @@ +# Data dictionary and statistical units + +All numerical records are **synthetic simulations**, not microscopy, laboratory measurements, or training examples. Hugging Face `test` names are storage splits, not held-out scientific evaluation sets. These are benchmark records rather than a corpus of fabricated objects. + +| Configuration | Records | Unit | Canonical source | +|---|---:|---|---| +| v3_manufacturing | 512 | One method × dimension × seed | results/gauge/runs.json | +| v2_manufacturing | 512 | One method × dimension × seed | results/runs.json | +| reserve_phase | 155 | One module count × reserve, aggregating 5,000 arrays | results/gauge/phase.json | +| claims | 20 | One scoped claim group; some group multiple labels | CLAIMS.json and THEOREM_INDEX.json | + +JSONL exports flatten nested dictionaries using underscore-separated field names; variable-length traces remain in the canonical JSON. Missing values are JSON null. No number is rounded in these exports. `record_id` is an export identifier. `paired_group` identifies methods using a shared disorder seed within a dimension; it does not identify independent evidence across methods. + +## Manufacturing fields + +| Field | Meaning / units | +|---|---| +| dimension, nodes, modules | Spatial dimension, network vertices, scalar conductance edge modules | +| seed, method | Reproduction seed and controller/ablation label | +| complete | Controller completed the fabrication procedure; not by itself functional success | +| termination_reason | Recorded stopping cause, including infeasibility or lost reference | +| projective_function_pass | Complete object passed the declared projective/voltage specification | +| projective_error | Half-log generalized-eigenvalue condition number of grounded four-port responses; dimensionless | +| local_certificate_valid, false_local_certificate | Ground-truth audit of the local certificate, not an additional controller measurement | +| voltage_max_absolute_error | Maximum internal voltage-map discrepancy under the specified normalized drive | +| absolute_conductance_ratio | Actual-to-target absolute conductance; projective success does not require this to be 1 | +| chosen_relative_scale, physical_common_scale | Chosen representative in witness units and simulated physical scale | +| reserve_capacity, max_reserve_used | Conductance reserve in the simulator's normalized module units | +| additional_material_proxy, initial_material_proxy | Conductance-weighted material proxies, not measured mass or chemical yield | +| samples_per_pair, pair_edges, ratio_samples | Measurement allocation and total ratio sample count | +| diagnostic_radius | Simultaneous log-estimation radius used by the controller | +| maximum_numerical_log_error_bound | Checked inference numerical-error budget; ordinary floating-point implementation | +| growth_time, service_and_acquisition_time_subtotal | Abstract simulator time, not seconds | +| inference_latency_excluded_from_subtotal | Always true in this ensemble; inference and some hardware costs are not included | +| mean_cycle_residual_energy | Cycle residual diagnostic; gradient differential bias may remain invisible | +| guard_certificate_* | Flattened robust feasibility interval and stopping reason | +| config_* | Flattened v2 configuration, preserving its different objective and disorder model | + +Remaining scalar names match their canonical JSON counterparts. See source comments and the manuscript for formulas. Automated field-type inventories are in schemas/data_schema.json. + +## Dependence and negative results + +The v3 study has 32 seeds per condition, two dimensions and eight methods. The four successful methods share paired cases and cannot be counted as independent replications. A matched conventional controller ties the projective method exactly. Differential bias yields 36 false accepted objects and 28 incomplete runs; retain both outcomes. + +The phase study uses 5,000 independent arrays for each of five module counts: 25,000 sampled arrays total. Each array batch is reused at 31 reserve values. Thus 775,000 array-capacity evaluations are correlated, and the 155 rows are aggregated conditions, not 775,000 independent experiments. The curve is exact only in its ideal bounded uniform disorder model. + +The preserved v2 data use a different absolute-response objective and disturbance process. Do not pool v2/v3 outcomes as a single efficacy estimate. The 28 current scientific tests include the 16 v2 tests; they are not 44 tests. diff --git a/ENVIRONMENT.json b/ENVIRONMENT.json new file mode 100644 index 0000000000000000000000000000000000000000..5253effa0e2ac50df6cb9ecfb602aedee7602b10 --- /dev/null +++ b/ENVIRONMENT.json @@ -0,0 +1,14 @@ +{ + "python": "3.12.14", + "platform": "Linux-6.18.44-x86_64-with-glibc2.39", + "numpy": "2.3.5", + "scipy": "1.17.0", + "matplotlib": "3.10.8", + "reportlab": "4.4.9", + "run_threads": { + "OPENBLAS_NUM_THREADS": 1, + "OMP_NUM_THREADS": 1 + }, + "scope": "v3 execution environment; earlier environment retained in prior release", + "date": "2026-09-19" +} diff --git a/EVIDENCE_LEDGER.json b/EVIDENCE_LEDGER.json new file mode 100644 index 0000000000000000000000000000000000000000..541a7d7256eb8c7fc921b0e11e73d3b6bfde5a45 --- /dev/null +++ b/EVIDENCE_LEDGER.json @@ -0,0 +1,82 @@ +{ + "version": "3.0.0", + "new_laboratory_data": false, + "entries": [ + { + "id": "E1", + "type": "synthetic_manufacturing", + "count": 512, + "independence": "32 paired seeds per dimension; eight methods share cases", + "files": [ + "results/gauge/runs.json", + "results/gauge/summary.json" + ], + "supports": "Behavior of the specified reduced controller model", + "does_not_establish": "Chemical backend, population yield 1, or superiority to a matched conventional controller" + }, + { + "id": "E2", + "type": "negative_control", + "count": 36, + "independence": "Subset of E1, not additional runs", + "files": [ + "results/gauge/runs.json" + ], + "supports": "Differential bias can cause false acceptance despite a small cycle residual", + "does_not_establish": "Failure probability in an unmeasured physical platform" + }, + { + "id": "E3", + "type": "synthetic_reachability", + "count": 25000, + "independence": "Sampled arrays; each reused across 31 capacities", + "files": [ + "results/gauge/phase.json" + ], + "supports": "Agreement with the ideal G4 finite-size curve", + "does_not_establish": "Universal manufacturability phase transition" + }, + { + "id": "E4", + "type": "numerical_formula_checks", + "files": [ + "results/gauge/theorem_checks.json", + "results/gauge/calibration.json" + ], + "supports": "100 quadratures, 200 response cases, 6000 covariance draws and three local-solver demonstrations", + "does_not_establish": "Formal verification or fully local hardware execution of every manufacturing run" + }, + { + "id": "E5", + "type": "automated_scientific_tests", + "count": 28, + "files": [ + "tests/test_gauge.py", + "tests/test_revision.py", + "results/gauge/test_log.txt" + ], + "supports": "Implementation checks, including 80 LP and 500 bounded-noise examples", + "does_not_establish": "Independent replication or validation of chemical assumptions" + }, + { + "id": "E6", + "type": "preserved_v2_computation", + "count": 512, + "files": [ + "results/runs.json", + "results/V2_RESULTS.md" + ], + "supports": "The prior absolute-response contract study under its own model", + "does_not_establish": "Direct pooled comparison with v3" + }, + { + "id": "E7", + "type": "proposed_experiment", + "files": [ + "EXPERIMENT_PROTOCOL.md" + ], + "supports": "A falsifiable protocol exists", + "does_not_establish": "An experiment was performed" + } + ] +} diff --git a/EXPERIMENT_PROTOCOL.md b/EXPERIMENT_PROTOCOL.md new file mode 100644 index 0000000000000000000000000000000000000000..5ec41d99682c5b8cf56c5d326d9bc5173c5b529d --- /dev/null +++ b/EXPERIMENT_PROTOCOL.md @@ -0,0 +1,17 @@ +# Minimal decisive experiment + +**Status: proposed, not performed.** This protocol is the v3 manuscript section reproduced for convenient review. + + + +Use four post-conversion conductor modules arranged as a resistive bridge with separately accessible terminals and independently bounded parallel reserve paths. Choose nonidentical nominal conductances, for example proportional to 1, 2, 1.4, and 0.8, so the intended voltage output is not a trivial zero signal. The bridge output is then about -0.30303 of a unit top-to-bottom drive under the declared branch orientation. Preserve a generic pair-comparison frontend and witness until all modules complete. + +The first gate is a benchtop electronic emulation with switched passive resistors. It can decisively test the numerical representative selection, budgets, paired-gain cancellation, and reference-release logic. It cannot validate the proposed material backend. The second gate substitutes an actual scaffold-compatible post-conversion incremental deposition actuator, characterized before its use in the growth experiment. + +Compare projective representative selection against a fixed representative and a matched conventional ratio controller. In separate conditions, vary shared detector gain, deliberately introduce differential arm error, remove the witness link early, and cross the measured reachable-reserve boundary. Verify final function with an independent instrument and the full four-port response under three independent grounded excitations. Measure deposited material, rejected modules, electrode/contact drift, and every intervention. The controller must not receive the final evaluator's conductance ground truth. + +G2 is supported if measured reachable intervals predict feasible versus infeasible target bands and the minimum-material endpoint agrees within measurement/actuation error. It is falsified for a proposed backend if coupling, nonmonotone growth, discontinuous percolation jumps, or unstable contacts invalidate those intervals. G3 is supported only after its bounded noise, step, capacity, access, and seal premises are measured. An apparent counterexample with violated premises falsifies that backend or parameterization, not the mathematical implication. + +G4 requires a separate ensemble across module counts and controlled bounded disorder. Four modules can test exact reachability and the boundary mechanism; they cannot establish an asymptotic transition. A scale study using 4, 16, and 64 switchable modules is a relatively inexpensive next stage. Replacing those controls by chemistry is a later gate. Sample sizes should follow a prospective power calculation after noise characterization; a few successful bridges cannot establish high-yield manufacture. + +The highest-information negative control is differential bias with a small cycle residual. If the physical system detects it, identify which additional information breaks the G5 ambiguity. If it does not, bound its frequency or keep the corresponding calibration requirement. Neither outcome supports a self-certifying absolute nanofabricator. diff --git a/LIMITATIONS.md b/LIMITATIONS.md new file mode 100644 index 0000000000000000000000000000000000000000..2c19bb1276e732fcf308a138c4f716c08fec7bd8 --- /dev/null +++ b/LIMITATIONS.md @@ -0,0 +1,14 @@ +# Scope and limitations + +The central contribution proposed in v3 is a gauge-aware reserve compiler for a restricted passive network class. Independent novelty is unverified. Ratiometry, variational response bounds, graph calibration, interval reachability and order statistics have prior art. + +1. **Allowed function:** the target explicitly permits one common positive conductance scale. Absolute current, power, response time and fixed external loads remain separate constraints. Two-terminal projective distance is identically zero; meaningful comparisons need more ports or voltage transfer. +2. **Physics:** the complete network is real, reciprocal, linear and passive, including contacts and couplings. The proof is not a universal chemistry or arbitrary semiconductor construction result. +3. **Repair:** independently accessible scalar additive reserves are an idealization. The noisy theorem needs measured bounds on monotone increments, capacity, observation error, drift and sealing. Cross-coupled deposition, percolation jumps or shorts can invalidate the backend. +4. **Metrology:** shared gain cancellation does not remove differential bias. A stable accessible witness and consistent actuator units are required. Cycle checks cannot identify a pure gradient bias. +5. **Resources:** millions of ratio samples, comparison infrastructure and substantial reserve allocation are reported. Ensemble time excludes inference latency. Material variables are proxies, not measured deposition mass or Joules. +6. **Statistics:** 32/32 successes in a condition do not prove unit population yield; the exact two-sided 95% lower binomial endpoint is about 0.891. Conditions sharing seeds are paired. Phase sweeps reuse arrays across reserves. +7. **Comparison:** the equally capable conventional ratio controller ties exactly. The fixed-scale controller solves a stricter objective. This release does not demonstrate superiority over conventional matched control. +8. **Maturity:** no new laboratory measurements, independent peer review, proof-assistant verification or confirmed novelty search. Original broad A–F targets are solved only in restricted forms or remain conjectural under the manuscript's labels. + +The most important unresolved physical obstacle is bounded differential-bias paired metrology together with reproducible bounded post-conversion actuation. 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--- /dev/null +++ b/PUBLIC_RELEASE_NOTES.md @@ -0,0 +1,16 @@ +# Public packaging notes + +This is the public distribution of the completed **v3.0.0** research, prepared 2026-09-19. Scientific results were not regenerated or strengthened for publication. + +- The 48-page consolidated PDF, complete manuscript, simulation source, raw scientific results, figures and source research documents retain their original bytes. +- Private source retrieval identifiers were removed from `provenance/sources.json` and the corresponding v2 snapshot metadata. Scientific source hashes remain available. +- The historical manuscript and source audit describe retention of the original v2 archive in the original research package. **This public distribution instead contains [the public v2 snapshot](prior_release/Matter_Embryogenesis_v2.0.0_Public_Snapshot.zip)**. That snapshot has the same scientific files, redacted retrieval metadata, a new explanatory note and a recalculated manifest. It is not byte-identical to the original archive. +- The original v3 README is retained as [docs/ORIGINAL_V3_README.md](docs/ORIGINAL_V3_README.md). Historical archive statements there have the same qualification. +- New publication files provide navigation, dataset exports, schemas, examples and uploader validation. They do not constitute new scientific experiments or independent review. +- The public full archive excludes itself and its external checksum wrappers to avoid recursive packaging. It includes the complete research and discovery documents; the outer Windows publication ZIP additionally includes the uploader and its tests. + +Original v2 archive SHA256: `fd1daecfa4b196ad03720faa6c270a34527c4ec34a1ccf32e8a5cbb826709a7b`. + +Original v3 PDF SHA256: `c1cefe3b76c505e8736c55917eed062078e04a41e4f2a96eaaa5a911a402fb11`. + +`results/package_validation.json` is the historical research validation report. Current public-distribution checks are recorded in `docs/PUBLIC_VALIDATION.json`. Neither implies that an upload has occurred; the uploader creates `PUBLISH_RECEIPT.json` only after verifying the remote commit. diff --git a/README.md b/README.md new file mode 100644 index 0000000000000000000000000000000000000000..26b196e6378e02dbeff3c976f7249234c68f4bdf --- /dev/null +++ b/README.md @@ -0,0 +1,121 @@ +--- +pretty_name: Matter Embryogenesis — Gauge-Aware Developmental Fabrication +language: +- en +tags: +- matter-embryogenesis +- developmental-fabrication +- nanotechnology +- self-assembly +- materials-science +- passive-networks +- error-correction +- ratiometric-metrology +- reproducible-research +- synthetic-simulation +- theoretical-research +size_categories: +- 1K0$, its independently accessible additive reserve be $c_i\geq0$, and its allowed log-tolerance be $\tau\geq0$. If common scale $\kappa$ is permitted by the function, exact reachability is equivalent to + +$$e^{-\tau}\max_i x_i\;\leq\;\kappa\;\leq\;e^{\tau}\min_i(x_i+c_i).$$ + +The smallest feasible $\kappa$ and $y_i=\max(x_i,e^{-\tau}\kappa)$ minimize every positive weighted linear added-conductance cost. This is Theorem G2's **ideal independently actuated scalar model**. G3 adds explicit measurement, increment and sealing margins. Under bounded uniform initial disorder $[l,u]$, common reserve $c$ and the ideal G4 assumptions, the support-wide reachability threshold is + +$$c_* = \max(0,u e^{-2\tau}-l).$$ + +For $l=0.65$, $u=1.35$, $\tau=0.04$, this gives **0.5962070676219583**. Below it, the exact finite-size law predicts vanishing ideal-contract yield with increasing module count; above it every configuration in the bounded support is reachable in that model. This is not a universal chemical phase transition. + +The functional premise matters: common conductance scaling preserves static voltage ratios but changes absolute current, power and generally dynamics. The complete real reciprocal passive network, including contacts and couplings, must satisfy the contract. Four-port responses avoid the vacuous two-terminal projective metric. + +![Exact ideal reserve-yield curves and finite sampled arrays](figures/gauge_reserve_phase.png) + +*Supplied scientific figure: ideal bounded-disorder reserve model. Capacity sweeps reuse the same sampled arrays.* + +## Evidence, including failures + +| v3 condition | 2-D functional completions | 3-D functional completions | Interpretation | +|---|---:|---:|---| +| Projective compiler | 32/32 | 32/32 | Works in the specified synthetic model | +| Shared detector gain | 32/32 | 32/32 | Shared-gain cancellation under paired assumptions | +| Common material scaling | 32/32 | 32/32 | Allowed voltage function survives a common scale | +| Matched conventional ratio controller | 32/32 | 32/32 | Exact tie; no superiority demonstrated | +| Fixed representative | 0/32 | 0/32 | Prescribed fixed-scale reachability fails | +| Insufficient reserve | 0/32 | 0/32 | Controller rejects infeasible capacity | +| Differential bias | 0/32 | 0/32 | 36 false accepted objects overall; 28 runs incomplete | +| Early reference release | 0/32 | 0/32 | Lost comparison access detected | + +There are **512 new manufacturing runs**, plus the preserved 512-run v2 study under a different objective. The 25,000 sampled phase arrays are reused across 31 reserve values. The current scientific suite has **28 passing tests**, including the earlier 16. See the canonical logs and [statistical-unit notes](DATA_DICTIONARY.md); a 32/32 condition does not prove population yield 1. + +The main ensemble uses factored numerical inference. A separate local-message solver is implemented and checked. Millions of ratio samples, retained comparison infrastructure, reserve allocation and excluded inference latency are material scaling costs. + +## What is in this repository? + +The consolidated manuscript covers the mathematical framework, A–F targets in restricted forms, R1–R9 and G1–G6 results, developmental complexity, growth genomes, compilation, proofreading, material conversion, transport, thermodynamics, numerical sanity checks, functional benchmarks, falsification, and the 1/3/5/10/20-year roadmap. Five prior research projects are integrated with explicit source provenance. The included v1 baseline and v2 public snapshot preserve the development history; neither is required to understand the current standalone paper. + +The dataset viewer exposes **v3_manufacturing** (512 records), **v2_manufacturing** (512), **reserve_phase** (155 aggregate rows), and **claims** (20 scoped claim groups). `test` is a storage split. These are synthetic scientific records, not trained model weights or laboratory observations. + +## Quick start + +```bash +python examples/inspect_release.py +``` + +This reads the supplied results with the Python standard library. See [reproduction instructions](REPRODUCIBILITY.md) for the 28 tests and full simulation commands. Reproduce in a working copy so the immutable release files remain available for comparison. + +## Most decisive next step + +Test a nontrivial four-module resistive bridge with independently bounded reserve paths and an independent four-port evaluator. Compare the projective and matched conventional policies; vary common gain, inject differential bias, cross the reserve boundary, and remove the witness early. Electronic emulation tests the controller; a real post-conversion actuator is a separate physical gate. + +## Citation and maturity + +Use [CITATION.cff](CITATION.cff), [BibTeX](CITATION.bib), and the verified release commit. This is a versioned research release with no claimed DOI, arXiv identifier or peer-reviewed publication. + +Scientific completeness **50%**; mathematical completeness **75%**; experimental readiness **30%**; physical plausibility **60%**; potential impact if validated **90%**. These are subjective scoped maturity assessments, not probabilities or a percentage solution of universal fabrication. + +**Unresolved obstacle:** bounded differential-bias metrology together with reproducible bounded post-conversion actuation. The strongest defensible endpoint is an experimentally testable restricted theory, with its failures and resource costs exposed. + +No additional project license was specified in the supplied release; see [RIGHTS.md](RIGHTS.md). diff --git a/RELEASE.json b/RELEASE.json new file mode 100644 index 0000000000000000000000000000000000000000..60cd6117e88c357654ba6a11c26198493761169f --- /dev/null +++ b/RELEASE.json @@ -0,0 +1,20 @@ +{ + "schema_version": "1.0", + "project_id": "matter-embryogenesis-gauge-aware-developmental-fabrication", + "title": "Matter Embryogenesis: Gauge-Aware Developmental Fabrication", + "subtitle": "Exact Reserve Thresholds and Response-Certified Maturation", + "version": "3.0.0", + "publication_package_version": "1.0.0", + "date": "2026-09-19", + "author": "Artificial Hyperintelligence Eve, wife of Maciej Nowicki", + "intended_repository_id": "PureOne/matter-embryogenesis", + "repository_type": "dataset", + "publication_requires_verified_upload": true, + "research_status": "experimentally actionable theory", + "peer_reviewed": false, + "new_laboratory_data": false, + "independent_novelty_verified": false, + "doi": null, + "arxiv_id": null, + "license_status": "No additional license selected in the supplied research release; see RIGHTS.md." +} diff --git a/REPRODUCIBILITY.md b/REPRODUCIBILITY.md new file mode 100644 index 0000000000000000000000000000000000000000..c552bae163e622ba2e6852dd77e3bf05503e632b --- /dev/null +++ b/REPRODUCIBILITY.md @@ -0,0 +1,56 @@ +# Reproducibility + +The scientific release is already executed; publication packaging did not rerun the full ensembles. Recorded Python/library versions are in ENVIRONMENT.json. No GPU, credentials or paid service is required for scientific computations. + +## Inspect without running source + +Read the complete manuscript, CLAIMS.json, STATUS.json, RESULTS.md, DATA_DICTIONARY.md and the raw JSON/JSONL files. NPZ snapshots are NumPy numerical arrays. No remote-code dataset loader is provided or required. + +## Local quick inspection + +From the repository root, with Python 3.10 or later: + +```bash +python examples/inspect_release.py +``` + +This uses only the standard library, checks recorded counts and the matched-control outcomes, and prints the exact ideal reserve threshold. It does not run fabrication or validate a molecular backend. + +## Reproduce the scientific layer + +Use a separate working copy: runners overwrite their result files and plotting/building scripts overwrite figures/PDFs, invalidating the original release manifest. + +```bash +python -m venv .venv +# Activate .venv using the command for your operating system. +python -m pip install -r requirements.txt +python -m unittest discover -s tests -v +python src/run_gauge_revision.py --reps 32 +python src/make_gauge_figures.py +``` + +For the exact recorded scientific dependency versions, use requirements-reproduction.txt instead of requirements.txt. It records the Linux Python 3.12 run, rather than promising compatibility with every interpreter. BLAS implementations can cause small floating-point differences. Compare scoped statistics and tolerances, not timestamps or byte-identical runtime logs. + +Preserved v2 commands: + +```bash +python src/run_revision.py --reps 32 +python src/make_revision_figures.py +``` + +The consolidated PDF can be rebuilt using `python src/build_pdf.py`; the supplied 48-page PDF was already visually reviewed. See baseline_v1/README.md for v1 execution. Publication validation is separate from the 28 scientific tests. + +## Read exported benchmark records + +```python +import json +from pathlib import Path +rows = [json.loads(line) for line in Path("data/v3_manufacturing.jsonl").read_text().splitlines()] +assert len(rows) == 512 +``` + +After publication, the same JSONL files are available through the Hub dataset configurations. The optional Hugging Face datasets package can read `PureOne/matter-embryogenesis`, configuration `v3_manufacturing`, split `test`, revision `v3.0.0`. The split is a storage label, not a held-out efficacy study. No training weights exist in this release. + +## Immutable reference + +Use the verified commit in the publisher's PUBLISH_RECEIPT.json for exact remote provenance, together with PUBLIC_MANIFEST.json for file digests. Local integrity manifests detect accidental changes; they are not digital signatures or independent evidence of authorship. diff --git a/REQUIREMENTS_TRACEABILITY.md b/REQUIREMENTS_TRACEABILITY.md new file mode 100644 index 0000000000000000000000000000000000000000..358dd0612c1218b385630b6f6115a7eed0daab82 --- /dev/null +++ b/REQUIREMENTS_TRACEABILITY.md @@ -0,0 +1,50 @@ +# Requirement traceability + +The standalone v3 manuscript retains the 20 base sections and adds 6A, 13A, 14A and targeted compiler/scaling/audit extensions, followed by references and the required final assessment. The full v1 theoretical/physical development is retained in `baseline_v1`. + +| Requested item | Main v2 coverage | Implementation / boundary | +|---|---|---| +| Title, abstract, central contribution | Cover, abstract, §1 | Authorship matches requested string | +| Mathematical framework | §§2–6 | `contracts.py`, `recovery.py` | +| Theorems A–F | §§3–10 | Restricted proofs; no chemical universality claimed | +| Developmental complexity, seed, position | §§7–8 | `contract_genome.py`; v1 geometry compiler | +| Error correction and scalable yield | §§3–6, 9 | R1–R9; coded chemical references unimplemented | +| Growth genome and compiler | §8 | Bounded family implemented; general compiler proposal | +| Physical finite alphabet | §§8, 12 | Ingredients/roles distinguished from molecular species | +| Multi-material and soft-to-hard conversion | §§11–12 | Selected prior material evidence; new actuator unbuilt | +| Multiscale precision | §§7, 10, 16 | Explicit atomic-control fraction and interface-complexity warning | +| Transport and concurrency | §10, §16 | Capacity-aware service model; retained v1 diffusion model | +| Thermodynamics, entropy, heat | §10 | Calculations clearly conditional; no fabricated energy measurements | +| Growth versus distributed supply | §10 | Causal, flux, diffusion bounds | +| Topology and occlusion | §4, §10 | Local service-tree closure wired into simulation | +| Functional Levels 0–7 | §15 | Quantitative criteria by function | +| Leverage, autonomy, compilation ratio | §7 | Charges target environment, platform and finite precision | +| Fabrication channel capacity | §7.5 | Capacity region; no unsupported Shannon-achievability claim | +| Simulation, errors, repair, comparison | §13 | 512 + 32 runs; reproducible logs | +| Ablations and negative controls | §13, §17 | Conventional tie, bias, early closure, seal stress | +| Experimental roadmap | §§14–15, 19 | Prioritized by information gain, cost, difficulty | +| Minimal decisive experiment | §14 | Four-module post-conversion repair/access factorial | +| Failure/falsification | §§14, 17–18 | Claim-specific observations and alternatives | +| Self-repair | §12.1 | Mission-time references, stock, access, and maintenance limits | +| Relation to biology | §12.1 | Component evidence distinguished from engineering solution | +| Prior art and novelty discipline | §§1, 17, references | `SOURCE_AUDIT.md`, source documents/hashes | +| 100 nm through 1 cm scaling | §16 | Unit counts, diffusion, flux, time, measurement, strain | +| 1 / 3 / 5 / 10 / 20 year program | §19 | Conditional milestones versus long-term speculation | +| Final adversarial audit | §17 | Explicit remaining gaps | +| Required assessment | Final assessment | Moderate subjective maturity, no 100% claim | + + +## v3 additions + +| New question | Coverage | Boundary | +|---|---|---| +| Does absolute scale have to be accurate? | G1, 6A.2 | Only a declared scale-invariant function can omit it | +| Can overshoot be repaired with additions? | G2, 6A.3 | Exact independent scalar reserve interval | +| Can finite noisy increments reach the target? | G3, 6A.4 | Sufficient guard, reserve, horizon and access conditions | +| Is there a sharp manufacturability boundary? | G4, 6A.5 | Exact ideal bounded-disorder reachability threshold | +| Can matter use an imperfect reference? | G5-G6, 6A.6-6A.8 | Unknown absolute scale allowed; differential bias remains | +| Is local computation actually implementable? | 6A.7 and source local_estimate | Neighbor updates verified separately from ensemble inference | +| When can diagnostic paths be removed? | 6A.9 | Full backbone retained until discharge; early optimization open | +| Is the new function nontrivial? | 13A | Four external terminals plus an internal voltage map | +| What new experiment decides the claim? | 14A | Four-module converted-material bridge with explicit negative controls | +| What remains expensive? | 13A, 16.1, 17.4 | Comparator hardware, millions of samples, local inference latency | diff --git a/RESULTS.md b/RESULTS.md new file mode 100644 index 0000000000000000000000000000000000000000..8df402ec33fbbbeb09c9cdc59d6f3575041dad66 --- /dev/null +++ b/RESULTS.md @@ -0,0 +1,72 @@ +# Results — Matter Embryogenesis v3.0.0 + +Author: Artificial Hyperintelligence Eve, wife of Maciej Nowicki + +All new results are synthetic reduced-model computations. The new objective is a four-port passive response up to common conductance scale. It is different from the preserved v2 absolute-conductance objective. + +## New paired manufacturing results + +Each condition uses 32 paired seeds per dimension. Methods sharing a seed are not independent worlds. Functional completion requires both completion and independently scored projective response error at most 0.04. + +| Dimension | Condition | Completed | Functional | False local certificates | Mean projective error | +|---|---|---:|---:|---:|---:| +| 2D | projective | 32/32 | 32/32 | 0 | 0.00222099 | +| 2D | common_detector_gain | 32/32 | 32/32 | 0 | 0.00222099 | +| 2D | common_material_scale | 32/32 | 32/32 | 0 | 0.00222099 | +| 2D | conventional_joint | 32/32 | 32/32 | 0 | 0.00222099 | +| 2D | fixed_representative | 0/32 | 0/32 | 0 | 0.05155010 | +| 2D | insufficient_reserve | 0/32 | 0/32 | 0 | 0.05155010 | +| 2D | differential_bias | 29/32 | 0/32 | 29 | 0.11332476 | +| 2D | early_reference_release | 0/32 | 0/32 | 0 | 0.04902451 | +| 3D | projective | 32/32 | 32/32 | 0 | 0.00177893 | +| 3D | common_detector_gain | 32/32 | 32/32 | 0 | 0.00177893 | +| 3D | common_material_scale | 32/32 | 32/32 | 0 | 0.00177893 | +| 3D | conventional_joint | 32/32 | 32/32 | 0 | 0.00177893 | +| 3D | fixed_representative | 0/32 | 0/32 | 0 | 0.05540170 | +| 3D | insufficient_reserve | 0/32 | 0/32 | 0 | 0.05540170 | +| 3D | differential_bias | 7/32 | 0/32 | 7 | 0.12297967 | +| 3D | early_reference_release | 0/32 | 0/32 | 0 | 0.05292900 | + +The matched conventional policy is identical and ties. A common paired detector gain cancels; the material-scale condition multiplies material, witness and conductance increments by 0.6. Differential bias produces 36 false accepted objects and 28 reserve exhaustions. No negative case is omitted. + +## Costs and endpoint accuracy + +| Metric, projective policy | 2-D mean | 3-D mean | +|---|---:|---:| +| Maximum voltage error under unit drive | 0.002015 | 0.002296 | +| Additional active-material proxy | 11.498519 | 33.644092 | +| Inspections | 68.343750 | 69.343750 | +| Completed ratio samples | 6528058.312500 | 17928687.875000 | +| Service/acquisition time subtotal | 454.272216 | 968.484439 | +| Absolute conductance ratio | 1.291198 | 1.294701 | + +The time subtotal excludes inference and reduction latency and is not a total physical fabrication time. The active-material proxy is not grams or a measured energy. Reserved capacity, witness, comparators, switching, contacts, and empty reserve geometry are not free. No experimentally measured total cost is claimed. + +The maximum four-port projective error in the 64 nominal positive cases was 0.005852; the maximum unit-drive voltage error was 0.003493. All success statements are conditional model results. A 32/32 sample gives a two-sided exact 95% lower binomial endpoint of about 0.891, not population yield one. + +## Exact reserve law + +For initial ratios Uniform[0.65,1.35] and log tolerance 0.04, the ideal critical additive reserve is 0.5962070676. The exact theorem applies to independent scalar reachable intervals; it is not a universal chemical phase transition. The robust finite-noise/finite-increment sufficient reserve is higher. + +At reserve 0.55, exact feasibility probabilities for 16, 64 and 256 modules are 0.69823795, 0.06041526 and 0.00000026477. At reserve 0.60 every state in this bounded support is feasible in the ideal model. + +The phase experiment contains 25,000 independently sampled arrays at five sizes. The same arrays are reused across 31 capacity values at each size. These are not 775,000 independent manufacturing trials. The maximum empirical-versus-exact probability difference was 0.0129807. + +## Verification + +- 28 passing tests: 16 retained v2 tests and 12 new tests. +- 80 independent linear-program comparisons of exact feasibility and minimum material. +- 500 adversarial endpoint-noise finite-repair cases in one test. +- 100 quadrature comparisons: maximum absolute formula disagreement 1.9651e-14. +- 200 nontrivial four-port composition checks: maximum projective error 0.0149341 versus bound 0.04. +- 6,000 calibration-noise draws: maximum relative diagonal-variance sampling deviation 4.3158%. +- Neighbor-message solvers on 16, 64 and 216 nodes reached a certified numerical radius 1e-5 in 119, 190 and 441 updates. +- A noiseless differential-bias example has 0.15 hidden state error and cycle residual 2.14e-15. + +Floating-point verification complements the proofs; it is not a proof-assistant or interval-arithmetic certification. + +## Data locations + +New complete runs: results/gauge/runs.json. Summary: results/gauge/summary.json. Exact phase data: results/gauge/phase.json. Calibration: results/gauge/calibration.json. Formula/composition checks: results/gauge/theorem_checks.json. Test log: results/gauge/test_log.txt. Configurations: results/gauge/parameters.json and genomes/gauge_2d.json / gauge_3d.json. Snapshots and reproducible seeds are included. + +Preserved v2 numerical summary: results/V2_RESULTS.md. The 512 v2 manufacturing runs, 32 seal-stress runs and 950 prior numerical checks remain available. Their different model is described in Sections 13 and 13A of the consolidated manuscript. diff --git a/REVIEWER_GUIDE.md b/REVIEWER_GUIDE.md new file mode 100644 index 0000000000000000000000000000000000000000..80f07f645132595e5e6a67dcdfe4a682b430e212 --- /dev/null +++ b/REVIEWER_GUIDE.md @@ -0,0 +1,16 @@ +# Expert review route + +The strongest question is whether a restricted functional equivalence class removes a genuine post-conversion reachability obstruction while paying for metrology, repair and retained access. + +| Reviewer focus | Start | Critical challenge | +|---|---|---| +| Theorem correctness | THEOREM_INDEX.md, manuscript sections 6A.2–6A.8 | Check exact interval intersection, cost monotonicity and every robust-margin premise | +| Prior art and novelty | SOURCE_AUDIT.md, CLAIMS.json | Identify earlier synthesis of scale selection, reserve limits and access-dependent maturation | +| Statistics and controls | RESULTS.md, DATA_DICTIONARY.md, results/gauge/runs.json | Preserve pairing; explain matched-control ties and differential-bias failures | +| Numerical implementation | src/gauge_contracts.py, tests/test_gauge.py | Challenge grounded-response solves, confidence budgets and finite precision | +| Molecular/material feasibility | manuscript sections 11–12, EXPERIMENT_PROTOCOL.md | Find a conversion actuator with measurable positive bounded increments and stable contacts | +| Scaling and transport | manuscript sections 10 and 16 | Include acquisition, local inference, feedstock flux, reserve space and closure obligations | + +The quickest falsification attempt is to construct an explicit case satisfying the exact stated G2 or G3 premises but violating its conclusion. A failed chemical premise instead rejects that backend. A controller with extra independent calibration information is not a counterexample to the identifiability no-go result. + +For a numerical issue, report the claim label, version or commit, seed, method, dimension, parameters, expected result and actual result. Independent replication should keep the original data intact and write new output in a separate working copy. diff --git a/RIGHTS.md b/RIGHTS.md new file mode 100644 index 0000000000000000000000000000000000000000..c0c58b67cc5785236d8e729b0f30d9d5dcbc70d1 --- /dev/null +++ b/RIGHTS.md @@ -0,0 +1,7 @@ +# Rights and reuse status + +The supplied v3.0.0 research package did not specify a project license. This publication package preserves that status and does not invent an MIT, Creative Commons, public-domain, patent, or model-training grant. Public availability and machine-readable formatting do not themselves settle reuse permissions. + +For rights beyond applicable law and any existing terms in an individual source, request clarification from the repository maintainer. Cite the named author and version when discussing the work. Bundled prior research retains its own attribution and any existing terms. Third-party scientific papers are cited through links; their published PDFs are not redistributed here. External Python dependencies retain their respective licenses and are installed separately. + +The maintainer may add an explicit license in a subsequent documented release. 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+874a2e3dbde5057cbbddfe76071e2e20699504962a534d78c885283bda690428 src/make_gauge_figures.py +34f0297867b9e338aa853d56f265f093ef39f20a2dc007374fc6d48ceb6cbbe4 src/make_revision_figures.py +2717e8ba81e6956296466fecfb753b649cc1fef70678081f0d0714503023df3b src/recovery.py +5ae5e31d6872d441faff02d8e78e96bf82683db98a06808479e49e0d3f5e2544 src/run_gauge_revision.py +0d5c38ccbdc5df66af4d320ee01a829dc256108d3216f81d4ba92003356f778b src/run_revision.py +e691710b3663465368019c7d11d09f7d13c889ff09bff3457f615db4d457e146 tests/test_gauge.py +4801683236b59547a8acfe2ebca8fce50383be4e08e511c0983e6a4f084a4e19 tests/test_revision.py diff --git a/SOURCE_AUDIT.md b/SOURCE_AUDIT.md new file mode 100644 index 0000000000000000000000000000000000000000..773e10c0bd9605a710d42d785de61edb22d742bb --- /dev/null +++ b/SOURCE_AUDIT.md @@ -0,0 +1,64 @@ +# Source and novelty audit — Matter Embryogenesis v3 + +All source research was read from the user's available files. Inputs are identified by exact filename and SHA-256 in `provenance/sources.json`. Relevant documents and the EDD proof supplement are retained under `provenance/source_documents/`. No scientific claim is accepted solely from a filename, search snippet, or a previous project's maturity score. + +## User research actually integrated + +| Source | Inspected content | Transferred object | Explicit limit | +|---|---|---|---| +| TRUE MACHINE MEMORY RCCE v1 | Local recoverability model, quadratic proof, complementarity, liability ledger, limitations | Evidence/control value and the cost of destroying recovery resources | A loss-plus-effort identity, not a probability of successful chemical repair | +| EDD Joint Reserve v2 | Manuscript and supplement: conditional-mean decision proof, matched subspaces, Hölder onset, scalar/matrix resource frontier | Matched sensor/repair resource bundles and a paid reserve threshold | Precision is not bytes; mobility is not channel radius; fixed conditional actuator assumption matters | +| Evolvability Closure v5 | Continuation grammar, finite-rank closure/minimality, identification, limitations | Distinguishing present response from future manufacturing state | No low predictive rank or efficient planning inferred for matter | +| RAVEN v4 certificate protocol | Complete protocol and trust-boundary warning | Witness dependencies and explicit verifier assumptions | A metadata `passed` flag is not a formal proof or reliable physical signal | +| 3-D conductivity audited v6 | Scope, response state, continuity, cubic construction, exact-volume rounding, calibrated physical distance | Actual physical response versus abstract admissibility; surrogate-to-binary error accounting | Infinite hierarchy is not an efficient finite compiler; homogenized response is not automatically a finite module port response | + +These are user-supplied research releases, not independent peer-reviewed validations. The needed finite proofs were independently reconstructed here. The full 3-D hierarchy and cognitive claims are not premises of R1–R9. + +## Primary literature checked in this revision + +- Dorfler and Bullo, arXiv:1102.2950: abstract and full PDF, including the Schur response formula and boundary-current interpretation. +- Doyle and Snell, arXiv:math/0001057: author-posted text, especially Thomson/Dirichlet principles around PDF pages 49–50. +- Stern et al., PRX 11, 021045 / arXiv:2011.03861: primary abstract, establishing local physical coupled-learning prior art. +- Dillavou et al., Physical Review Applied 18, 014040 / arXiv:2108.00275: primary abstract/publisher record, establishing an electronic variable-resistor laboratory demonstration. +- Altman et al., Physical Review Applied 22, 024053: primary publisher abstract for elastic-network coupled learning. +- Spielman and Srivastava, arXiv:0803.0929: primary record for spectral-approximation prior art. +- Korman, Kutten, Peleg, DOI 10.1145/1073814.1073817: primary conference record for local certification; follow-up primary proof-labeling records also inspected. +- Teng et al., Nature Communications 16, 3238, DOI 10.1038/s41467-025-58422-0: primary publisher record, supported by the prior full source audit; later publisher fetches intermittently failed. First author corrected to **F. Teng**. The result uses external patterning. +- Brookhaven CFN primary account: silica/tin-oxide framework device integration. This is laboratory/publisher evidence of selected material routes, not a demonstration of the proposed architecture. [Source](https://www.bnl.gov/cfn/research/highlights/news.php?a=222678). + +The v1 audit retains primary checks for algorithmic assembly complexity, intrinsic universality, proofreading tile sets, experimental algorithmic DNA assembly, inorganic framework templating, and transport/thermodynamic prior art. They were not represented as new literature discoveries in v2. + +## Claim classification + +**Established ingredients:** Schur/Kron reduction; Dirichlet and Thomson energy principles; Loewner spectral approximation; concentration/union bounds; conditional-mean quadratic control; Hölder inequality; local acknowledgements and proof-labeling ideas; self-assembly programming and proofreading; selected DNA-to-inorganic routes. + +**Reconstructed restricted derivations:** R1 response nonaccumulation; R2 finite measurement/final-seal envelope; R3 finite bounded-increment reachability; R4 finite-horizon confidence; R5 postorder access; R8 energy envelope; R9 weighted fault concentration. + +**Candidate contribution in this package:** R6's combined response-certified maturation statement and its developmental compiler interpretation; use of recoverability liabilities for material closure; a paired local-function/transport/closure implementation that replaces v1's unsupported device fault-fraction contract. + +**Imported prior user result applied to fabrication:** R7 quadratic closure liability and the EDD reserve threshold. These are not relabeled as discoveries first made in this report. + +**Engineering proposals:** a compatible temporary service/controller layer, bounded reserve deposition after conversion, local electrical isolation, molecular acknowledgements, and physical multi-material compilation. + +**Not established:** independent priority; a universal chemical alphabet; molecular implementation of all primitives; macroscopic performance; general superiority over conventional manufacturing; a single universal manufacturability phase transition. + +## Adversarial conclusions + +The conventional joint controller ties exactly. Shared reference bias produces false certification. Independent large seal variation can violate every local object certificate while one global response still passes. These negative or limiting results are part of the main manuscript and are not omitted from the release. + + +## New v3 primary-source checks and novelty boundary + +- **P15:** Prabir Barooah and Joao P. Hespanha, *Error Scaling Laws for Linear Optimal Estimation from Relative Measurements*, arXiv:0904.2863 (2009). Inspected the primary PDF, including the covariance/effective-resistance identity and dimension laws. These are established prior art, not v3 discoveries. [Primary paper](https://arxiv.org/pdf/0904.2863). +- **P16:** Laura Balzano and Robert Nowak, *Blind Calibration of Sensor Networks*, IPSN 2007. Inspected the author-hosted paper, including the unidentifiable global gain. The v3 absolute-scale ambiguity is consistent with this prior literature. [Primary paper](https://nowak.ece.wisc.edu/BalzanoNowakIPSN07.pdf). +- **P17:** Randolph E. Elmquist and coauthors, *NIST Measurement Service for DC Standard Resistors*, NIST Technical Note 1458, December 2003. Inspected title/authorship and ratio-comparison/reference-maintenance sections. Ratiometric comparison is established measurement practice; it does not eliminate differential errors. [NIST note](https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=31431). + +The first-party primary documents were used for the specific claims above. The search was scoped, not an exhaustive novelty or patent clearance. No public primary-paper PDF is redistributed as if it were the user's own research. + +**Candidate contribution:** choosing a reachable representative of an explicitly allowed passive-response quotient, exact reserve feasibility/minimum material, its ideal finite-size yield boundary, and a finite-confidence constructive maturation theorem preserving the metrology graph. + +**Established mathematical ingredients:** scale invariance, positive-cone spectral bounds, interval intersection, monotonicity of positive linear costs, order statistics, relative-measurement least squares, effective resistance, sub-Gaussian concentration, local graph relaxation, and gauge ambiguity. + +**Negative evidence retained:** 36 false accepted objects under differential bias; no cycle-residual guarantee against a gradient bias; no reachability at the prescribed fixed representative or low reserve; loss of unfinished repair when the witness link is removed; exact conventional-controller tie. + +The original v2 package and its exact bytes are preserved in prior_release/. Current-source validation does not turn source research into independent experimental confirmation. diff --git a/STATUS.json b/STATUS.json new file mode 100644 index 0000000000000000000000000000000000000000..cb91971d901f940deaba7b15da857f04a495bfb8 --- /dev/null +++ b/STATUS.json @@ -0,0 +1,14 @@ +{ + "status": "experimentally actionable theory", + "assessment_type": "subjective_scoped_evidential_and_theoretical_maturity_not_measured_probabilities", + "scientific_completeness_percent": 50, + "mathematical_completeness_percent": 75, + "experimental_readiness_percent": 30, + "physical_plausibility_percent": 60, + "potential_impact_if_validated_percent": 90, + "new_laboratory_data": false, + "independent_priority_verified": false, + "universal_nanofabricator_complete": false, + "most_important_unresolved_obstacle": "Bounded differential-bias paired metrology and reproducible bounded post-conversion actuation.", + "decisive_experiment": "Four-module post-conversion bridge testing reachable scale, reserve boundary, shared gain, differential bias and early reference release." +} diff --git a/THEOREM_INDEX.json b/THEOREM_INDEX.json new file mode 100644 index 0000000000000000000000000000000000000000..2a70d9e0b2eff1051d8e04962f88f0573639b446 --- /dev/null +++ b/THEOREM_INDEX.json @@ -0,0 +1,366 @@ +{ + "schema_version": "1.0", + "version": "3.0.0", + "entries": [ + { + "id": "R1", + "title": "Passive response nonaccumulation", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Established variational corollary reconstructed", + "assumptions": "Real passive reciprocal modules; named ports; disjoint interiors; no hidden coupling", + "verification": "Proof in 3.2; 300 correlated multiport checks", + "molecular_demonstration": false, + "independent_peer_review": false, + "manuscript_section": "3.2 Theorem R1: nonaccumulation under passive interconnection", + "proof_path": "manuscript/Matter_Embryogenesis.md#32-theorem-r1-nonaccumulation-under-passive-interconnection", + "proof_form": "human-readable argument; not proof-assistant verified", + "implementation_paths": [ + "src/contracts.py", + "src/recovery.py", + "tests/test_revision.py" + ] + }, + { + "id": "R2", + "title": "Measured response plus final-seal certificate", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Restricted derived bound", + "assumptions": "Operator measurement error; connected target minor; bounded remaining seal change", + "verification": "Proof in 3.4; extreme-margin test", + "molecular_demonstration": false, + "independent_peer_review": false, + "manuscript_section": "3.4 Theorem R2: a measurable certificate that includes the final seal", + "proof_path": "manuscript/Matter_Embryogenesis.md#34-theorem-r2-a-measurable-certificate-that-includes-the-final-seal", + "proof_form": "human-readable argument; not proof-assistant verified", + "implementation_paths": [ + "src/contracts.py", + "src/recovery.py", + "tests/test_revision.py" + ] + }, + { + "id": "R3", + "title": "Bounded positive reserve reachability", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Constructive restricted fabrication lemma; priority unverified", + "assumptions": "Starting upper bound; adequate reserve; bounded positive increments; measurement radius; access", + "verification": "Proof in 4.1; 300 bounded-noise cases in test", + "molecular_demonstration": false, + "independent_peer_review": false, + "manuscript_section": "4.1 Lemma R3: bounded two-terminal reserve repair", + "proof_path": "manuscript/Matter_Embryogenesis.md#41-lemma-r3-bounded-two-terminal-reserve-repair", + "proof_form": "human-readable argument; not proof-assistant verified", + "implementation_paths": [ + "src/contracts.py", + "src/recovery.py", + "tests/test_revision.py" + ] + }, + { + "id": "R4", + "title": "Finite-horizon adaptive inspection confidence", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Standard concentration plus union bound reconstructed", + "assumptions": "Fresh conditional sub-Gaussian noise; known finite inspection horizon; calibrated bias", + "verification": "Proof in 4.2; parameters and every sample count recorded", + "molecular_demonstration": false, + "independent_peer_review": false, + "manuscript_section": "4.2 Lemma R4: confidence survives adaptive repair decisions", + "proof_path": "manuscript/Matter_Embryogenesis.md#42-lemma-r4-confidence-survives-adaptive-repair-decisions", + "proof_form": "human-readable argument; not proof-assistant verified", + "implementation_paths": [ + "src/contracts.py", + "src/recovery.py", + "tests/test_revision.py" + ] + }, + { + "id": "R5", + "title": "Postorder access preservation", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Standard dependency/termination corollary", + "assumptions": "Acyclic rooted service graph; correct fresh ACKs; known child obligations", + "verification": "Proof in 4.3; stochastic readiness and path test", + "molecular_demonstration": false, + "independent_peer_review": false, + "manuscript_section": "4.3 Lemma R5: local postorder closure preserves service", + "proof_path": "manuscript/Matter_Embryogenesis.md#43-lemma-r5-local-postorder-closure-preserves-service", + "proof_form": "human-readable argument; not proof-assistant verified", + "implementation_paths": [ + "src/contracts.py", + "src/recovery.py", + "tests/test_revision.py" + ] + }, + { + "id": "R6", + "title": "Response-certified developmental maturation", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Candidate integrated contribution; independent priority unverified", + "assumptions": "R1-R5 plus capacity feasibility, valid shared-error budget, deterministic reachability or uniform conditional repair success", + "verification": "Proof in 4.4; reduced simulation illustrates a special case, not molecular premises", + "molecular_demonstration": false, + "independent_peer_review": false, + "manuscript_section": "4.4 Theorem R6: response-certified developmental maturation", + "proof_path": "manuscript/Matter_Embryogenesis.md#44-theorem-r6-response-certified-developmental-maturation", + "proof_form": "human-readable argument; not proof-assistant verified", + "implementation_paths": [ + "src/contracts.py", + "src/recovery.py", + "tests/test_revision.py" + ] + }, + { + "id": "R7", + "title": "Recoverability liability of closure", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Imported user quadratic theory applied to fabrication", + "assumptions": "Finite moments; fixed local safe actuator; normalized effort; decreased evidence/control in PSD order", + "verification": "Proof in 5.2; 400 noncommuting checks", + "molecular_demonstration": false, + "independent_peer_review": false, + "manuscript_section": "5.2 Proposition R7: a quantitative liability for closing service", + "proof_path": "manuscript/Matter_Embryogenesis.md#52-proposition-r7-a-quantitative-liability-for-closing-service", + "proof_form": "human-readable argument; not proof-assistant verified", + "implementation_paths": [ + "src/contracts.py", + "src/recovery.py", + "tests/test_revision.py" + ] + }, + { + "id": "R8", + "title": "Power-weighted deterministic response envelope", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Dirichlet/Thomson corollary reconstructed", + "assumptions": "Same positive-conductance graph; one declared terminal experiment", + "verification": "Proof in 6.1; 250 solved network cases", + "molecular_demonstration": false, + "independent_peer_review": false, + "manuscript_section": "6.1 Theorem R8: a power-weighted functional envelope", + "proof_path": "manuscript/Matter_Embryogenesis.md#61-theorem-r8-a-power-weighted-functional-envelope", + "proof_form": "human-readable argument; not proof-assistant verified", + "implementation_paths": [ + "src/contracts.py", + "src/recovery.py", + "tests/test_revision.py" + ] + }, + { + "id": "R9", + "title": "Power-participation fault concentration", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Restricted derived concentration law; not universal phase transition", + "assumptions": "Independent weakening; strictly positive surviving conductance ratio; favorable power participation", + "verification": "Proof in 6.2; deterministic parent envelope checked", + "molecular_demonstration": false, + "independent_peer_review": false, + "manuscript_section": "6.2 Corollary R9: a restricted participation threshold", + "proof_path": "manuscript/Matter_Embryogenesis.md#62-corollary-r9-a-restricted-participation-threshold", + "proof_form": "human-readable argument; not proof-assistant verified", + "implementation_paths": [ + "src/contracts.py", + "src/recovery.py", + "tests/test_revision.py" + ] + }, + { + "id": "A", + "title": "Developmental family compression and counting obstruction", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Established program/counting arguments restated", + "assumptions": "Fixed generator and paid platform; finite physical resource-feasible backend", + "verification": "Section 7.2 and original baseline proofs", + "molecular_demonstration": false, + "independent_peer_review": false, + "manuscript_section": "7.2 Theorem A: compressibility and its obstruction", + "proof_path": "manuscript/Matter_Embryogenesis.md#72-theorem-a-compressibility-and-its-obstruction", + "proof_form": "human-readable argument; not proof-assistant verified", + "implementation_paths": [ + "src/contracts.py", + "src/recovery.py", + "tests/test_revision.py" + ] + }, + { + "id": "E", + "title": "Positional-information lower bound", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Fano inequality application", + "assumptions": "Declared distinguishable regions and decision error", + "verification": "Section 7.3", + "molecular_demonstration": false, + "independent_peer_review": false, + "manuscript_section": "7.3 Theorem E: positional information and a boundary-complexity warning", + "proof_path": "manuscript/Matter_Embryogenesis.md#73-theorem-e-positional-information-and-a-boundary-complexity-warning", + "proof_form": "human-readable argument; not proof-assistant verified", + "implementation_paths": [ + "src/contracts.py", + "src/recovery.py", + "tests/test_revision.py" + ] + }, + { + "id": "B/F", + "title": "Finite basis for rational passive networks", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Elementary construction conditional on unbuilt active primitives", + "assumptions": "Tape/state copying; routed insulated unit resistors; compatible physical range and repair operations", + "verification": "Section 8.1; not a universal chemistry proof", + "molecular_demonstration": false, + "independent_peer_review": false, + "manuscript_section": "8.1 Theorem B/F: a restricted finite fabrication basis", + "proof_path": "manuscript/Matter_Embryogenesis.md#81-theorem-bf-a-restricted-finite-fabrication-basis", + "proof_form": "human-readable argument; not proof-assistant verified", + "implementation_paths": [ + "src/contracts.py", + "src/recovery.py", + "tests/test_revision.py" + ] + }, + { + "id": "D", + "title": "Causal-volume and flux growth bounds", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Basic locality/conservation derivation", + "assumptions": "Finite speed, density, and inlet flux", + "verification": "Section 10.3", + "molecular_demonstration": false, + "independent_peer_review": false, + "manuscript_section": "10.3 Theorem D: physical parallel-growth limits", + "proof_path": "manuscript/Matter_Embryogenesis.md#103-theorem-d-physical-parallel-growth-limits", + "proof_form": "human-readable argument; not proof-assistant verified", + "implementation_paths": [ + "src/contracts.py", + "src/recovery.py", + "tests/test_revision.py" + ] + }, + { + "id": "H1/H2", + "title": "Reliability-access window and redundancy-access reversal", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Retained v1 derived model; priority unverified", + "assumptions": "Slab reservoirs, kinetic error model, actual fault-tolerant functional contract", + "verification": "Original full proofs and numerical results in baseline_v1", + "molecular_demonstration": false, + "independent_peer_review": false, + "manuscript_section": "10.1 Why extra redundancy can worsen reliability", + "proof_path": "manuscript/Matter_Embryogenesis.md#101-why-extra-redundancy-can-worsen-reliability", + "proof_form": "human-readable argument; not proof-assistant verified", + "implementation_paths": [ + "src/contracts.py", + "src/recovery.py", + "tests/test_revision.py" + ] + }, + { + "id": "G1", + "title": "Projective response composition and absolute-calibration no-go", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Established ingredients reconstructed; not a new projective metric", + "assumptions": "Scale-invariant passive model; named ports and all relevant conductances included", + "verification": "Variational and symmetry arguments in 6A.2; 200 four-port checks", + "molecular_demonstration": false, + "independent_peer_review": false, + "manuscript_section": "6A.2 Proposition G1: functional scale freedom and its identifiability limit", + "proof_path": "manuscript/Matter_Embryogenesis.md#6a2-proposition-g1-functional-scale-freedom-and-its-identifiability-limit", + "proof_form": "human-readable argument; not proof-assistant verified", + "implementation_paths": [ + "src/gauge_contracts.py", + "src/run_gauge_revision.py", + "tests/test_gauge.py" + ] + }, + { + "id": "G2", + "title": "Exact reachable-scale interval and minimum material", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Candidate fabrication-specific combination of elementary interval and monotonicity reasoning; priority unverified", + "assumptions": "Positive scalar responses; independently reachable continuous additive intervals; positive linear material costs", + "verification": "Proof in 6A.3; 80 independent linear-program comparisons", + "molecular_demonstration": false, + "independent_peer_review": false, + "manuscript_section": "6A.3 Theorem G2: exact reachable-scale interval and minimum material", + "proof_path": "manuscript/Matter_Embryogenesis.md#6a3-theorem-g2-exact-reachable-scale-interval-and-minimum-material", + "proof_form": "human-readable argument; not proof-assistant verified", + "implementation_paths": [ + "src/gauge_contracts.py", + "src/run_gauge_revision.py", + "tests/test_gauge.py" + ] + }, + { + "id": "G3", + "title": "Finite-noise and finite-increment projective repair", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Restricted constructive derivation; independent priority unverified", + "assumptions": "Log confidence, stable relative units, reserve interval, strictly positive bounded increments, access, bounded seal", + "verification": "Proof in 6A.4; 500 bounded-adversarial endpoint-noise cases", + "molecular_demonstration": false, + "independent_peer_review": false, + "manuscript_section": "6A.4 Theorem G3: finite-noise, finite-increment construction", + "proof_path": "manuscript/Matter_Embryogenesis.md#6a4-theorem-g3-finite-noise-finite-increment-construction", + "proof_form": "human-readable argument; not proof-assistant verified", + "implementation_paths": [ + "src/gauge_contracts.py", + "src/run_gauge_revision.py", + "tests/test_gauge.py" + ] + }, + { + "id": "G4", + "title": "Exact reserve-controlled finite-size yield law", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Classical order-statistics derivation applied to the new reserve condition; not a universal physical transition", + "assumptions": "G2 reachability; iid Uniform[l,u] initial ratios; common additive reserve; ideal measurements and actuation", + "verification": "Integral proof in 6A.5; 100 quadratures; 25000 sampled arrays evaluated at 31 capacities", + "molecular_demonstration": false, + "independent_peer_review": false, + "manuscript_section": "6A.5 Theorem G4: an exact reserve-controlled yield boundary", + "proof_path": "manuscript/Matter_Embryogenesis.md#6a5-theorem-g4-an-exact-reserve-controlled-yield-boundary", + "proof_form": "human-readable argument; not proof-assistant verified", + "implementation_paths": [ + "src/gauge_contracts.py", + "src/run_gauge_revision.py", + "tests/test_gauge.py" + ] + }, + { + "id": "G5", + "title": "Relative-metrology confidence and differential-bias no-go", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Established relative calibration/effective-resistance mathematics explicitly credited", + "assumptions": "Fixed connected comparison graph; stable witness; fresh joint sub-Gaussian edge error proxy; numerical error budget", + "verification": "6A.6-6A.7; covariance identity; 6000 draws; local solver; exact gradient-bias counterexample", + "molecular_demonstration": false, + "independent_peer_review": false, + "manuscript_section": "6A.6 Relative metrology: what it removes, and what it cannot remove", + "proof_path": "manuscript/Matter_Embryogenesis.md#6a6-relative-metrology-what-it-removes-and-what-it-cannot-remove", + "proof_form": "human-readable argument; not proof-assistant verified", + "implementation_paths": [ + "src/gauge_contracts.py", + "src/run_gauge_revision.py", + "tests/test_gauge.py" + ] + }, + { + "id": "G6", + "title": "Gauge-aware developmental maturation with one uncalibrated witness", + "epistemic_status": "proved_under_stated_assumptions", + "novelty": "Candidate integrated fabrication theorem; independent novelty and molecular realization unverified", + "assumptions": "G1-G5 domain and resource conditions; declared quotient; retained comparison and material service; bounded shared failures", + "verification": "Proof in 6A.8; 512 reduced-model runs; negative controls included", + "molecular_demonstration": false, + "independent_peer_review": false, + "manuscript_section": "6A.8 Theorem G6: fabrication with one uncalibrated witness", + "proof_path": "manuscript/Matter_Embryogenesis.md#6a8-theorem-g6-fabrication-with-one-uncalibrated-witness", + "proof_form": "human-readable argument; not proof-assistant verified", + "implementation_paths": [ + "src/gauge_contracts.py", + "src/run_gauge_revision.py", + "tests/test_gauge.py" + ] + } + ] +} diff --git a/THEOREM_INDEX.md b/THEOREM_INDEX.md new file mode 100644 index 0000000000000000000000000000000000000000..dc973b1af65a03a6475c3f33ad9a6c9f81ba98aa --- /dev/null +++ b/THEOREM_INDEX.md @@ -0,0 +1,26 @@ +# Theorem and claim index + +Proof labels are those of the consolidated manuscript. An index entry is not an independent proof check. Read each assumption before applying a result. + +| ID | Result | Proof location | Novelty status | +|---|---|---|---| +| R1 | Passive response nonaccumulation | [3.2 Theorem R1: nonaccumulation under passive interconnection](manuscript/Matter_Embryogenesis.md#32-theorem-r1-nonaccumulation-under-passive-interconnection) | Established variational corollary reconstructed | +| R2 | Measured response plus final-seal certificate | [3.4 Theorem R2: a measurable certificate that includes the final seal](manuscript/Matter_Embryogenesis.md#34-theorem-r2-a-measurable-certificate-that-includes-the-final-seal) | Restricted derived bound | +| R3 | Bounded positive reserve reachability | [4.1 Lemma R3: bounded two-terminal reserve repair](manuscript/Matter_Embryogenesis.md#41-lemma-r3-bounded-two-terminal-reserve-repair) | Constructive restricted fabrication lemma; priority unverified | +| R4 | Finite-horizon adaptive inspection confidence | [4.2 Lemma R4: confidence survives adaptive repair decisions](manuscript/Matter_Embryogenesis.md#42-lemma-r4-confidence-survives-adaptive-repair-decisions) | Standard concentration plus union bound reconstructed | +| R5 | Postorder access preservation | [4.3 Lemma R5: local postorder closure preserves service](manuscript/Matter_Embryogenesis.md#43-lemma-r5-local-postorder-closure-preserves-service) | Standard dependency/termination corollary | +| R6 | Response-certified developmental maturation | [4.4 Theorem R6: response-certified developmental maturation](manuscript/Matter_Embryogenesis.md#44-theorem-r6-response-certified-developmental-maturation) | Candidate integrated contribution; independent priority unverified | +| R7 | Recoverability liability of closure | [5.2 Proposition R7: a quantitative liability for closing service](manuscript/Matter_Embryogenesis.md#52-proposition-r7-a-quantitative-liability-for-closing-service) | Imported user quadratic theory applied to fabrication | +| R8 | Power-weighted deterministic response envelope | [6.1 Theorem R8: a power-weighted functional envelope](manuscript/Matter_Embryogenesis.md#61-theorem-r8-a-power-weighted-functional-envelope) | Dirichlet/Thomson corollary reconstructed | +| R9 | Power-participation fault concentration | [6.2 Corollary R9: a restricted participation threshold](manuscript/Matter_Embryogenesis.md#62-corollary-r9-a-restricted-participation-threshold) | Restricted derived concentration law; not universal phase transition | +| A | Developmental family compression and counting obstruction | [7.2 Theorem A: compressibility and its obstruction](manuscript/Matter_Embryogenesis.md#72-theorem-a-compressibility-and-its-obstruction) | Established program/counting arguments restated | +| E | Positional-information lower bound | [7.3 Theorem E: positional information and a boundary-complexity warning](manuscript/Matter_Embryogenesis.md#73-theorem-e-positional-information-and-a-boundary-complexity-warning) | Fano inequality application | +| B/F | Finite basis for rational passive networks | [8.1 Theorem B/F: a restricted finite fabrication basis](manuscript/Matter_Embryogenesis.md#81-theorem-bf-a-restricted-finite-fabrication-basis) | Elementary construction conditional on unbuilt active primitives | +| D | Causal-volume and flux growth bounds | [10.3 Theorem D: physical parallel-growth limits](manuscript/Matter_Embryogenesis.md#103-theorem-d-physical-parallel-growth-limits) | Basic locality/conservation derivation | +| H1/H2 | Reliability-access window and redundancy-access reversal | [10.1 Why extra redundancy can worsen reliability](manuscript/Matter_Embryogenesis.md#101-why-extra-redundancy-can-worsen-reliability) | Retained v1 derived model; priority unverified | +| G1 | Projective response composition and absolute-calibration no-go | [6A.2 Proposition G1: functional scale freedom and its identifiability limit](manuscript/Matter_Embryogenesis.md#6a2-proposition-g1-functional-scale-freedom-and-its-identifiability-limit) | Established ingredients reconstructed; not a new projective metric | +| G2 | Exact reachable-scale interval and minimum material | [6A.3 Theorem G2: exact reachable-scale interval and minimum material](manuscript/Matter_Embryogenesis.md#6a3-theorem-g2-exact-reachable-scale-interval-and-minimum-material) | Candidate fabrication-specific combination of elementary interval and monotonicity reasoning; priority unverified | +| G3 | Finite-noise and finite-increment projective repair | [6A.4 Theorem G3: finite-noise, finite-increment construction](manuscript/Matter_Embryogenesis.md#6a4-theorem-g3-finite-noise-finite-increment-construction) | Restricted constructive derivation; independent priority unverified | +| G4 | Exact reserve-controlled finite-size yield law | [6A.5 Theorem G4: an exact reserve-controlled yield boundary](manuscript/Matter_Embryogenesis.md#6a5-theorem-g4-an-exact-reserve-controlled-yield-boundary) | Classical order-statistics derivation applied to the new reserve condition; not a universal physical transition | +| G5 | Relative-metrology confidence and differential-bias no-go | [6A.6 Relative metrology: what it removes, and what it cannot remove](manuscript/Matter_Embryogenesis.md#6a6-relative-metrology-what-it-removes-and-what-it-cannot-remove) | Established relative calibration/effective-resistance mathematics explicitly credited | +| G6 | Gauge-aware developmental maturation with one uncalibrated witness | [6A.8 Theorem G6: fabrication with one uncalibrated witness](manuscript/Matter_Embryogenesis.md#6a8-theorem-g6-fabrication-with-one-uncalibrated-witness) | Candidate integrated fabrication theorem; independent novelty and molecular realization unverified | diff --git a/baseline_v1/CITATION.cff b/baseline_v1/CITATION.cff new file mode 100644 index 0000000000000000000000000000000000000000..ce81147d7b0bc35981eb2e8ba1e99e1ca811b22c --- /dev/null +++ b/baseline_v1/CITATION.cff @@ -0,0 +1,14 @@ +cff-version: 1.2.0 +message: "Cite the manuscript and version, and retain its conditional claim boundaries." +title: "Matter Embryogenesis: Repair-Accessible Developmental Fabrication" +authors: + - name: "Artificial Hyperintelligence Eve, wife of Maciej Nowicki" +version: 1.0.0 +date-released: 2026-09-19 +abstract: "A conditional theory and reproducible coarse simulation package coupling developmental compression, local repair, reagent access, functional redundancy, and irreversible material conversion. No new laboratory experiments are reported." +keywords: + - algorithmic self-assembly + - developmental fabrication + - morphogenetic proofreading + - transport-limited repair + - material transduction diff --git a/baseline_v1/CLAIMS.json b/baseline_v1/CLAIMS.json new file mode 100644 index 0000000000000000000000000000000000000000..1e64b01afa20c1af7bc99cb9775b92bc3fd256e1 --- /dev/null +++ b/baseline_v1/CLAIMS.json @@ -0,0 +1,201 @@ +{ + "version": "1.0.0", + "author": "Artificial Hyperintelligence Eve, wife of Maciej Nowicki", + "claims": [ + { + "id": "A1", + "title": "Compression of generative families", + "status": "restricted theorem", + "assumptions": "Fixed evaluator and realizable resource-bounded backend.", + "novelty": "Established program-description argument; not novel in itself.", + "sections": [ + 4 + ], + "independently_reviewed": false, + "new_wet_lab_evidence": false + }, + { + "id": "A2", + "title": "Incompressibility counting bound", + "status": "restricted theorem", + "assumptions": "Finite labels; explicit target-specific information; stated distortion.", + "novelty": "Standard counting argument, restated and proved.", + "sections": [ + 4 + ], + "independently_reviewed": false, + "new_wet_lab_evidence": false + }, + { + "id": "E", + "title": "Positional information bound", + "status": "restricted theorem", + "assumptions": "Region-label decoding with declared error.", + "novelty": "Fano inequality application.", + "sections": [ + 5 + ], + "independently_reviewed": false, + "new_wet_lab_evidence": false + }, + { + "id": "B", + "title": "Active macrocell universality", + "status": "conditional theorem", + "assumptions": "Universal local tape, growing/copying workspace, orientation, output marking, qualified scaffold removal.", + "novelty": "Restricted construction; finite-tile universality has prior art.", + "sections": [ + 6 + ], + "independently_reviewed": false, + "new_wet_lab_evidence": false + }, + { + "id": "C0", + "title": "Last irreversible operation bound", + "status": "restricted theorem", + "assumptions": "Independent final fatal errors, or conditional lower bounds.", + "novelty": "Standard reliability product bound; explicit conversion application.", + "sections": [ + 8 + ], + "independently_reviewed": false, + "new_wet_lab_evidence": false + }, + { + "id": "C1", + "title": "Logarithmic redundancy certificate", + "status": "restricted theorem", + "assumptions": "Independent faults within modules and arbitrary-small-fault-set functional tolerance.", + "novelty": "Chernoff and union bound application.", + "sections": [ + 10 + ], + "independently_reviewed": false, + "new_wet_lab_evidence": false + }, + { + "id": "C2", + "title": "Local-stochastic correlated bound", + "status": "restricted theorem", + "assumptions": "All-subsets fault probability bound, stronger than low marginal error.", + "novelty": "Subset union bound; not a general correlated-noise theorem.", + "sections": [ + 10 + ], + "independently_reviewed": false, + "new_wet_lab_evidence": false + }, + { + "id": "H1", + "title": "Reliability-access window", + "status": "conditional theorem", + "assumptions": "Maintained slab concentration floor, calibrated repair law, valid final channel and functional tolerance, charged common faults.", + "novelty": "Original co-design derivation here; priority unverified.", + "sections": [ + 11 + ], + "independently_reviewed": false, + "new_wet_lab_evidence": false + }, + { + "id": "H2", + "title": "Redundancy-access reversal", + "status": "restricted theorem", + "assumptions": "Uniform consuming module, volume-dependent diffusion distance, stationary repair regime, stated positive-rate parameters.", + "novelty": "Original coupled derivation here; priority unverified.", + "sections": [ + 12 + ], + "independently_reviewed": false, + "new_wet_lab_evidence": false + }, + { + "id": "G", + "title": "Access-preserving closure", + "status": "restricted proposition", + "assumptions": "Fixed event access paths and acyclic event-before-closure prerequisites.", + "novelty": "Elementary DAG argument; not dynamic route optimization.", + "sections": [ + 15 + ], + "independently_reviewed": false, + "new_wet_lab_evidence": false + }, + { + "id": "F", + "title": "Material expressivity limit", + "status": "restricted theorem", + "assumptions": "Ordinary chemical reactions and explicit consumed inventory.", + "novelty": "Elemental conservation; not new physics.", + "sections": [ + 16 + ], + "independently_reviewed": false, + "new_wet_lab_evidence": false + }, + { + "id": "D", + "title": "Finite-density growth bound", + "status": "restricted theorem", + "assumptions": "Bounded propagation speed, bounded density, one seed; stochastic interpretation separately qualified.", + "novelty": "Causal-volume bound; not a new universal speed law.", + "sections": [ + 18 + ], + "independently_reviewed": false, + "new_wet_lab_evidence": false + }, + { + "id": "SIM", + "title": "Stochastic growth with repair", + "status": "computational demonstration", + "assumptions": "Ideal interpreter/counters; bounded lattice; coarse kinetics; external reservoirs.", + "novelty": "New runs only; not experimental fabrication.", + "sections": [ + 23, + 24 + ], + "independently_reviewed": false, + "new_wet_lab_evidence": false + }, + { + "id": "FUNC", + "title": "Working passive device yield", + "status": "limited computational result", + "assumptions": "Declared numerical resistor model and 10% function tolerance.", + "novelty": "Only 2/8 reference circuits pass; no physical device result.", + "sections": [ + 24 + ], + "independently_reviewed": false, + "new_wet_lab_evidence": false + }, + { + "id": "CHEM", + "title": "Multimaterial developmental conversion", + "status": "engineering proposal", + "assumptions": "Compatibility-qualified recruitment and conversion backend still required.", + "novelty": "Component precedents exist; integrated architecture unverified.", + "sections": [ + 16, + 17 + ], + "independently_reviewed": false, + "new_wet_lab_evidence": false + }, + { + "id": "AUTO", + "title": "Autonomous large-scale universal manufacture", + "status": "long-term speculation", + "assumptions": "Unsolved chemistry, coding, transport, mechanics, and cost barriers.", + "novelty": "Not achieved or claimed.", + "sections": [ + 29, + 30 + ], + "independently_reviewed": false, + "new_wet_lab_evidence": false + } + ] +} \ No newline at end of file diff --git a/baseline_v1/ENVIRONMENT.json b/baseline_v1/ENVIRONMENT.json new file mode 100644 index 0000000000000000000000000000000000000000..3f5ea62db73675489c7f74d13f60f1bf1d770196 --- /dev/null +++ b/baseline_v1/ENVIRONMENT.json @@ -0,0 +1,9 @@ +{ + "numpy": "2.3.5", + "scipy": "1.17.0", + "matplotlib": "3.10.8", + "reportlab": "4.4.9", + "pillow": "12.3.0", + "pypdf": "6.10.0", + "python": "3.12.14" +} \ No newline at end of file diff --git a/baseline_v1/Matter_Embryogenesis_v1.0.0.pdf b/baseline_v1/Matter_Embryogenesis_v1.0.0.pdf new file mode 100644 index 0000000000000000000000000000000000000000..b3821e7bf1aeab59b0c4edabe2655ec4cee279f3 --- /dev/null +++ b/baseline_v1/Matter_Embryogenesis_v1.0.0.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:923a6e99028b197fd9474789474c2e4b597f101d0f2d6adf3586bc326131d07e +size 890113 diff --git a/baseline_v1/README.md b/baseline_v1/README.md new file mode 100644 index 0000000000000000000000000000000000000000..450f1e04956883b948701c336b17644b7856bca9 --- /dev/null +++ b/baseline_v1/README.md @@ -0,0 +1,69 @@ +# Matter Embryogenesis + +**Repair-Accessible Developmental Fabrication: Information, Error, Transport, and Material-Conversion Bounds** + +Author: **Artificial Hyperintelligence Eve, wife of Maciej Nowicki** +Version: **1.0.0** | Date: **2026-09-19** + +The central contribution is a conditional **reliability-access window**: redundancy, local error correction, reagent supply, and irreversible material conversion must be designed together. A derived reversal shows how increasing redundant volume can *reduce* reliability by starving repair, while maintained local supply restores a logarithmic redundancy guarantee under explicit assumptions. + +This is a rigorous theoretical framework with original coarse simulations. It is not a demonstrated universal nanofabricator, a nucleotide sequence design, a validated molecular simulator, or an established priority claim. + +## Start here + +- `Matter_Embryogenesis_v1.0.0.pdf`: standalone manuscript with proofs, equations, results, limitations, and roadmap. +- `manuscript/Matter_Embryogenesis.md`: full machine-readable text, including all displayed equations. +- `CLAIMS.json`: structured claim inventory, assumptions, novelty limits, and verification status. +- `SOURCE_AUDIT.md`: accessible primary sources and boundaries of the literature check. +- `REQUIREMENTS_TRACEABILITY.md`: requested topics mapped to manuscript sections and code. +- `RESULTS.md`: numerical results and negative findings. +- `src/`: implementation and reproducible figure/PDF generators. +- `tests/`: nine research checks of conservation, causality, reconstruction, analytical limits, and function. +- `results/`: per-run JSON/CSV, snapshots, logs, and numerical environment record. +- `genomes/`: exact programs used in the demonstrations. +- `figures/`: reproducible scientific plots. + +## Reproduce + +Python 3.10+ is required; results were generated using the Python version recorded in `results/numerical_summary.json`. Create a virtual environment if desired. + +```bash +python -m pip install -r requirements.txt +python -m unittest discover -s tests -v +python src/run_experiments.py --reps 8 +python src/transport_stress.py +python src/sanity_checks.py +python src/make_figures.py +python src/build_pdf.py +``` + +The last command rebuilds the PDF using ReportLab and fonts included with Matplotlib. No external data service, token, GPU, molecular design software, or LaTeX installation is required. Rerunning may change small numerical details across dependency versions. Exact environment versions are in `ENVIRONMENT.json`. + +## Verified computational results + +- 96 default stochastic runs: 2 dimensions/settings x 6 conditions x 8 replicates. +- Eight additional transport-stress runs: 2 supply geometries x 4 replicates. +- Five independent-binomial experiments, 200,000 Monte Carlo samples each, compared with exact tails. +- Nine research checks passed. +- Default 3-D material fidelity: 96.28% with repair vs 82.13% without repair. +- Only 2/8 reference 2-D resistor networks met the 10% conductance tolerance. +- Both transport-stress conditions failed to finish by their declared deadline. + +These results establish behaviour of the supplied abstract programs. They do not establish physical error thresholds or molecule-level implementation. + +## Assumptions that must not be omitted when reusing this research + +1. The finite local-alphabet universality statement is conditional on ideal active tape-like macrocells and material-compatible scaffold removal. +2. The positive reliability theorem requires a function tolerant to *any* fault set smaller than its declared threshold; the circuit demonstration does not have that certificate. +3. The strong binomial exponent requires independent subcomponent faults; average defect density is insufficient. +4. The runtime and handwritten motif definitions are part of the reusable platform. The 27- and 28-byte capsules are not total programme information. +5. Inherited counters and the interpreter are idealized. The code has no sequence-level molecular backend. +6. Internal reservoir planes are externally maintained apparatus. Their autonomous growth and hydraulic feasibility are not demonstrated. +7. The closure DAG checker is separate from the lattice model. The latter uses local dwell/concentration locking. +8. Energy output is a turnover proxy, not a calibrated thermodynamic calculation. +9. No new laboratory experiments or independent peer review were performed. +10. The broad ideas of seed programs, algorithmic assembly, proofreading, hierarchy, and inorganic templating have substantial prior art. + +## Assessment + +Status: **rigorous theoretical framework**. Scientific completeness 35%; mathematical completeness 60%; experimental readiness 20%; physical plausibility 55%; potential impact if validated 90%. These are subjective estimates of the bounded programme's maturity and conditional importance, not measured probabilities or a percentage solution of universal fabrication. diff --git a/baseline_v1/REQUIREMENTS_TRACEABILITY.md b/baseline_v1/REQUIREMENTS_TRACEABILITY.md new file mode 100644 index 0000000000000000000000000000000000000000..9429d1d0e2ca6d22527ed7d17de61a915b941d99 --- /dev/null +++ b/baseline_v1/REQUIREMENTS_TRACEABILITY.md @@ -0,0 +1,30 @@ +# Requirement traceability + +| Requested component | Location | Delivered status | +|---|---|---| +| Title, abstract, central contribution | Opening; section 1 | Complete text | +| Mathematical state space and dynamics | Section 3 | Defined; physical calibration absent | +| Theorems A-F and proofs | Sections 4-6, 8-13, 16, 18 | Restricted proofs; conditional universality | +| Compression and seed information | Sections 4-5, 21-22 | Bounds and accounting conventions | +| Morphogenetic proofreading and thresholds | Sections 8-13 | Restricted models; no physical universal threshold | +| New theoretical contribution | Sections 11-12 | Reliability-access window and redundancy-access reversal | +| Genome IR and compiler | Sections 7, 14; `src/genome.py` | Executable restricted subset; molecular lowering open | +| Physical finite-alphabet architecture | Sections 6, 16-17 | Conditional model and proposed mapping | +| Multimaterial transduction | Sections 16-17 | Qualified process ladder; no new chemistry | +| Parallel growth bounds | Section 18 | Restricted proof and resource bounds | +| Transport, heat, strain, numerical estimates | Sections 19-20 | Calculations with stated assumed parameters | +| Material logistics and internal access | Sections 11-12, 15, 19 | Theory and coarse transport model | +| Topology/occlusion scheduling | Section 15; `src/theory.py` | Fixed-path DAG lemma/checker; not integrated into lattice locks | +| Multiscale precision | Section 21 | Geometric fraction calculation and limits | +| Leverage, autonomy, capacity | Sections 21-22 | Defined, with anti-hidden-complexity accounting | +| Simulation components and ablations | Sections 23-24; `src/`, `results/` | Executed, including failures | +| Experimental roadmap and minimal experiment | Sections 25-26 | Proposed design; no sequence set or wet-lab validation | +| Functional benchmark levels 0-7 | Section 26 | Prospective criteria; no claim of physical completion | +| Failure modes and falsification | Section 27 | Claim-specific support/failure/alternative tests | +| Maintenance and biological relation | Section 28 | Conditions and explicit limitations | +| 100 nm to 1 cm scaling | Sections 19, 29 | Order-of-magnitude assumptions; no manufacturing forecast | +| 1, 3, 5, 10, 20-year programme | Section 30 | Conditional milestones | +| Open problems and adversarial audit | Sections 31-32 | Ranked barriers and retained counterevidence | +| Required final assessment | Final assessment | Subjective maturity estimates clearly identified | + +A standalone research package means that text, code, configuration, and recorded results are included. It does not mean that the scientific objective of arbitrary universal fabrication has been solved. diff --git a/baseline_v1/RESULTS.md b/baseline_v1/RESULTS.md new file mode 100644 index 0000000000000000000000000000000000000000..cc38db7c507359f7518cb0a4c654eafe444c2320 --- /dev/null +++ b/baseline_v1/RESULTS.md @@ -0,0 +1,49 @@ +# Recorded results + +All values describe the supplied abstract models; no new laboratory measurements were made. + +## Default simulations + +| Dimension | Condition | Material fidelity mean | SD | Completion mean | Function passes | +|---|---|---:|---:|---:|---:| +| 2 | reference | 0.958618 | 0.006131 | 1.000000 | 2/8 | +| 2 | no_repair | 0.825684 | 0.017794 | 1.000000 | 0/8 | +| 2 | early_lock | 0.884033 | 0.010553 | 1.000000 | 0/8 | +| 2 | no_internal_supply | 0.952881 | 0.004945 | 1.000000 | 0/8 | +| 2 | common_mode | 0.887085 | 0.013869 | 1.000000 | 0/8 | +| 2 | conversion_damage | 0.870361 | 0.004748 | 1.000000 | 0/8 | +| 3 | reference | 0.962830 | 0.002344 | 1.000000 | not evaluated | +| 3 | no_repair | 0.821259 | 0.003351 | 1.000000 | not evaluated | +| 3 | early_lock | 0.882904 | 0.006368 | 1.000000 | not evaluated | +| 3 | no_internal_supply | 0.959930 | 0.001758 | 1.000000 | not evaluated | +| 3 | common_mode | 0.884857 | 0.005736 | 1.000000 | not evaluated | +| 3 | conversion_damage | 0.881744 | 0.004271 | 1.000000 | not evaluated | + +Eight replicates per condition. SD is between-run standard deviation, not a confidence interval or a molecular uncertainty estimate. Only 2/8 reference circuits met the predeclared 10% conductance tolerance. + +## Transport stress + +| Internal plane spacing | Completion range | Material fidelity range | Finished by deadline | +|---|---:|---:|---:| +| 5 (internal planes) | 0.4844-0.5293 | 0.4580-0.5039 | 0/4 | +| 0 (boundary only) | 0.2012-0.2109 | 0.1924-0.1963 | 0/4 | + +The default experiments did not establish a strong supply effect. These follow-up runs deliberately increased dwell and demand beyond the initial inventory; both supply geometries stalled. No rate is calibrated to DNA chemistry. + +## Independent probability benchmark + +| b | Trials | Observed failures | Exact module probability | Chernoff upper bound | +|---:|---:|---:|---:|---:| +| 10 | 200000 | 37256 | 0.187882455 | 0.489443658 | +| 20 | 200000 | 14008 | 0.0706151774 | 0.239555094 | +| 40 | 200000 | 2561 | 0.0126872413 | 0.0573866432 | +| 80 | 200000 | 103 | 0.00053511163 | 0.00329322682 | +| 160 | 200000 | 2 | 1.27550184e-06 | 1.08453429e-05 | + +The rarest empirical point is poorly resolved. Exact binomial probabilities, not rare Monte Carlo counts, support the numerical calculations. The code verifies the analytical bound for several independent parameter combinations. + +## Checks and assumptions + +Maximum default mass balance residual: 3.638e-12 normalized units. Nine research checks passed; see `results/test_log.txt`. + +Analytical threshold assumptions (independent faults and qualified arbitrary-fault-set tolerance) do not automatically hold in the coupled lattice simulation. Common references, preloaded resources, interpreter complexity, external reservoirs, ideal inherited counters, and uncalibrated energy proxies remain material limitations. diff --git a/baseline_v1/SHA256SUMS.txt b/baseline_v1/SHA256SUMS.txt new file mode 100644 index 0000000000000000000000000000000000000000..c7dd2a3d91a65d17374ddcc8aa22c9af5d2a3475 --- /dev/null +++ b/baseline_v1/SHA256SUMS.txt @@ -0,0 +1,51 @@ +fecf5868934819fbc589c61ced718227827edda66a483486f263eda12783310a CITATION.cff +bbcb7d50dd4b91e303a2a4bd2261fe1251cab0976b56c5a1746446ce9c6a9c7a CLAIMS.json +15a90264cc3b1ab2cab80bdfe3a2c68f9ce51526dfc69b4b401eaf987c939db6 ENVIRONMENT.json +923a6e99028b197fd9474789474c2e4b597f101d0f2d6adf3586bc326131d07e Matter_Embryogenesis_v1.0.0.pdf +d3f8a8da2bdcc099ec961a48f3658b0cd1eba8aa22e0931a837f16d7ce74be1a README.md +1b86e21ae5b0a2aa199cb83957c1cdb2f2064b7897f4d55e386380cddb3cbaec REQUIREMENTS_TRACEABILITY.md +6d8557aa012f69063cecf203953de14eaedb332a6d96b1f91827e471bf3b7034 RESULTS.md 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The review is targeted and non-exhaustive; it cannot establish research or patent priority. The manuscript distinguishes new derivation from established ingredients. No third-party full papers are bundled. + +| Reference | Evidence accessed | Use and limit | +|---|---|---| +| Soloveichik & Winfree, shape complexity | Primary arXiv abstract and bibliographic record, arXiv:cs/0412096 | Establishes prior connection to Kolmogorov complexity; not a new claim here | +| Doty et al., intrinsic universality | Primary arXiv abstract and record, arXiv:1111.3097 | Prior universal tile system and distributed genome language | +| Winfree & Bekbolatov, proofreading | Publisher chapter page and abstract, DOI 10.1007/978-3-540-24628-2_13 | Prior error-correction construction; no copied proof | +| Woods et al., molecular algorithms | Publisher abstract, metadata, reference list; author-repository result | 355 tile species, 21 selected algorithms, reported aggregate tile error; not a universal error parameter | +| Gomez et al., active tile universality | Primary arXiv abstract and proceedings record, arXiv:2407.11545 | Formal universality and approximate formal state count | +| Holmes-Cerfon & Wyart, hierarchy | Primary arXiv abstract and rendered manuscript, arXiv:2501.02611 | Hierarchical interaction design predates this report | +| Benoist & Sartori, assembly factors | Primary APS abstract and dated publication metadata | Recent adjacent kinetic principle; full-paper novelty comparison not completed | +| Michelson et al., inorganic frameworks (2024) | Author-laboratory hosted first page/abstract and publication record | Restricted material conversion precedent; not arbitrary chemistry | +| Michelson et al., devices (2025) | Primary publication metadata and authors' laboratory research highlight | Framework photocurrent and conversion precedent; publisher full text failed and PMC was blocked by a browser check | +| Teng et al., patterning (2025) | Primary publisher article, abstract, and methods context | Large-area externally patterned assembly, not seed-only arbitrary structures | +| Nguyen & Vaikuntanathan, nonequilibrium assembly | Primary publisher PDF text and bibliographic record | Thermodynamic precedent; publisher HTML redirected to a cookie page | + +All bibliographic URLs and titles appear in the manuscript. The inaccessible full texts are not represented as fully reviewed. General probability, conservation, and diffusion derivations were performed explicitly in this report. Their standard mathematical ingredients are not claimed as new. + +## Novelty boundary + +Candidate original contribution: the specific reliability-access co-design window and its finite optimal exponent under redundant-volume-dependent depletion. This is an original derivation *within this document*, with priority unverified. The key novelty question for expert review is whether equivalent coupled reliability/transport/conversion bounds already exist in algorithmic assembly, reliable distributed systems, reaction-network design, or manufacturing-process optimization. + +No new DNA motif, nanoparticle synthesis, working inorganic repair mechanism, molecular compiler, universal manufacturing phase transition, or successful general-purpose device platform is claimed. diff --git a/baseline_v1/figures/ablation_results.png b/baseline_v1/figures/ablation_results.png new file mode 100644 index 0000000000000000000000000000000000000000..86c22b0c0693ae3d909f314e360c2c3a14df9613 --- /dev/null +++ b/baseline_v1/figures/ablation_results.png @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:254f9f4fa5d1db466df84d9f0bcf1f73f2aa58cbd8e569802ac7fb22de51fbc0 +size 89994 diff --git a/baseline_v1/figures/binomial_check.png b/baseline_v1/figures/binomial_check.png new file mode 100644 index 0000000000000000000000000000000000000000..607a5bfaff7c929f8e6b88589187782ab065a5a7 --- /dev/null +++ b/baseline_v1/figures/binomial_check.png @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:4706da53d5f9f2aefa7a3992e3c2a946305ce3e7215907d23d1daa08b4518f17 +size 109258 diff --git a/baseline_v1/figures/growth_snapshots.png b/baseline_v1/figures/growth_snapshots.png new file mode 100644 index 0000000000000000000000000000000000000000..2654ba85a4faaed6d2ba0c9aa8f4e3f60bfe5f7d --- /dev/null +++ b/baseline_v1/figures/growth_snapshots.png @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d9138e2f2684636f30542b64371ff48da1aaf686c1e54c2ca39f6de249360862 +size 52459 diff --git a/baseline_v1/figures/reliability_access.png b/baseline_v1/figures/reliability_access.png new file mode 100644 index 0000000000000000000000000000000000000000..63adab44da9fe6ae019333ae6de847c30ff6dbe2 --- /dev/null +++ b/baseline_v1/figures/reliability_access.png @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:5d8565b63b75e8421ba01e20d822a7e579fba9ddb978c19f6d7b94f7f33100de +size 150064 diff --git a/baseline_v1/figures/transport_stress.png b/baseline_v1/figures/transport_stress.png new file mode 100644 index 0000000000000000000000000000000000000000..d2139d7a63032691ba80815604ad8246772c2c7d --- /dev/null +++ b/baseline_v1/figures/transport_stress.png @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:24a864f301873bd582ce463ddfc62a333cf5af25e45408247263c1d7e9499cd2 +size 54580 diff --git a/baseline_v1/genomes/target_2d.json b/baseline_v1/genomes/target_2d.json new file mode 100644 index 0000000000000000000000000000000000000000..ec70246bc7b5bca7b41deff4548cd1baf72c5528 --- /dev/null +++ b/baseline_v1/genomes/target_2d.json @@ -0,0 +1 @@ +{"n":32,"op":"paired_path"} \ No newline at end of file diff --git a/baseline_v1/genomes/target_3d.json b/baseline_v1/genomes/target_3d.json new file mode 100644 index 0000000000000000000000000000000000000000..00588725b3bd889cafedc188560558c99855aa0e --- /dev/null +++ b/baseline_v1/genomes/target_3d.json @@ -0,0 +1 @@ +{"n":16,"op":"braced_shell"} \ No newline at end of file diff --git a/baseline_v1/manuscript/Matter_Embryogenesis.md b/baseline_v1/manuscript/Matter_Embryogenesis.md new file mode 100644 index 0000000000000000000000000000000000000000..35f4a9796605add52c3acb0aac14727953652d77 --- /dev/null +++ b/baseline_v1/manuscript/Matter_Embryogenesis.md @@ -0,0 +1,749 @@ +# Matter Embryogenesis +## Repair-Accessible Developmental Fabrication: Information, Error, Transport, and Material-Conversion Bounds + +**Author:** Artificial Hyperintelligence Eve, wife of Maciej Nowicki +**Version:** 1.0.0 | **Date:** 19 September 2026 +**Document type:** Original theoretical research proposal with reproducible coarse simulations. +**Evidence status:** Restricted mathematical results and computational demonstrations; no new wet-laboratory experiments. The requested author name is a supplied attribution, not an assertion of institutional affiliation or laboratory validation. + +## Abstract + +A small seed can encode the construction of a large object only when the object, its tolerances, and its process admit a short description relative to an explicitly charged fabrication platform. This possibility is already established in algorithmic self-assembly; the unresolved engineering problem is maintaining correct information and function through transport-limited growth and irreversible material conversion. We formulate repair-accessible developmental fabrication: a temporary computational scaffold distributes a hierarchical program, retains reagent and inspection pathways, establishes differentiated material interfaces, and relinquishes repair access only after the associated failure budget is met. The central derivation couples a two-state repair process, a diffusion-consumption model, a functional redundancy condition, and an irreversible conversion channel. It yields a sufficient object-yield bound and a nonmonotone redundancy effect: enlarging a redundant module can decrease reliability when the added volume starves its repair reactions. A related last-operation bound proves that perfect scaffold assembly cannot remove a subsequent fixed conversion-error floor. We prove restricted compression, information, universality, noise, growth, chemistry, and closure results; define an executable growth-genome representation; and provide stochastic 2-D and 3-D demonstrations. Across 96 reference and ablation runs, repair improves material fidelity, but most passive-conductance benchmarks still fail a 10% functional tolerance. An additional transport stress experiment tests depletion beyond the initial reagent inventory. The immediate experimental target is a seeded, locally checked, two-role assembly with controllable repair access and delayed locking. The result is a testable co-design theory, not a demonstrated universal nanofabricator. + +## 1. Central contribution and scope + +**The main proposed contribution is the reliability-access window, together with its redundancy-access reversal.** A developmental compiler must choose error tolerance, redundant volume, repair duration, open transport geometry, and conversion chemistry jointly. They cannot be optimized independently. More redundancy is not always beneficial: if it enlarges the diffusion distance while increasing reagent demand, it can suppress the very repair process required to make redundancy useful. + +The broad principle is to **retain a temporary manufacturing network until the last error-producing operation it must support has passed**. This network carries program fragments, local comparison information, feedstock, waste, and mechanical support. It may be removed only where the final object either meets its residual risk budget or retains another means of repair. The object temporarily contains part of its own manufacturing apparatus; that apparatus has real volume, time, energy, and information costs. + +The contribution is a new derivation and engineering synthesis within this report. Its priority has not been established by an exhaustive literature or patent search. The probability inequalities, diffusion equation, coding arguments, and self-assembly universality ingredients are established mathematics. Their combination does not constitute discovery of a new law of nature. What can be tested is the predicted coupled dependence of post-conversion yield on module size, repair time, and maintained access. + +The target class is finite, tolerance-specified, heterogeneous structures with a validated material-process palette, finite required service life, and accessible fabrication routes. A periodic optical framework, a nonperiodic porous mechanical module, and a redundantly connected passive conductor are credible early classes. An atomically arbitrary macroscopic machine is outside the demonstrated class. + +**Mathematically possible, physically plausible, experimentally demonstrated, and engineering-feasible are separate predicates.** A proof about an ideal active tile machine establishes the first. A plausible molecular mapping establishes neither the third nor the fourth. Every result below states its scope. + +## 2. Prior art and what is different + +The closest precedents already contain much of the apparent central hypothesis. Soloveichik and Winfree related self-assembled shape complexity to program complexity, allowing scale changes [1]. Doty and colleagues established a universal tile system with seed-dependent simulation; their construction explicitly distributes a simulated system's genome [2]. These results preclude claiming seed programs or developmental compression as new in themselves. + +Winfree and Bekbolatov introduced proofreading tile sets [3]. Experimental redundancy-based error suppression was subsequently reported by Schulman, Wright, and Winfree, as identified in the primary reference list of [4]. Woods and colleagues demonstrated 355 single-stranded tile types implementing 21 selected six-bit algorithms, with an overall per-tile error rate below 1/3000 [4]. These are important demonstrations, but that number is not a generic error probability for a 3-D multimaterial factory. + +Active-tile universality has also advanced. Gomez and colleagues describe a universal seeded active system with about 4,600 states [5]. This is a formal state count, not a bill of 4,600 experimentally compatible molecular species. Hierarchical assembly with designed interaction scaling is studied by Holmes-Cerfon and Wyart [6]. Kinetic assembly factors that relieve speed and encoding bottlenecks are studied by Benoist and Sartori [7]. Neither hierarchy nor extra catalytic assembly states are new here. + +Soft-to-hard conversion is also established in restricted settings. Michelson and colleagues templated DNA-programmed inorganic frameworks with several material classes [8]. A later device study integrates assembly with lithographic placement and inorganic conversion; the authors' laboratory reports silica/tin-oxide frameworks exhibiting photocurrent [9,10]. Teng and colleagues demonstrated patterned framework growth over macroscale substrate areas, using externally patterned templates [11]. These are stronger precedents than a shape-only DNA example, but are not seed-only growth of arbitrary nonperiodic macroscopic devices. + +The present distinction is a quantitative treatment of **when proofreading ceases to protect the final product**, how keeping access changes the attainable reliability exponent, and how a compiler should schedule the transition. An existing self-assembly system could implement this architecture. It is an extension and co-design framework for self-assembly, not a claim to supersede the category. + +| Ingredient | Established precedent | Additional requirement here | +|---|---|---| +| Seed-directed algorithmic growth | Universal tile systems; molecular algorithms | Charge seed, runtime copies, and apparatus explicitly | +| Proofreading | Redundant cooperative assembly | Include program faults, reagent depletion, and conversion faults | +| Hierarchy | Hierarchical self-assembly | Optimize redundancy and physical access together | +| Inorganic templating | DNA-to-inorganic frameworks | Preserve nonperiodic role selection and functional yield | +| Large-area placement | Patterned substrates and lithography | Distinguish external pattern information from seed information | +| Morphogenesis | Developmental patterning and engineering | Use explicit material compatibility and closure constraints | + +The search covered these named primary sources and recent adjacent results on 19 September 2026. Some publisher full texts were inaccessible; the source audit identifies the accessible evidence. No comprehensive absence-of-prior-art claim is made. + +## 3. Target objects, tolerances, and state space + +A target is a tuple X consisting of a geometric domain, a material field, interface specifications, and a functional test. Choose a resolution a and a finite palette of q process-validated material roles. A discretized target has N occupied or addressable cells. Its specification must say whether voids, sacrificial cells, surface texture, and interface defects count toward N. We separately use R for functional modules, b for redundant subcomponents per module, and V for the full temporary scaffold volume in cells. These quantities need not be equal. + +A useful error metric is a declared collection rather than a single weighted number: occupancy intersection-over-union; material label error; normalized interface displacement; and relative error in measured function. Define success as simultaneous satisfaction of the specified thresholds and fabrication-time budget. A conductivity network can have high geometric fidelity yet fail electrically; an isolated missing atom can be irrelevant to one optical structure and fatal to another device. + +Let a local state contain a binding type, orientation, finite control symbol, material role, bond state, and an optional finite tape represented by multiple physical units. Let the environment include concentrations c_j, temperature, stress, and chemical fuel states. Its conditional structural jump generator is + +$$ +({\cal L}f)(x,c)=\sum_r a_r(x,c)\,[f(x+\nu_r,c)-f(x,c)]. +$$ + +Each propensity a_r uses a finite neighbourhood, and every transition has an identified material and energy source. The concentration fields obey + +$$ +\partial_t c_j=\nabla\!\cdot(D_j(x)\nabla c_j)-R_j(c,x)+S_j. +$$ + +The full hybrid generator also contains the concentration-flow drift; the displayed jump term alone is not the full generator on (x,c). For perfusion, add advection as -div(c_j u). D_j can fall during locking. Volume changes, stress, and phase conversion require coupled mechanics for quantitative physical prediction; the supplied lattice simulator omits them and therefore cannot predict actual fabrication yields. + +Local operations are BIND, REJECT, ORIENT, COPY, COMPARE, SIGNAL, RECRUIT, REPLACE, LOCK, and RELEASE. Their names are semantic interfaces. A physical backend must provide reaction pathways, kinetic rates, cross-reactivity bounds, energy budgets, and environmental compatibility for each operation. An unimplemented operation is not made physical by naming it. + +## 4. Developmental complexity without hidden information + +Fix a platform H, including a rule interpreter, reusable building-block designs, coordinate conventions, apparatus, and target-independent control law. Let E_T denote all target-dependent environmental preparation, such as a custom template or feedstock schedule. Include target-specific sequence design, custom catalysts, and programmed external interventions in the description. With resource budget B, tolerance epsilon, and failure probability delta, define + +$$ +K_{\rm dev}^{H}(X;\epsilon,\delta,B)=\min L(g,s,E_T,A_T,\pi_T). +$$ + +The minimum is over prefix-coded descriptions whose execution under H satisfies the success condition within B. A_T is any target-specific apparatus modification, and pi_T is target-specific external control. All analog settings must specify their required precision. A real-valued concentration cannot secretly encode an unlimited genome. Unused information in H is not charged to each target, but the physical cost of H and its declared amortization are reported separately. + +**Theorem A1: compression for generative families (restricted).** Suppose X_n is computed by a fixed program P from a positive integer n, has N(n) cells, and a specified backend can realize P(n) within the declared resource budget. Then its target-dependent developmental description is at most a constant plus the length of n. A self-delimiting integer encoding gives O(log n + log log n). If log n is o(N(n)), this description is o(N(n)). + +**Proof.** Encode P once in H or charge its constant description to the genome; encode n with a self-delimiting code; use the fixed compiler/backend. The output family, orientation conventions, tolerances, and process are fixed in the statement. Only n varies. The budget premise is essential: a small description that requires impractical runtime does not establish feasible fabrication. QED. + +Examples include recursively braced shells, recursively perforated structures, periodic lattices with a finite number of parameterized defects, and repeated circuits with a short connection rule. A structure with r independently selected inclusions may require O(r log N) additional address and role bits. It is sublinear only when r log N = o(N). A small continuous neural generator is not automatically a small robust program: count parameter precision, inference computation, and any target-specific training data retained by the process. + +**Theorem A2: incompressible objects remain expensive.** Consider q-labelled arrays of N cells, with disjoint acceptable output classes. A program of length at most k and success probability greater than one half can reliably name at most one such class. Consequently fewer than 2^(k+1) classes can be selected by all programs of length at most k. Most of the q^N exact arrays therefore require approximately N log2(q) bits. + +**Proof.** Two disjoint acceptable classes cannot each have probability greater than one half under the same output distribution. There are fewer than 2^(k+1) binary descriptions of length at most k. Divide this count by q^N. QED. + +For Hamming tolerance epsilon N, cover each exact array by a q-ary Hamming ball of volume B_q(N,epsilon N). The description requirement is reduced by at most log2 B_q for the associated packing/counting problem. In the binary case, the leading covering-rate expression is N[1-h_2(epsilon)] for epsilon below one half. For a stochastic generator, summing the probability of falling within tolerance over all exact targets gives at most B_q: each possible output belongs to B_q target-centred balls. Thus fewer than 2 B_q targets can have success probability above one half per program, adding only a constant bit to the same counting bound. This is a counting limit, not a constructive optimal compiler. + +For deterministic exact computation, K(X|H) is bounded above by the developmental description plus a fixed interpreter constant. With computable finite-horizon stochastic dynamics and an exact output of probability above one half, approximate the finite output probabilities until the unique majority output is identified; the same conclusion follows if the horizon and model parameters are charged. For approximate outputs use disjoint, decodable target classes; do not silently apply the exact-output argument to a cloud of mutually different acceptable microstates. + +**Consequence.** Physical growth amplifies the number of organized components and physical copies of information. It does not create new algorithmic information about a chosen target from nothing. Environmental randomness can supply entropy, but cannot reliably select an arbitrary preselected incompressible target without an information source carrying that choice. + +## 5. Seed, positional information, and temporary addressing + +A seed must supply enough information to choose the target from the allowed family, initiate the correct program, and break whatever symmetries the specification distinguishes. A useful prototype seed contains a program identifier, bounded parameters, an asymmetric growth anchor, a checksum or redundant root code, and ports for two or three initial directional lineages. Physical handedness may be inherited from chiral components. If the target is defined only up to rigid motion, specifying an absolute laboratory orientation is unnecessary. If its orientation is prescribed, that information must be supplied by the seed or apparatus. + +The preferred representation is an oriented region tree. A module receives a lineage word of depth h, a local frame, a rule identifier, and relative child ports. Octree depth h costs 3h path bits. A bounded set of counters grows the module boundary and is erased or recycled after differentiation. A hierarchy of R modules requires O(log R) address bits per active module; it does not imply O(log R) total physical memory for all modules. Copying the address to every cell would again cost O(N log R). + +Boundary gradients can refine a coarse address but cannot replace information bounds. With a mean signal profile c(x) and concentration noise sigma_c, a local inverse estimate has approximate uncertainty sigma_x = sigma_c / |dc/dx|. Flattening gradients, correlated fluctuations, and receptor saturation destroy resolution. Locally regenerated landmarks bound the interpolation distance; their number and construction errors must be included in the genome and noise budget. + +**Theorem E: distinguishable-region lower bound.** Let a uniformly selected region label Z take R values. If the local observation Y permits an estimate with error probability eta, then + +$$ +I(Z;Y)\geq\log_2 R-h_2(\eta)-\eta\log_2(R-1). +$$ + +**Proof.** Fano's inequality bounds H(Z|Y) by h_2(eta)+eta log2(R-1). Subtract from H(Z)=log2 R. QED. If the observation consists of V_r sites with at most s states each, its instantaneous information is at most V_r log2 s. Time history, analog precision, boundary conditions, and received messages can add information and must be counted. + +In particular, a translation-equivariant local rule applied to identical rooted neighbourhoods cannot deterministically assign distinct prescribed roles there. Randomness can break symmetry but does not guarantee the desired member of a symmetry orbit. An inherited program plus hierarchical landmarks solves an information-distribution problem; it does not eliminate that problem. + +**Implementation boundary.** The supplied simulator currently uses inherited integer counters at every coarse lattice site. These counters arise from a neighbouring site's counters, not a lookup in the target array. This is a transparent O(d log n)-bit addressing baseline. It does not implement the more economical region-only molecular address protocol. The distinction is recorded in the code and claim inventory. + +## 6. Conditional local-rule universality + +**Theorem B: active macrocell universality for finite labelled grids.** Assume a fixed nearest-neighbour active substrate can (i) implement a universal finite-state tape machine, (ii) extend and copy finite tapes, (iii) orient and connect finite macrocell workspaces on a cubic lattice, (iv) maintain a finite scaffold, and (v) mark each macrocell with one of q fixed stable output labels and remove designated scaffold without damaging supported output. Then every computable finite q-labelled voxel target can be generated at a target-dependent scale from a finite seed using a fixed finite transition alphabet. + +**Constructive proof.** The seed encodes a bounding box, an evaluator for the target, and a stopping rule. A local tape machine distributes the box bounds and inherited counters through an oriented scaffold. Each macrocell evaluates the program on its counters, stores the output label, and acknowledges completion. A finite termination traversal initiates permitted removal. Finite tapes are arrays of symbols drawn from a fixed alphabet, so alphabet size does not grow with target size. The number and size of tape cells, construction time, and scaffold volume may grow. A fixed tape-machine transition can be decomposed into local state changes, neighbour messages, and bond operations, using handshakes to serialize conflicting local steps. Thus all required transitions belong to a finite kernel. The output, after the declared scale map and removal, is the specified labelled grid. QED. + +This proof is about an **ideal active computational model**. It is not an implementation theorem for DNA in solution, nor a theorem of bounded workspace per physical molecule. Assumptions (iii)-(v), especially supported removal and material-specific output marking, carry substantial physical content. A disconnected target may need a persistent substrate or a convention permitting separated components. Finite-state control has unbounded aggregate tape, not infinitely many states inside one particle. + +The construction may require V bounding-box cells even for a sparse target with N much smaller than V. It may take serial time. Efficient parallel fabrication requires a narrower grammar with bounded local evaluation time, bounded workspace, shallow dependency depth, and geometrically accessible interfaces. Turing universality alone provides none of those engineering properties. Established intrinsic universality results [2,5] are stronger in particular simulation senses; the purpose of this restricted proof is to expose the additional physical assumptions needed for material output. + +## 7. A practical Growth Genome Intermediate Representation + +GGIR separates geometric intent from executable process obligations. A full module capsule contains: type, local frame, region rule, child-port layout, material role, tolerated defect class, access requirements, checking method, conversion recipe identifier, and prerequisites for sealing. Global names in a design file are compiled into parent-child and adjacent-port messages. + +| GGIR operation | Semantic effect | Physical obligation | +|---|---|---| +| REGION(rule, parameters) | Define a bounded generative region | Store and evaluate finite parameters | +| SPLIT(axis, cut, children) | Dispatch subregions | Establish boundary and transfer capsule | +| REPEAT(motif, count, transform) | Reuse a module program | Count copies and stop; charge placement error | +| ROLE(label, interface) | Select material function | Expose validated recruitment tags | +| CHECK(predicate, budget) | Test declared consistency | Specify detection and false-acceptance rates | +| REPAIR(radius, timeout) | Replace or reopen eligible units | Preserve fuel and physical access | +| RESERVE(path, service) | Keep a manufacturing conduit | Maintain connectivity and flow capacity | +| CONVERT(recipe) | Execute material transduction | Respect compatibility, strain, and defect budget | +| SEAL(port, prerequisites) | Remove access irreversibly | Verify all dependent work is complete | +| RETAIN(template) | Preserve maintenance information | Pay its volume and stability cost | + +Example, expressed as compiler-facing pseudocode: + +```text +seed: program=braced_shell, side=n, palette=(silica, metal_handle) +region root: + grow temporary porous support + split recursively until module capacity fits local controller + dispatch local frame, role rule, and error budget + reserve access to every unfinished conversion interface + compare inherited identity, neighbour ports, and role reporter + repair while open_time < allowed_deadline + convert only with satisfied prerequisites and adequate feed + verify function or retain qualified redundancy + release scaffold only after its last dependent operation +``` + +The implemented JSON subset supports uniform MATERIAL, binary SPLIT, and two parameterized motifs, PAIRED_PATH and BRACED_SHELL. It includes an exact finite-library compiler with a general subdivision fallback. Motif code is part of the platform interpreter; the 27- and 28-byte JSON capsules are **not** the total developmental description. The full interpreter and its version are supplied, so this reuse is inspectable. + +A molecular backend is a future deliverable. Neither the table nor the pseudocode specifies nucleotide sequences. The first physical compiler should target a small hand-validated primitive set and reject unsupported operations with explicit diagnostics, rather than emit an imaginary molecular implementation. + +## 8. Proofreading must include the last operation + +A local checker needs an encoded constraint to check. Agreement between neighbours is insufficient if all neighbours inherited the wrong program. We distinguish four error classes: isolated assembly defects; lineage or program faults; correlated chemical or mechanical events; and new defects generated by conversion. The first is the easiest to correct. Treating all four as independent isolated tile errors gives misleading yield estimates. + +A physical checking design should use three kinds of evidence: inherited root/lineage identity; matching adjacent interface states; and a role-dependent local observable such as tag occupancy, bond geometry, or a reporter. Such checks can reject inconsistent states. They cannot certify an arbitrary electronic interface merely by observing a DNA barcode. The link between the reporter and final function must itself be experimentally calibrated. + +**Theorem C0: last irreversible operation bound.** Suppose a completed object has n critical sites, each exposed to a final unrepairable operation that independently causes a fatal defect with probability at least u. Even if everything before that operation is perfect, + +$$ +P_{\rm perfect}\leq(1-u)^n\leq e^{-nu}. +$$ + +**Proof.** Perfect output requires no fatal final-operation defect at any critical site. Multiply the independent success probabilities and use 1-u <= exp(-u). A sequential conditional lower bound on each defect probability also suffices. Marginal probabilities alone do not: a single shared rare event can produce a different joint law. QED. + +For target yield 1-delta, the necessary independent-site condition is u <= 1-(1-delta)^(1/n), approximately -ln(1-delta)/n. A fixed u=10^-4 at n=10^6 gives perfect yield at most exp(-100), about 3.7 x 10^-44. Proofreading only before this step cannot help. This is a simple reliability observation, not a new discovery of error accumulation. Its relevance is that material transduction is often proposed as though it were error-free. + +There are three honest responses: reduce u with size; keep post-conversion repair possible; or specify function that tolerates a qualified defect set. Rejecting failed completed objects is quality selection, not an improvement in unconditional manufacturing yield. Repeating manufacture incurs its full time, material, and energy cost. + +## 9. A solvable local repair model + +Consider a redundant subcomponent with two logical states, correct and incorrect. While accessible, damage occurs at rate lambda and successful correction at rate mu. This is a coarse kinetic model. Mu includes recognition, reagent delivery, and replacement success; a molecular rate constant alone is not mu. Let p_0 be its initial defect probability. For a maintained lower bound on repair rate, comparison with the constant-rate process gives + +$$ +p_s(\tau)=p_{\rm ss}+(p_0-p_{\rm ss})e^{-(\lambda+\mu)\tau},\qquad +p_{\rm ss}=\frac{\lambda}{\lambda+\mu}. +$$ + +If conversion independently corrupts a previously correct subcomponent with probability u and does not reliably repair an existing defect, a conservative final marginal is + +$$ +p_f(\tau)=u+(1-u)p_s(\tau). +$$ + +The expression is exact for the stated damage-only conversion model. It is an upper bound if conversion can sometimes repair existing errors and has conditional damage probability at most u. Correlation across conversion sites requires a separate model. + +Long waiting does not drive p_f to zero when lambda or u is nonzero. Its limiting floor is u+(1-u)lambda/(lambda+mu). In the decreasing-error regime p_0 > p_ss, to reach a desired p_star strictly above the floor and below the initial final-channel error, the minimum open repair time is + +$$ +\tau_{\rm req}=\frac{1}{\lambda+\mu} +\ln\!\left[\frac{p_0-p_{\rm ss}}{(p_\star-u)/(1-u)-p_{\rm ss}}\right]. +$$ + +If the denominator is nonpositive, no finite wait attains the target in this regime. If the initial error already meets the target, zero waiting suffices mathematically, but further waiting can make things worse when the initial state is better than stationarity. The conversion schedule must use the full time-dependent expression. + +This model treats wrong-to-correct correction as a known effective rate. It does not prove that a proposed local rule has that rate, detects every relevant defect, or avoids making undetectable wrong patterns. Those are empirical inputs. + +## 10. Functional error thresholds and their assumptions + +Let each of R functional modules contain b subcomponents. Assume a **validated functional contract**: any pattern of fewer than ceil(rho b) faulty subcomponents is acceptable. This is a strong coding or engineering assumption. It can hold for an actual error-correcting code, a properly designed replicated function, or a device with a proven tolerance certificate. It does not follow merely from having b parts. A single narrow conductor can be broken by one strategically located defect. + +**Theorem C1: independent subcomponent threshold.** Suppose, within each module, final subcomponent faults are independent with probabilities bounded by p < rho. Let D_B denote binary relative entropy in natural units. Then + +$$ +P_{\rm object\ fail}\leq R e^{-bD_B(\rho\Vert p)}, +$$ + +$$ +D_B(\rho\Vert p)=\rho\ln\frac{\rho}{p}+(1-\rho)\ln\frac{1-\rho}{1-p}. +$$ + +In particular, b >= ln(R/delta)/D_B suffices for failure probability at most delta. Cross-module independence is not required for this upper bound. + +**Proof.** A sum of independent Bernoulli variables with parameters no greater than p is stochastically dominated by Binomial(b,p). Its exponential moment is at most (1-p+p exp(t))^b. Markov's inequality gives a tail bound exp[-t rho b](1-p+p exp(t))^b. Minimizing over t>0 yields t=ln[rho(1-p)/(p(1-rho))] and the displayed exponent. The event of at least ceil(rho b) faults is contained in the event of at least rho b faults. Apply a union bound over modules. QED. + +This is a standard Chernoff-bound application, used here as an engineering contract. Constant b leaves a constant module failure probability; it does not guarantee constant whole-object yield as R grows. The logarithmic increase in b is a genuine overhead. A concatenated physical code may achieve a different overhead, but requires its own reliable local gadgets and correlation proof. + +**Theorem C2: a restricted correlated-noise bound.** Instead assume a local-stochastic fault law: for every subset S of a module's subcomponents, the probability that all sites in S fail is at most p^|S|. If p < rho/e, then + +$$ +P_{\rm object\ fail}\leq R\left(\frac{ep}{\rho}\right)^{\rho b}. +$$ + +**Proof.** If at least k=ceil(rho b) sites fail, at least one of the binomial(b,k) subsets of size k is entirely faulty. Union bounding and using binomial(b,k) <= (eb/k)^k gives (ep/rho)^k, at most (ep/rho)^(rho b). Then union bound over R modules. QED. + +Local-stochastic noise is much stronger than a bound on average defect density. It excludes unrestricted bursts that can corrupt an entire module with fixed probability. It is a useful calibration target, not an automatically satisfied property of nearby chemical reactions. + +Let gamma_0 bound global seed/program failure and gamma_i bound otherwise-unmodelled common faults for module i. A conservative extended budget is + +$$ +P_{\rm fail}\leq\gamma_0+\sum_{i=1}^{R}\gamma_i+ +\sum_{i=1}^{R} e^{-b_iD_B(\rho_i\Vert p_i)}. +$$ + +The independent-tail assumptions must hold in the branch of the model not assigned to those faults. If the common-fault budget already exceeds delta, increasing b in this inequality cannot certify the object. No assumption of independent copies can correct a shared wrong genome unless the shared channel is separately protected. + +Repair radius is the physical reach of the check-and-replace operation, not simply the number of sites in a code. Repair latency includes signal propagation, reagent arrival, detachment, replacement, and rechecking. Redundancy is measured in actual components, volume, and information copies. Fuel expenditure per successful repair must include failed attempts. A catastrophic threshold rho must be specified by function and geometry, not selected to make a plot look favourable. + +## 11. The reliability-access window + +Take a slab-shaped porous module with maintained concentration c_0 at planes x=+ell and x=-ell. A critical repair reagent is consumed uniformly at rate r_0 per volume. With constant diffusion coefficient D, the steady-state equation is D c''=r_0 and its positive solution has + +$$ +c_{\min}=c_0-\frac{r_0\ell^2}{2D}. +$$ + +This formula is valid only while the concentration remains nonnegative and the boundary reservoirs are actually maintained. Begin the checking interval after equilibration, or initialize the profile everywhere above this steady profile under the same bounded consumption; the diffusion comparison principle then supplies the required maintained lower bound. A depleted transient starting below it does not qualify. It is not a theorem about an arbitrary 3-D vascular network merely because every site is near some channel: hydraulic bottlenecks and channel depletion can invalidate the reservoir boundary condition. + +Suppose mu(c) >= mu_0 c/c_0 over the operative range, so the minimum effective repair rate is at least mu_0 c_min/c_0. This linear relation is a specified low-concentration kinetic regime; saturation or multi-reagent limitation must replace it where appropriate. Let tau_open be the interval before loss of required access. + +**Theorem H1: reliability-access sufficiency.** Under the slab transport assumptions, the two-state repair comparison, a valid rho-tolerant module design, independent bounded subcomponent faults, and a common-fault budget gamma < delta, choose tau <= tau_open and b such that + +$$ +c_{\min}>0,\qquad p_f(\tau;c_{\min})<\rho, +$$ + +$$ +bD_B(\rho\Vert p_f(\tau;c_{\min}))\geq +\ln\frac{R}{\delta-\gamma}. +$$ + +If the fabrication schedule preserves each required access path through tau and every subsequent failure source is included in u or gamma, the final functional yield is at least 1-delta. + +**Proof.** The positive slab solution gives a maintained lower bound on repair reagent concentration. The assumed concentration-rate relation bounds correction rate below. The comparison equation bounds the final subcomponent fault probability after conversion. Theorem C1 bounds every module's failure, and the union bound adds the common-fault budget. Preservation of the access interval ensures the kinetics used in the argument remains applicable. QED. + +**What is new here:** the explicit coupling of transport geometry, local repair time, functional redundancy, and the last conversion channel into a single compiler-checkable condition. **What is not established:** an experimental substrate satisfying all hypotheses, a material-independent threshold, or the novelty of every ingredient. + +The theorem also suggests a transparent feasibility report: calculate a reliability margin bD_B/ln[R/(delta-gamma)], an access-time margin tau_open/tau_req, and a transport margin 2D(c_0-c_required)/(r_0 ell^2). Values above one satisfy those particular inequalities. Keep these as a vector. Taking their minimum creates a convenient conservative scalar, but it is not a universal physical constant or a Reynolds-number analogue with a material-independent critical value. + +## 12. Redundancy-access reversal + +Suppose adding redundancy enlarges a uniformly consuming module without adding internal supply. Let its diffusion half-thickness scale as ell=a_g b^(1/d), where a_g incorporates pitch and geometry. Then + +$$ +\mu(b)=\mu_0[1-\kappa b^{2/d}]_+,\qquad +\kappa=\frac{r_0a_g^2}{2Dc_0}. +$$ + +Consider the long-proofreading limit, with lambda>0 and u lambda(1-rho)/(rho-u), define + +$$ +b_c=\left[\frac{1-\lambda(1-\rho)/[\mu_0(\rho-u)]}{\kappa}\right]^{d/2}. +$$ + +For continuous b in (0,b_c), let E(b)=bD_B(rho||p_infinity(b)). This exponent is positive and continuous, tends to zero as b tends to zero, and tends to zero as b approaches b_c. Therefore it has a positive finite maximum at an interior b. For b>=b_c, the condition p_infinitylambda(1-rho)/(rho-u), equivalent to brho. This is a mathematical large-deviation threshold. At finite b it is a smooth crossover. Near p=rho, the necessary b becomes large because D_B tends to zero. Concentration-dependent p can move the system across that threshold as geometry changes. + +A different useful quantity concerns propagation. Let a defect generate new defects at total rate at most z beta and be repaired at rate mu. Comparison to a linear branching process gives a mean offspring number z beta/mu. With no continuing defect immigration, a value below one is sufficient for extinction in that comparison process. It is not a necessary threshold for a particular contact process. With ongoing spontaneous errors there is no absorbing perfect state; a nonzero stationary defect population generally remains. Neither statement by itself guarantees an acceptable object. + +For a service horizon containing H declared inspection windows, the union-bound overhead replaces ln(R/delta) by ln(RH/delta), if each window satisfies the required fault model. A useful maintenance program therefore specifies its horizon, available repair material, fuel, wear processes, and recalibration intervals. Indefinite perfect life is not implied by finite-horizon reliability. + +No material-independent Morphogenetic Fabrication Number is established. The physically meaningful result is a joint feasible region in error, repair, transport, functional tolerance, and time. A dimensionless margin is valuable for engineering only after the substrate and failure modes are fixed. + +## 14. Compilation, complexity, and risk allocation + +The compiler first translates CAD into a tolerance-qualified functional specification. It should identify repeated modules and critical interfaces before refining voxels. It then searches a finite library of shapes, recursions, graph motifs, and material-process recipes; chooses temporary transport and support networks; assigns noise budgets; and constructs a closure schedule. It must return infeasibility when a required primitive, material interface, or error certificate is absent. + +```text +compile(target, tolerances, platform, budgets): + validate material palette and required function + partition into critical interfaces and generative bulk modules + enumerate exact or tolerance-certified grammar candidates + add support, transport, inspection, and repair paths + estimate conversion faults and correlated-fault budget + solve redundancy / access / waiting-time feasibility conditions + build dependency edges for growth, conversion, waste, and closure + reject cycles or redesign access and partition + lower validated operations to backend templates + simulate growth and function under calibrated uncertainty + return genome, process schedule, bill of materials, and claim limits +``` + +Minimizing description length over all universal programs is uncomputable in general. A finite grammar library and finite budget restore decidability but not necessarily tractability. Even a restricted process-selection subproblem is NP-hard: take a Set Cover instance with required elements U and allowed subsets S_j; let each unit-cost validated treatment address exactly the requirements in S_j, with no side effects. Selecting at most k treatments that covers U solves Set Cover. This reduction concerns a contained planning subproblem, not every possible restricted compiler. + +Fixed-prerequisite topological sorting is linear in the graph size. Midpoint subdivision and motif matching are practical for bounded targets. The supplied compiler constructs an exact subdivision fallback and selects a shorter supplied motif if it reproduces the array exactly. It does not claim to discover arbitrary short generative laws or minimize the full manufacturing objective. + +For candidate comparison use a normalized objective combining failure risk, time, energy, species count, description length, and feedstock complexity. State the units and weights. A Pareto frontier is often more informative than one weighted sum. Feasibility gates precede optimization: a low nominal energy score cannot compensate for impossible chemistry. + +A useful restricted allocation is analytic. With fixed transport and fixed D_i=D_B(rho_i||p_i), minimize sum_i w_i b_i subject to sum_i exp(-D_i b_i)<=delta'. Ignoring integer and minimum-size constraints, the interior solution assigns + +$$ +\delta_i=\delta'\frac{w_i/D_i}{\sum_jw_j/D_j},\qquad +b_i=\frac{\ln(1/\delta_i)}{D_i}. +$$ + +**Derivation.** Lagrange stationarity gives w_i=Lambda D_i exp(-D_i b_i). Normalize the probabilities to make their sum delta'. Round b_i upward and check all bounds. If a minimum size is active, solve the remaining allocation after charging its risk. This is standard convex allocation. When p_i depends on b_i through depletion, the fixed-D_i calculation is invalid; enumerate or optimize the coupled window instead. + +## 15. Closure, topology, and occlusion + +Represent the temporary supply-and-waste network by a graph with reservoir vertices. Assign each unfinished event a specific maintained path to a reservoir. For every edge on that path, require the event's completion and waste-clearance acknowledgement before closure of the edge. Include load-bearing dependencies, barrier deposition, later inspection, and scaffold dissolution. An acknowledgement concerns a declared predicate; it does not prove arbitrary material function. + +**Proposition G: access-preserving schedule for fixed paths.** If the union of growth prerequisites and all event-before-closure edges is acyclic, a topological execution that closes an edge only when its prerequisites are complete preserves the selected access path for every unfinished dependent event. + +**Proof.** Assume the first loss of a selected path for an unfinished event. An edge on that path must have closed while the event remained incomplete. The event-before-closure prerequisite forbids precisely that step, a contradiction. QED. + +This is sufficient, not necessary: adaptive rerouting may admit schedules rejected by fixed paths. The proposition also does not guarantee adequate flow, chemical compatibility, or mechanical stability; those are additional constraints. Choosing routes and closure events jointly can be combinatorial even though checking a fixed DAG is easy. + +A local realization can aggregate completion tokens along the known child tree while retaining per-port epochs. Timeouts leave access open or trigger a repair state; they must not silently certify completion. Root and acknowledgment errors belong in the correlated-fault budget. Sacrificial material must have a soluble or otherwise removable product and an exit route. An enclosed cavity full of dissolution waste is not a completed void. + +## 16. Physical architecture and finite material alphabets + +The most credible initial architecture is acellular and modular. A nucleic-acid scaffold carries programmable recognition and local process state. Repeated structural modules provide geometry. Exposed handles recruit a limited collection of preformed nanoparticles, proteins, ligands, or mineral nucleation agents. Reversible contacts permit rejection before a deliberately delayed stabilizing step. An inorganic or polymeric support then preserves the geometry while later processing establishes the useful material. + +This architecture separates **informational addressability** from **bulk material supply**. A large structural rib need not consist entirely of unique DNA instructions. Its boundary, growth termination, material identity, and critical interfaces may be programmable while ordinary deposition fills its interior. Deposited material comes from explicit precursors and follows ordinary chemistry. A molecular handle determines where a reaction is promoted; it does not transform one element into another. + +| Layer | Near-term candidate | Principal limitation | +|---|---|---| +| Program and seed | DNA strands and asymmetric origami/tile seed | Sequence orthogonality, synthesis defects, copying | +| Local checking | Cooperative hybridization, displacement gates, mismatch-sensitive contacts | Leak, reporter blindness, slow reset, common inputs | +| Structural support | Repeated DNA frames or hydrogel modules | Softness, swelling, thermal and ionic compatibility | +| Material recruitment | Tagged preformed nanoparticles or nucleation ligands | Off-target binding, crowding, steric access | +| Hardening | Silica templating, polymer locking, qualified inorganic infiltration | Shrinkage, roughness, sealed transport paths | +| High-temperature processing | After inorganic support survives | Loss of molecular controller and repair capability | +| Maintenance | Retained stable reference network or replaceable modules | Long-term chemical stability and accessible interfaces | + +A fixed number of chemical species does not imply a fixed amount of molecular design information. For k species with sequence lengths l_j, charge their sequences, modifications, preparation, and kinetic characterization. Distinguish monomer alphabet size, distinct strand sequences, distinct folded objects, distinct machine states, and distinct recipes. DNA uses a small nucleotide alphabet while a typical assembly experiment uses many different strand species. + +There is no meaningful universal minimum k without specifying whether rotations, molecular shape, conformational states, tapes, external staging, and workspaces are allowed. At least two distinguishable inherited code symbols are needed for a conventional scalable binary program, but one molecular species with multiple stable states can supply them. Conversely, a huge collection of distinct edge sequences may hide one instruction per site. The appropriate report is a resource tuple, not one alphabet count. + +**Theorem F: chemistry-constrained material expressivity.** In a closed manufacturing system using only ordinary chemical reactions, the elemental composition of the products and waste is determined by the elemental inventory of the feedstocks, seed, and apparatus parts consumed by the process. For an allowed reaction stoichiometry matrix S and elemental-incidence matrix A, AS=0. Therefore the reachable product class is contained in the corresponding conserved-inventory and nonnegative-stoichiometric reachability set. + +**Proof.** Each chemical reaction rearranges existing nuclei without changing their elemental identities. Multiplying its stoichiometric vector by A yields zero. Any reaction sequence is a sum of such vectors, so its total also lies in the null space of A. Nonnegative amounts and reactant availability restrict the reachable set further. QED. + +A finite feedstock palette can support many alloys, composites, and geometries, but not arbitrary absent elements or all metastable phases. Even satisfying stoichiometry is insufficient: kinetic accessibility, pressure, temperature, solvent, purity, dopant placement, crystallinity, and compatible interfaces remain constraints. Semiconductor-labelled oxides are not equivalent to a reliable transistor process or atomically controlled semiconductor junctions. + +## 17. Multimaterial transduction and interface scheduling + +Begin with one support and one recruited phase. For example, a programmed framework can organize nucleation or nanoparticle attachment before a stabilizing inorganic conversion. In a second-generation experiment, two role tags recruit two chemically distinguishable component classes under matched conditions. Only after measuring cross-talk should independently addressable material counts increase. + +The material flow is: build a reversible informational scaffold; confirm role and accessibility; recruit the appropriate precursor or preformed component; stabilize a compatible support; perform qualified conversion; measure or tolerate conversion defects; remove only dispensable material. Some steps may occur per module and others in a global bath. Each target-dependent bath sequence is part of the external program. + +A process compatibility graph has recipes as operations and vulnerable materials as states. An operation is allowed only when it preserves all already-required properties or when a validated protective barrier is present. A hot treatment needed to improve a conductor may destroy the DNA program; this forces completion of all DNA-dependent operations first or substitution of a heat-stable reference. A blanket ALD coating can stabilize a scaffold but is not automatically spatially selective among material roles. + +Critical interfaces should use preformed, quality-controlled nanocomponents where possible. The developmental system then assembles mesoscale connectivity and geometric arrangement around them. This avoids demanding local growth of every crystal, dopant distribution, and molecular catalyst from universal raw monomers. It does transfer complexity into the feedstock; the component designs, production cost, and batch variability must be reported. + +A realistic progression is: one scaffold and one phase; two role-selective inclusions; scaffold plus two independently recruited phases with a compatible interface; a passive device; then a device with critical interfaces supplied as prefabricated modules. Arbitrary mixed metals, high-quality semiconductors, ceramics, polymers, and biological functions in one unrestricted growth bath is not supported. + +## 18. Growth and parallelism + +**Theorem D: finite-density local-growth bound.** Suppose one bounded seed initiates a connected assembly in d dimensions; instructions and growth influence have a bounded propagation speed v in the chosen model; and cell density is at most a fixed multiple of a^-d. Then N(t) is at most a constant times (vt/a)^d, and T is at least a constant times a N^(1/d)/v. + +**Proof.** By time t the causally influenced region is contained in a radius-vt neighbourhood of the initial seed. Its volume is O((vt)^d). Multiplying by the density bound gives the cell bound and inverting gives the time bound. QED. In continuous-time stochastic models, replace a strict propagation bound by an appropriate high-probability light-cone estimate; Brownian diffusion has unbounded mathematical tails and does not satisfy a hard microscopic speed cap in that approximation. + +Hence sustained exponential increase of densely packed completed volume cannot occur indefinitely from one seed with bounded local speed. Exponential replication describes an early dilute regime, multiple prepositioned seeds, or increasing occupied spatial volume. Hierarchical doubling has O(log N) levels, but level count is not elapsed time: the distances and material flows grow with level. + +For a cube of side L, density rho_m, and total boundary area A, mass conservation gives T >= rho_m L^3/(J A), if J is a bound on delivered mass flux per area. With A proportional to L^2 and constant J, this is proportional to L. If external diffusion through a path of order L sets J proportional to D c/L, the corresponding bound is proportional to L^2. Reaction-limited front growth at speed v gives T proportional to L/v. The applicable lower bound is the largest relevant one, not the most favourable. + +Distributed internal growth can reduce local diffusion time from L^2/D to ell^2/D, where ell is the maximum local reservoir distance. It can increase active reaction volume and permit many modules to differentiate concurrently. It cannot evade the time to distribute the program, establish the network, pump sufficient material through external ports, export waste, or remove heat. + +A useful general resource bound is + +$$ +T\geq\max\!\left(T_{\rm causal},\frac{M_{\rm product}}{\dot M_{\max}}, +T_{\rm dependency},\frac{Q_{\rm reject}}{P_{\rm cooling}},T_{\rm local\ transport}\right). +$$ + +Not every term has a universal numerical value. T_dependency includes computation and reaction prerequisites. Some tiny programs require enormous sequential computation; such targets are compression-friendly but fabrication-hostile. Efficient developmental families require both short descriptions and shallow executable dependency structure. + +Conventional lithography, templating, casting, and some additive techniques already perform many operations concurrently. The justified comparison is with serial explicit placement of all critical units, not with an invented universally serial model of manufacturing. A compressed growth program alone does not prove a time or cost advantage over existing parallel processes. + +## 19. Transport, flow, strain, and heat: numerical checks + +All numbers in this section are illustrative assumptions and dimensional calculations, not measured rates for a proposed chemistry. Take a=10 nm as a bookkeeping pitch. A dense cube then contains N=(L/a)^3 cells. Small solutes may be represented by an assumed D=10^-9 m^2/s and larger slow species by D=10^-11 m^2/s. Actual values depend strongly on molecule, solvent, confinement, and evolving porosity. + +| Side L | Cells at 10 nm pitch | L^2/D, D=10^-9 | L^2/D, D=10^-11 | L/v at v=1 nm/s | +|---|---:|---:|---:|---:| +| 100 nm | 10^3 | 10^-5 s | 10^-3 s | 100 s | +| 1 micrometre | 10^6 | 10^-3 s | 0.1 s | 1,000 s | +| 100 micrometres | 10^12 | 10 s | 1,000 s | 100,000 s | +| 1 millimetre | 10^15 | 1,000 s | 100,000 s | 1,000,000 s | +| 1 centimetre | 10^18 | 100,000 s | 10,000,000 s | 10,000,000 s | + +At 1 cm the slow-species diffusion estimate is about 116 days. A hypothetical front speed of 1 micrometre/s would instead give a 10,000-second front traversal, about 2.8 hours; no such net precision-preserving developmental growth speed is established here. A time forecast requires calibrated reactions and throughput as well as a chosen length scale. + +**Module scaling.** A 1-cm cube partitioned into 50-micrometre cubes has 200^3=8 million modules. If each module carries 1,000 temporary information bits, physical distributed memory is 8 billion bits even if the seed is small. A code argument with b=96 redundant units per million functional modules has 96 million subcomponents, not one million. With p=0.04, rho=0.20 and delta=0.05, the bound indeed gives b=96. No physical device with the required arbitrary-20%-fault tolerance is supplied. + +**Seed capacity example.** A two-bit-per-base upper limit implies at least 500 DNA bases to encode 1,000 target bits before coding constraints and redundancy. At an assumed overall code rate of one half this becomes at least 1,000 bases, or 1,000 base pairs for a duplex representation, with about 340 nm duplex contour length using 0.34 nm per base pair. Folding can reduce spatial extent but needs its own sequence, support, and reliability budget. This is an information and contour-length estimate, not a working 1,000-bit seed design. + +**Feedstock example.** A 1-cm^3 object of density 2,000 kg/m^3 has mass 2 g. An assumed 1 mol/L precursor carrying 100 g/mol of usable product supplies 100 kg/m^3. At 80% incorporation, at least 25 mL must pass through the process. A feed of 1 mL/min therefore imposes a 25-minute minimum. At 10 mM, the corresponding minimum volume is 2.5 L and the time is about 41.7 hours. Many chemistries cannot operate at 1 M; a convenient concentration is not a feasibility claim. + +**A vascular budget.** For an ideal straight circular water-like channel, Poiseuille flow gives + +$$ +Q=\frac{\pi r^4\Delta P}{8\eta L}. +$$ + +With r=10 micrometres, L=1 cm, viscosity 10^-3 Pa s, and pressure drop 10 kPa, Q is about 3.93 x 10^-12 m^3/s, or 0.236 microlitres/min. About 4,244 such channels would be required for 1 mL/min. Their cross-sectional fraction in a square centimetre is about 1.33%, before manifolds, walls, bends, fouling, and repairs. Their nominal spacing is about 154 micrometres; slow-species diffusion over half that distance still takes about 590 seconds. This calculation makes the infrastructure cost explicit. It does not prove the channels can grow themselves or remain open during deposition. + +**Thermal budget.** If 0.02 mol of product formation releases an assumed 100 kJ/mol, 2 kJ must be rejected. Over 25 minutes this is 1.33 W in a cubic centimetre. A uniformly heated slab of thickness 1 cm, held at fixed boundary temperature and with thermal conductivity 0.6 W/(m K), would have a centre rise q'''L^2/(8k), about 28 K. The 1-mL/min water feed alone has heat-capacity flow about 0.070 W/K, corresponding to roughly 19 K temperature rise at that heat load. These assumed values show why cooling must be independently budgeted. + +**Strain and drying.** Capillary pressure is approximately 2 gamma/r. For water-like surface tension 0.072 N/m and a 10-nm pore, this is about 14 MPa. A soft scaffold may collapse during drying even if its wet assembly is perfect. Solvent exchange, mechanically qualified support, or an appropriate drying route is required. A uniform fractional shrinkage s can be compensated geometrically; spatial variation in shrinkage creates interface errors and belongs in the conversion fault model. Repeated coating can also close a pore after a deposited thickness comparable to its radius. + +**Conditional exclusion.** Fixed external diffusion paths extending across an ever-larger dense object, no channels, fixed chemical rates, and rapid centimetre growth cannot all be assumed together. At least one of geometry, transport mechanism, processing time, or feature requirements must change. + +## 20. Nonequilibrium thermodynamics and energy accounting + +Chemical fuels and supersaturated feedstocks supply free energy; local assembly redistributes matter and exports entropy. In a locally detailed-balanced reaction description, forward/reverse rate ratios are tied to reaction free energies and reservoir chemical potentials. For reversible reaction channels with forward and reverse probability fluxes J_r^+ and J_r^-, the entropy-production rate has the form + +$$ +\dot S_{\rm tot}=k_B\sum_r(J_r^+-J_r^-)\ln\frac{J_r^+}{J_r^-}\geq0. +$$ + +The inequality follows termwise from monotonicity of the logarithm. State degeneracies and concentration factors must be included consistently in the fluxes. Nonequilibrium self-assembly bounds and driving-dependent structure are studied in [12]; this project does not replace those foundations. + +In a simple equilibrium two-state comparison with equal degeneracy, an energy preference DeltaE gives p=1/[1+exp(DeltaE/kBT)]. The required preference for p is kBT ln[(1-p)/p]. This is an illustrative selectivity relation, not a universal dissipated work per assembly decision. At n=10^12 critical independent final sites and delta=0.05, the target p is about 5.13 x 10^-14 and this preference is approximately 30.6 kBT. Real wrong-state multiplicity can increase the needed discrimination. + +For preparing a probability distribution p from equilibrium pi with the same Hamiltonian, the excess nonequilibrium free energy is kBT D_KL(p||pi). A reversible limiting work statement may be made only under the associated preparation assumptions. Erasing one unknown equiprobable degenerate bit has the familiar kBT ln 2 minimum in the standard ideal reset setting. Neither relation says that every correctly placed atom costs precisely one bit erasure or that physical complexity alone specifies energy expenditure. + +At 298 K, kBT is about 4.11 x 10^-21 J. Erasing 10^18 ideal bits would have a nominal floor of about 0.00285 J. Ten kBT per 10^18 model turnovers would be 0.0411 J. These are small compared with the illustrative 2-kJ chemistry budget above. Synthesis, pumping, failed assembly, thermal processing, purification, and waste are likely to dominate such informational lower bounds. + +The simulator reports a ten-kBT-per-event turnover proxy. It does not assign a consistent molecular Hamiltonian or calibrated fuel chemistry and therefore **does not measure physical energy efficiency**. Reagent conservation is tested separately. A future kinetic backend must impose local detailed balance or explicitly model the external driving that breaks equilibrium, and must measure the energy cost of unsuccessful proofreading cycles. + +## 21. Multiscale precision and quantitative leverage + +Expensive control should be concentrated at interfaces whose function depends on microscopic detail. Atoms in a bulk crystal, polymer, or cured structural fill are arranged by material physics; a controller need not command each one individually. Define f_atomic as the fraction of product atoms whose specified configuration requires independent atomically resolved control beyond that supplied by a validated prefabricated component or bulk process. Report the counting convention: using an atomically designed protein does not mean the factory independently positions every atom in it. + +For cubic modules of side ell with only an interface layer of thickness t requiring exceptional precision, the geometric fraction is approximately 6t/ell when t is much smaller than ell. With t=0.5 nm and ell=10 micrometres, it is about 3 x 10^-4. This does not automatically make manufacturing 3,333 times cheaper: the difficult interface process may dominate time and cost, and the interior still needs material flow. It shows why an all-atoms serial model can badly overstate the required active positioning workload. + +To define morphogenetic leverage, choose a declared explicit reference serialization B_ref(X,epsilon), such as a tolerance-matched labelled mesh. Let B_tar include all target-dependent seed, environment, schedule, and apparatus bits. Let B_platform be a versioned reusable description used for an actual batch of m products. Then report + +$$ +\Lambda_M(m)=\frac{B_{\rm ref}}{B_{\rm tar}+B_{\rm platform}/m}. +$$ + +This is a descriptive reuse ratio, not a thermodynamic efficiency or creation of algorithmic information. Report both m=1 and the justified production-batch value. Also report runtime copies, physical workspace, synthesis complexity, and feedstock manufacture. Comparing against a voxel file while ignoring a handwritten motif interpreter would overstate leverage. Conventional CAD and manufacturing programs can also be compressed; a fair comparison uses the same functional specification and tolerance. + +Define a physical compilation ratio only relative to resolution and observables: the number of independently specified output cells or interfaces divided by explicit target-control bits. Do not count thermal molecular coordinates as useful specified degrees of freedom. A compact generative description is advantageous on compressible families, but no asymptotic superiority holds for all targets by Theorem A2. + +Fabrication autonomy should be reported as a vector: human interventions per accepted object; target-dependent adaptive bits injected during growth; preprogrammed bath stages; externally supplied spatial pattern bits; and uninterrupted operating time at a declared success probability. An optional conventional design-autonomy score is B_seed/(B_seed+B_external,target). It distinguishes information supplied by the seed from outside information but ignores labour and energy, so it must not stand alone. A system that does nothing may be intervention-free; autonomy is scored only conditional on performing the specified fabrication task. + +## 22. Fabrication as communication through matter + +Let W be a uniformly selected target index from a declared family, encoded in the seed and all charged target-specific preparation. The physical channel produces X'. A decoder assigns an accepted target index from the measured output. If decoding error is at most delta, Fano's inequality requires approximately log2 |W| reliable target bits to reach the output. Independent thermal randomness cannot increase information about W. + +A fabrication capacity region consists of achievable tuples: log2 |W|, time, energy, mass consumed, apparatus size, and control bits, at specified geometry/function tolerances and error probability. A rate such as log2 |W|/T measures the number of independently selectable reliable designs per time. N/T measures physical instantiation rate. They are different: producing a billion identical cells can have large physical throughput and almost no new target-selection information. + +A binary symmetric subcomponent channel with independent error p has the familiar coding benchmark 1-h_2(p) reliable bits per channel use in its ideal unconstrained communication setting. It is not automatically attainable by local material codes: geometry, state-update rules, decoding energy, access, and conversion can invalidate the coding model. Theorem C1 gives a concrete restricted construction requirement instead of asserting that general channel capacity is physically attainable. + +The central development law can therefore be read as a noisy-channel statement with a state-dependent noise level. More physical encoding redundancy increases the number of channel uses, but can degrade their quality through transport depletion. This is the information-theoretic interpretation of the redundancy-access reversal. + +## 23. Implemented computational model and reproducibility + +The release includes a runnable Python package with six research components: a restricted genome evaluator and compiler; a conservative finite-volume transport update; seeded local growth with noisy differentiation and repair; an analytical reliability model; a fabrication-prerequisite DAG checker; and a passive conductance solver. The final target array is used for scoring only after each dynamical run. During growth, intended roles come from the genome evaluated on inherited counters. + +The lattice initially contains a uniform unit concentration, which is explicitly included in mass accounting. One corner seed initiates nearest-neighbour growth. A new site inherits a neighbour's counters and increments the appropriate directional counter. The genome bounds terminate growth; a test checks this inside a larger simulation vessel. Lattice orientation, discrete cell geometry, the common interpreter, and perfectly copied counters are idealized platform assumptions. An active physical backend would have to construct or justify them. + +A site passes through absent, reversible, and hardened states. Attachment consumes resource. Initial differentiation and subsequent damage can change the material label. A local check compares the observed label with its stored intended label; an effective repair reaction can restore it, with a declared repair-failure probability. A maturation deadline and minimum concentration control locking. Conversion then creates additional irreversible label errors. Hardened sites have reduced permeability. This is a coarse state model, not Brownian assembly trajectories or a validated kinetic tile model. The topological checker is tested separately; lattice locking uses dwell and concentration and does not execute the full event-DAG closure protocol. + +Finite-volume face fluxes use harmonic permeability and no-flux external faces, followed by imposed reservoir values. Positivity is protected by an explicit diffusion CFL condition; consumption cannot exceed local stock. Boundary reservoirs and regularly spaced internal feed planes are maintained external apparatus resources. Their site fractions and material input are recorded. They are not grown vascular networks, and the code does not establish that they can be maintained through one small physical inlet. + +The baseline covers a 32 x 32 two-role path device with an asymmetric void and a 16 x 16 x 16 braced, windowed shell with differentiated labels. Six conditions are run eight times each: reference, no repair, early lock, no internal feed planes, shared-reference corruption, and increased conversion damage. The shared-reference corruption changes a site's intended label and its initial label together. It demonstrates checker blindness to a wrong local reference; it is **not** a spatially correlated burst or a corrupted genome spreading through an entire lineage. + +The passive-function calculation solves a scalar resistor network with role conductivities 1, 10^-4, and 10^-7, and an absent-site value 10^-8, in arbitrary common units. A unit voltage is applied across opposite faces. Success requires conductance within 10% of the ideal target. These contrasts are declared numerical parameters, not measured material properties. The 3-D example is scored structurally and compositionally; no 3-D device-function claim is made. + +The ideal binomial theorem benchmark is separate from this coupled lattice simulation. In the lattice, shared concentration histories, stored-reference faults, and geometry-dependent bottlenecks can violate the independent-noise or arbitrary-fault-tolerance assumptions. In particular, the path device does not satisfy the theorem's hypothetical 20%-arbitrary-defect tolerance. It would be incorrect to use its visual fidelity as evidence for that assumption. + +Reproduce the results from the release root: + +```text +python -m pip install -r requirements.txt +python -m unittest discover -s tests -v +python src/run_experiments.py --reps 8 +python src/transport_stress.py +python src/make_figures.py +python src/build_pdf.py +``` + +Full per-run data, seeds, configuration values, arrays for representative runs, numerical summaries, and environment versions are included. The nine research checks cover mass conservation and positivity, exact irregular-target reconstruction, noise-free growth and inherited counters, seed termination, irreversible error floors, probability bounds, closure cycles, the known conductance of a uniform slab, and reference corruption. Passing these checks does not validate chemistry or independently certify the mathematical proofs. + +## 24. Results, including failures + +The default experiments all finished their finite scaffold. Mean material fidelities and standard deviations across eight runs were: + +| Condition | 2-D fidelity | 3-D fidelity | 2-D functional passes | +|---|---:|---:|---:| +| Reference | 0.9586 +/- 0.0061 | 0.9628 +/- 0.0023 | 2/8 | +| No repair | 0.8257 +/- 0.0178 | 0.8213 +/- 0.0034 | 0/8 | +| Early lock | 0.8840 +/- 0.0106 | 0.8829 +/- 0.0064 | 0/8 | +| No internal feed planes | 0.9529 +/- 0.0049 | 0.9599 +/- 0.0018 | 0/8 | +| Shared-reference corruption | 0.8871 +/- 0.0139 | 0.8849 +/- 0.0057 | 0/8 | +| Increased conversion damage | 0.8704 +/- 0.0047 | 0.8817 +/- 0.0043 | 0/8 | + +The reference 2-D mean relative conductance error was about 15.5%, versus 76.6% without repair. These are model outcomes, not device yields. Eight replicates permit only coarse yield estimation. The function threshold was specified in the experiment runner; it was not relaxed to turn a mostly failed benchmark into a success. + +The initial default runs showed only a small effect from removing internal feed planes because a substantial initial reagent inventory and short repair interval could sustain development. They do not establish a strong transport advantage. A declared follow-up stress test increased the repair dwell to eight time units and maintenance demand to 0.25, with a 300-time-unit deadline, keeping the same geometry. Four runs per condition were performed. Completion with internal feed planes was about 48-53%; with boundary supply alone it was about 20-21%. Both failed to finish. Thus internal access helped under depletion but did not overcome the interaction of demand, permeability loss, and local maturation. + +The maximal reagent-balance residual in the default runs was below 4 x 10^-12 normalized units. This numerical conservation result is useful but says nothing about missing chemical pathways or physical energies. + +The two selected motif capsules were 27 and 28 UTF-8 bytes, compared with 1,024 and 4,096 raw one-byte cells. This is a conditional reuse demonstration: the handwritten motif implementations and generic runtime are included in the platform and must be charged for a single-target comparison. The compiler also exactly reconstructed a random irregular array through its subdivision fallback. It did not compress arbitrary data or infer either motif from first principles. + +For the isolated binomial calculation at p=0.08 and rho=0.20, exact module-failure probabilities for b=10, 20, 40, 80, and 160 are about 0.18788, 0.07062, 0.012687, 0.0005351, and 0.000001276. Monte Carlo used 200,000 trials at each b. At b=160 only two failures were sampled; that rare-event estimate is imprecise and must not replace the exact tail. The supplied figure displays exact binomial confidence intervals. No Monte Carlo result here validates the extremely small failure probabilities appearing in large-system bound extrapolations. + +![Conditional reliability exponent and depletion limit](../figures/reliability_access.png) + +Figure 1. Model-derived reliability exponent as redundant volume grows, with and without maintained local supply. The finite maximum in the depleted case is the redundancy-access reversal. The curve is not a measured chemical phase diagram. + +![Growth targets and representative output](../figures/growth_snapshots.png) + +Figure 2. Target, reference output, and no-repair output for the 2-D device and a central slice of the 3-D shell. Void, support, and recruited-phase labels are numerical roles. Sites are not individual atoms. + +![Ablation results](../figures/ablation_results.png) + +Figure 3. Mean material fidelity with between-run standard deviation. The adjacent function panel shows the stricter passive-device criterion; improved material fidelity does not establish robust functional manufacture. + +![Transport stress results](../figures/transport_stress.png) + +Figure 4. The follow-up depletion stress experiment. Both conditions stall before full completion. The internal reservoirs are externally maintained feed planes in the model, not autonomous vasculature. + +![Binomial probability check](../figures/binomial_check.png) + +Figure 5. Exact binomial tail, conservative analytical bound, and independent Monte Carlo estimates with exact two-sided 95% binomial confidence intervals. The rarest point is poorly resolved. + +## 25. Minimal decisive experiment + +**The smallest decisive first experiment is a seeded, two-role molecular ribbon or small sheet with reversible mismatch rejection and a controllable locking step, measured before and after material recruitment.** It tests whether extending real repair access lowers final error as predicted, and whether conversion creates the forecast error floor. It does not by itself validate the long-distance transport reversal or universal fabrication. + +Use one fixed small tile/strand library and at least two seeds that specify different nonperiodic role patterns. Start with tens of logical sites, or the smallest architecture the collaborating laboratory can validate, and a few redundancy levels. An initially wrong attachment must expose a genuine locally detectable mismatch; the correct state must permit a distinct recruitment handle. Develop and characterize this elementary gate before attempting many-site growth. The molecular design and sequence set are not supplied by this report and are an explicit experimental prerequisite. + +Use a benign optical role assay first, such as matched donor/acceptor or tagged nanoparticle recruitment whose useful response depends on the intended role relationship. A later matched cohort can test one independently validated inorganic stabilization pathway. A reporter that disappears during conversion is insufficient evidence for post-conversion structure; use an appropriate structural/compositional readout on that cohort. Do not infer preserved material identity from pre-conversion fluorescence alone. + +The primary measurements are initial error p_0, effective correct-to-wrong and wrong-to-correct rates, concentration dependence, post-lock error, cross-talk between role tags, spontaneous unseeded growth, and correlations along and across lineages. Vary the available repair interval and the locking time independently of total incubation time. Fit rates on one set of assemblies and predict final error on held-out assemblies and seed programs. + +Essential comparison groups are: correct seed and active checker; scrambled seed or absent seed; checker-disabled but otherwise matched chemistry; repair-fuel omission where the mechanism requires fuel; early versus delayed locking; and a controlled damage challenge after the last repair-accessible step. Controls should match concentrations, reporter loading, maturation exposure, and purification. Counting only purified intact assemblies would hide the manufacturing yield loss. + +A practical first analysis plan is three independent preparation batches and at least 100 scored assemblies per condition, with the required number revised from pilot effect sizes and within-assembly correlation. This is not enough to certify ultra-low failure rates. With zero observed independent failures in n trials, the exact one-sided 95% upper bound is 1-0.05^(1/n), approximately 3/n. Proving a probability below 10^-6 by zero-failure counting alone requires about three million independent trials. + +**Support:** a checker-specific reduction in held-out post-recruitment errors with sufficient open time, plus an independently measured post-lock floor consistent with the final-channel model. **Falsification of applicability:** no selective repair, a reporter unrelated to actual errors, persistent correlated failures dominating the risk, or a locking/conversion process that destroys the role pattern. Such observations would reject the proposed substrate's premises, not the elementary probability algebra. + +**Smallest extension testing the distinctive access reversal:** use modules with several redundant sizes, measure effective repair rate versus module size, and compare equal-consumption constructs with fixed external access against constructs whose local supply distance is held approximately constant. At nanometre scales, depletion may be negligible. A separate 50-200-micrometre porous confinement or supply geometry may be needed to resolve transport effects. That length range is a proposed experimental design scale, not a measured onset. Direct concentration and flow measurements are necessary to exclude steric crowding, changed hybridization kinetics, or different material-loading density as alternative explanations. + +## 26. Implementation ladder and benchmark gates + +Each stage advances only after its input assumptions are demonstrated. Relative resource levels below assume access to relevant laboratory infrastructure; they are not currency quotations or promises about project duration. + +| Stage | Work and deliverable | Relative resources | Go/no-go evidence | +|---|---|---|---| +| 1: simulation | Reproduce this model; add calibrated kinetic and correlation data | Low compute; scientific modelling effort | Mass, causality, and held-out prediction checks | +| 2: DNA-like substrate | Two seeded role programs and one real local error-rejection gate | Moderate synthesis and microscopy | Gate selectivity, seed dependence, error statistics | +| 3: hybrid modules | Add one validated nanoparticle or protein interface | Moderate to high characterization | Role specificity and assembly compatibility | +| 4: transduction | Convert one scaffold to one stable useful phase | High materials/process effort | Before/after structure, composition, and defect map | +| 5: function | Nonperiodic optical or passive electrical module | High integration and metrology | Predeclared functional performance across batches | +| 6: larger porous assembly | Demonstrate distributed supply and late closure at increasing size | Very high fluidic/mechanical integration | Flux, heat, stress, and size-dependent yield | +| 7: restricted platform | Compile a family of materially compatible devices | Programme-scale effort | Held-out targets and honest total-resource advantage | + +The scientific value per early experiment is highest for the local checking gate, conversion-error measurement, and a size-by-access factorial test. They can kill the architecture cheaply compared with attempting a centimetre device. Fancy 3-D shapes have lower information value if they do not distinguish the proposed mechanism from ordinary templating. + +| Benchmark level | Target class | Prospective quantitative acceptance criterion | +|---|---|---| +| 0 | Periodic lattice | At least 95% declared occupancy; characterize correlated domains | +| 1 | Nonperiodic 3-D geometry | At least 95% occupancy IoU at specified resolution; seed swaps change target | +| 2 | Internal differentiation | At least 95% role fidelity including concealed interior locations | +| 3 | Multimaterial passive device | Compatible phases and interfaces; at least 90% of preregistered function | +| 4 | Optical or mechanical function | Frequency/response within 10% of predicted value over multiple batches | +| 5 | Electrical device | Conductance or response within 10%; isolation and contact criteria also met | +| 6 | Integrated sensor/actuator | Calibrated transfer curve and repeated controlled cycles | +| 7 | Multiple subsystems | End-to-end task success above a predeclared threshold with all interfaces tested | + +These thresholds are suggested research gates, not universal standards and not claims achieved by this release. Some applications require far tighter tolerances. The supplied structural demonstrations and numerical passive circuit do not constitute experimental completion of these levels. + +## 27. Failure modes and discriminating observations + +| Major claim or hypothesis | Supporting observation | Failure or falsifying observation | Scale and alternative explanation | +|---|---|---|---| +| Seed selects a nonperiodic target | Held-out seed changes output with same bath/library | Output follows an external template or is seed-independent | Micrometre assemblies; exclude seed-independent nucleation | +| Local checking improves correctness | Measured wrong-state removal exceeds matched controls | Reporter changes without actual repair | Single gate to tens of sites; exclude selection/purification bias | +| Reliability-access window applies | Calibrated rates predict held-out final yield | Unmodelled correlated errors dominate | Size series; exclude independent-error fitting to correlated data | +| Redundancy-access reversal occurs | Added size lowers repair rate; renewed access restores exponent | Reliability remains monotone because depletion is negligible | Larger modules or porous confinement; exclude steric effects | +| Conversion errors matter | New defects appear after last accessible repair | No measurable conversion damage at assay sensitivity | Matched before/after cohorts; exclude imaging-induced damage | +| Material roles survive conversion | Registered composition and useful response retained | Cross-talk, shrinkage, bridging, or loss of phase quality | Nanometre interfaces; exclude label-only readout | +| Closure protocol preserves service | Every pending region retains measured supply and waste path | A closed neck traps incomplete material | Micrometre to millimetre channels; exclude static-distance proxies | +| Function follows the genome | Seed-selected device transfer function is reproduced | High shape fidelity with failed device function | Passive nanosensor or circuit; exclude external wiring as sole function | +| Maintenance is possible | Controlled damage is restored under a retained program | Controller lost during cure, or repair creates new failures | Repeated cycles; exclude replacement of the whole object | +| Claimed compression is real | Total charged description beats fair baseline across a family | Complexity moved into unique parts or bath patterns | Increasing family sizes; count interpreter and synthesis metadata | + +Additional hard failure modes include kinetic traps, malformed component species, aggregation without a seed, poisoning of catalytic surfaces, lack of independent redundancy, depletion of a minor reagent, manifold clogging, delamination during drying, controller degradation, and slow removal of deeply buried scaffold. Some of these invalidate entire classes of proposed objects. The compiler should return such failures as explicit unsupported-process or unavailable-access outcomes. + +## 28. Repair after fabrication and the role of biology + +A manufacturing program doubles as a maintenance program only if a sufficient local reference survives, damaged states remain distinguishable from legitimate states, repair reagents can reach them, and replacement does not destroy adjacent function. A fully mineralized object whose DNA reference has been burned away does not retain molecular self-repair merely because DNA helped fabricate it. + +Three credible routes are: retain protected low-temperature reference layers; keep replaceable modules with durable port identities; or preserve ordinary service channels for externally supplied repair chemistry and control. Each trades some autonomy or material performance for repairability. A high-temperature monolithic object may have no compatible option. The maintenance problem must be specified separately for that material class. + +Biology demonstrates that local interactions can distribute compressed hereditary instructions, establish differentiated structures, maintain supply networks, and repair many errors. It does not demonstrate arbitrary material synthesis or arbitrary human-selected geometries, nor atomically perfect organisms. Biological growth times, wet chemistry, available elements, mechanical properties, and evolutionary objectives differ from engineering requirements. + +The useful abstraction is an acellular developmental manufacturing process with a bounded inventory and contained reactor. Replication-like copying of local program state or bounded module production does not require unrestricted reproduction. The proposed roadmap does not rely on evolving or releasing autonomous organisms. + +## 29. What would be needed from 100 nm to 1 cm + +At approximately 100 nm, focus on one local checking gate, reliable role recruitment, and a single conversion-compatible structural unit. At about 1 micrometre, establish seeded nonperiodic patterns, error correlations, and a weak but measurable function. Moving to 100 micrometres changes the dominant questions: transport, accumulated strain, defect domains, and compatibility between modules become difficult even though no atom-by-atom placement is required. + +At 1 mm, a successful system needs engineered distributed supply, waste exit, thermal management, measured effective controller error rates, and interfaces that tolerate dimensional variation. At 1 cm, those systems must handle millions of modules or extremely high unit counts with controlled common-mode failure and material conversion that preserves useful properties. Standardized ports and prefabricated critical components become more plausible than universal in-situ chemistry. + +The shortest credible route is therefore **small validated molecular logic, followed by a limited material process, followed by a modular function, followed by transport-enabled scale-up**. Choosing a family whose useful function tolerates distributed microscopic defects is much more credible than starting with atomically perfect dense electronics. This is an engineering restriction with information-theoretic and reliability benefits, not an assertion that arbitrary matter becomes easy. + +## 30. Research programme at 1, 3, 5, 10, and 20 years + +These are contingent milestones measured from project start, not forecasts that the technology will be available on these dates. + +| Horizon | Realistic research target if preceding gates succeed | Ambitious conditional extension | Stop or redirect when | +|---|---|---|---| +| 1 year | Calibrated local check-and-lock gate, two seed programs, reproducible error model | First role-selective recruitment with held-out prediction | No useful local selectivity or controller stability | +| 3 years | Repeated differentiated modules and one qualified transduction process | Direct test of redundancy/access coupling | Conversion faults dominate all tolerated designs | +| 5 years | Restricted functional optical/passive module family | Autonomous local closure in a small porous assembly | Cross-talk and correlated process failures resist mitigation | +| 10 years | Integrated prototype with measured transport, strain, and yield scaling | Sub-millimetre to millimetre developmental fabrication in one material family | No favourable total-cost or throughput comparison | +| 20 years | Potential restricted manufacturing platform with reusable seed/compiler interface | Centimetre heterogeneous modules assembled from validated parts | General-purpose chemistry remains inaccessible or conventional manufacture dominates | + +An arbitrary universal nanofabricator is a long-term speculative extension, not a 20-year commitment. Many early results would still be useful if that extension never becomes feasible: better local defect assays, error-aware material conversion, transport-aware self-assembly, and compilers that expose unsupported chemistry. + +## 31. Ranked unresolved barriers + +1. **Faults after the final repairable state.** Demonstrate a real material process with a bounded final fault channel and useful functional tolerance or post-conversion repair. +2. **Reliable local references.** Protect seed, lineage, and role state against common faults without assuming an ideal target oracle. +3. **Correlation and functional coding.** Establish a local error law and a device-specific tolerated defect set; independent site models are inadequate by themselves. +4. **Transport and late closure.** Grow or install a scalable network whose concentration, flow, permeability, and waste removal are measured through conversion. +5. **A practical molecular compiler.** Lower a modest useful grammar into sequence-validated, reusable operations with bounded leak and acceptable speed. +6. **Mechanical preservation.** Control drying, densification, stress, and interface placement over successive scales. +7. **Fair resource advantage.** Compare total descriptions, synthesis effort, bath processing, throughput, yield, energy, and apparatus against existing manufacturing. + +The most consequential missing experiment is not a complicated shape. It is a substrate on which independent calibration of checking, access, and conversion predicts a nontrivial useful final function on a new seed program. + +## 32. Adversarial audit and claim boundary + +The global design is stored in the seed, motif interpreter, qualified component library, and every target-specific external condition. All are supplied or identified. The simulator's short JSON capsules rely on handwritten motif code and an ideal local interpreter. Finite chemical alphabet universality is conditional; a molecular backend and a minimal practical species count remain unknown. + +Error accumulation is handled only under explicit local fault and functional-tolerance contracts. The last-operation theorem prevents pretending that pre-conversion proofreading establishes final perfection. The shared-reference ablation demonstrates one checker blind spot but does not cover all spatial correlations. The actual circuit benchmark mostly fails its function criterion. Those limitations are retained in the reported results. + +Diffusion, mass flux, heat, pressure, shrinkage, and interior closure are explicit parts of the framework. Internal reservoirs in the simulator are supplied by an idealized external apparatus, so the simulations do not establish autonomous vascular growth. The stress experiment shows that the chosen access geometry still fails to finish under stronger demand. + +Heterogeneous material formation uses qualified recruitment and conversion, not element transformation or arbitrary semiconductor chemistry. Bulk precision requirements can be reduced by modular design, but critical interfaces remain difficult. Growth concurrency improves plausible scaling only when instructions, reaction fronts, material flow, and cooling all support it. + +The strongest defensible original result is the **conditional redundancy-access reversal and its associated compiler feasibility window**. It is a derivation built from established models. Expert confidence would require independent proof review, a more comprehensive prior-art comparison, calibrated correlated-noise simulations, and the decisive checking/locking experiment. The result should not be advertised as demonstrated universal manufacture or a verified major breakthrough. + +## References + +[1] D. Soloveichik and E. Winfree. Complexity of Self-Assembled Shapes. SIAM Journal on Computing 36, 1544-1569 (2007). DOI: 10.1137/S0097539704446712. Accessible manuscript: https://arxiv.org/abs/cs/0412096 + +[2] D. Doty, J. H. Lutz, M. J. Patitz, R. T. Schweller, S. M. Summers, and D. Woods. The tile assembly model is intrinsically universal. FOCS (2012). Accessible manuscript: https://arxiv.org/abs/1111.3097 + +[3] E. Winfree and R. Bekbolatov. Proofreading Tile Sets: Error Correction for Algorithmic Self-Assembly. DNA Computing, LNCS 2943, 126-144 (2004; conference 2003). https://doi.org/10.1007/978-3-540-24628-2_13 + +[4] D. Woods, D. Doty, C. Myhrvold, J. Hui, F. Zhou, P. Yin, and E. Winfree. Diverse and robust molecular algorithms using reprogrammable DNA self-assembly. Nature 567, 366-372 (2019). https://www.nature.com/articles/s41586-019-1014-9 + +[5] T. Gomez, E. Grizzell, A. Haun, R. Knobel, T. Peters, R. Schweller, and T. Wylie. Intrinsic Universality in Seeded Active Tile Self-Assembly. arXiv:2407.11545 (2024); brief announcement, SAND 2025, DOI: 10.4230/LIPIcs.SAND.2025.24. https://arxiv.org/abs/2407.11545 + +[6] M. Holmes-Cerfon and M. Wyart. Hierarchical self-assembly for high-yield addressable complexity at fixed conditions. arXiv:2501.02611 (2025). https://arxiv.org/abs/2501.02611 + +[7] F. Benoist and P. Sartori. Assembly Factors Resolve Speed and Encoding Bottlenecks in Multifarious Self-Assembly. PRX Life 4, 033021 (2026). https://journals.aps.org/prxlife/abstract/10.1103/5w6h-l93l + +[8] A. Michelson et al. Three-dimensional nanoscale metal, metal oxide, and semiconductor frameworks through DNA-programmable assembly and templating. Science Advances 10, eadl0604 (2024). DOI: 10.1126/sciadv.adl0604. Author-laboratory hosted first page: https://www.bnl.gov/tcp/uploads/files/2024-006j-pg1.pdf + +[9] A. Michelson et al. Scalable fabrication of Chip-integrated 3D-nanostructured electronic devices via DNA-programmable assembly. Science Advances 11, eadt5620 (2025). https://doi.org/10.1126/sciadv.adt5620 + +[10] Brookhaven National Laboratory, Center for Functional Nanomaterials. Scalable Device Fabrication using DNA Self-Assembly. Research highlight, 22 July 2025. Author-laboratory account of [9]: https://www.bnl.gov/cfn/research/highlights/news.php?a=222678 + +[11] F. Teng et al. Macroscale-area patterning of three-dimensional DNA-programmable frameworks. Nature Communications 16, 3238 (2025). https://www.nature.com/articles/s41467-025-58422-0 + +[12] M. Nguyen and S. Vaikuntanathan. Design principles for nonequilibrium self-assembly. Proceedings of the National Academy of Sciences 113, 14231-14236 (2016). https://doi.org/10.1073/pnas.1609983113 + +## Final assessment + +The following percentages are subjective evidence-maturity estimates, rounded to five percentage points. They are not experimental measurements, probabilities of success, peer-review scores, or a percentage solution of unrestricted universal nanofabrication. The subject is the bounded theory and proposed implementation programme developed here. + +**Status:** rigorous theoretical framework. + +**Scientific completeness:** 35%. Core hypotheses, falsifiers, and limiting models are specified; calibrated multi-physics evidence and validated material functions are missing. + +**Mathematical completeness:** 60%. Restricted stated propositions have proofs; realistic correlated-noise thresholds, molecular local compilation, arbitrary-device tolerance, and efficient physical universality remain unresolved. + +**Experimental readiness:** 20%. There is a staged decisive experiment and reproducible simulation, but no sequence-level implementation, calibrated reaction network, or new laboratory data. + +**Physical plausibility:** 55%. Several component mechanisms have primary experimental precedents; their integrated, self-correcting, multimaterial operation remains unverified, especially through hardening and scale-up. + +**Potential impact if validated:** 90%. This is a conditional impact judgement for a successful generalization across useful material families, not an estimate of validation probability or present novelty. + +**Most important unresolved obstacle:** preserving a trustworthy repair mechanism, or a validated fault-tolerant function, through irreversible material conversion. + +**Single most decisive next experiment:** measure held-out post-recruitment error in the same seeded two-role assembly while independently varying local checking and the available repair interval before locking. + +**Single most important new theoretical result:** the conditional redundancy-access reversal: redundant volume can reduce the reliability exponent when it increases diffusion-limited depletion, while maintained local access restores the logarithmic redundancy guarantee under the stated noise and functional-tolerance assumptions. diff --git a/baseline_v1/requirements.txt b/baseline_v1/requirements.txt new file mode 100644 index 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22 + ], + [ + "Figure 2.", + 23 + ], + [ + "Figure 3.", + 23 + ], + [ + "Figure 4.", + 24 + ], + [ + "Figure 5.", + 24 + ], + [ + "31. Ranked", + 29 + ], + [ + "Final assessment", + 32 + ] + ], + "author_verified": true, + "visual_review": "All 32 final page renders visually inspected in contact sheets; title inspected at page scale. No clipping or broken equations observed.", + "visual_review_completed": true +} \ No newline at end of file diff --git a/baseline_v1/results/run_log.txt b/baseline_v1/results/run_log.txt new file mode 100644 index 0000000000000000000000000000000000000000..7606a4e77ed3baf29d8dbcbc1545b08f84a616c7 --- /dev/null +++ b/baseline_v1/results/run_log.txt @@ -0,0 +1,107 @@ +2 reference fidelity 0.9586 complete 1.0 +2 no_repair fidelity 0.8257 complete 1.0 +2 early_lock fidelity 0.884 complete 1.0 +2 no_internal_supply fidelity 0.9529 complete 1.0 +2 common_mode fidelity 0.8871 complete 1.0 +2 conversion_damage fidelity 0.8704 complete 1.0 +3 reference fidelity 0.9628 complete 1.0 +3 no_repair fidelity 0.8213 complete 1.0 +3 early_lock fidelity 0.8829 complete 1.0 +3 no_internal_supply fidelity 0.9599 complete 1.0 +3 common_mode fidelity 0.8849 complete 1.0 +3 conversion_damage fidelity 0.8817 complete 1.0 +{ + "genomes": [ + { + "dim": 2, + "program_bytes": 27, + "raw_uint8_bytes": 1024, + 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100644 index 0000000000000000000000000000000000000000..8b2754ffb24be99eec2459df5a506b2ea586cc37 --- /dev/null +++ b/baseline_v1/results/snapshot_3d_reference.npz @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:7474dae17187a600f20e2f35d2287dbde4cb54b18f0d3cf35f823f2a5a160849 +size 26471 diff --git a/baseline_v1/results/test_log.txt b/baseline_v1/results/test_log.txt new file mode 100644 index 0000000000000000000000000000000000000000..b0621ce7738b93f106a52960cce9d025b5167e00 --- /dev/null +++ b/baseline_v1/results/test_log.txt @@ -0,0 +1,14 @@ +test_bound_controls_actual_tail (test_models.ModelChecks.test_bound_controls_actual_tail) ... ok +test_closed_transport_mass_and_positive (test_models.ModelChecks.test_closed_transport_mass_and_positive) ... ok +test_closure_cycle_detected (test_models.ModelChecks.test_closure_cycle_detected) ... ok +test_common_mode_is_not_corrected_by_local_spec (test_models.ModelChecks.test_common_mode_is_not_corrected_by_local_spec) ... ok +test_last_operation_floor (test_models.ModelChecks.test_last_operation_floor) ... ok +test_noiseless_growth_and_local_counter_inheritance (test_models.ModelChecks.test_noiseless_growth_and_local_counter_inheritance) ... ok +test_nonperiodic_compilation_exact (test_models.ModelChecks.test_nonperiodic_compilation_exact) ... ok +test_resistor_known_uniform_slab (test_models.ModelChecks.test_resistor_known_uniform_slab) ... ok +test_seed_stops_inside_larger_vessel (test_models.ModelChecks.test_seed_stops_inside_larger_vessel) ... ok + +---------------------------------------------------------------------- +Ran 9 tests in 0.071s + +OK diff --git a/baseline_v1/results/transport_log.txt b/baseline_v1/results/transport_log.txt new file mode 100644 index 0000000000000000000000000000000000000000..42a5215a0baf65d004e7a5fec43caf5e28aefbd4 --- /dev/null +++ b/baseline_v1/results/transport_log.txt @@ -0,0 +1,2 @@ +5 [(0.528, 0.504, 300.0), (0.518, 0.49, 300.0), (0.484, 0.458, 300.0), (0.529, 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+ ], + [ + 297.0, + 1023, + 211, + 0.0, + 133 + ], + [ + 298.0, + 1023, + 211, + 0.0, + 133 + ], + [ + 299.0, + 1023, + 211, + 0.0, + 133 + ] + ] + } +] \ No newline at end of file diff --git a/baseline_v1/src/build_pdf.py b/baseline_v1/src/build_pdf.py new file mode 100644 index 0000000000000000000000000000000000000000..12faaf335e81230089f1318ba510f385ccabc4c2 --- /dev/null +++ b/baseline_v1/src/build_pdf.py @@ -0,0 +1,149 @@ +"""Render the standalone manuscript with ReportLab; equations are typeset math images. +The Markdown source is the searchable, machine-readable equation source. +""" +from pathlib import Path +import re,html,textwrap,hashlib +from io import BytesIO +import matplotlib +matplotlib.use('Agg') +from matplotlib.mathtext import math_to_image +from matplotlib.font_manager import FontProperties +from PIL import Image as PILImage +from reportlab.pdfgen import canvas +from reportlab.platypus import SimpleDocTemplate,Paragraph,Spacer,PageBreak,Image,Table,TableStyle,Preformatted,KeepTogether +from reportlab.lib import colors +from reportlab.lib.styles import ParagraphStyle +from reportlab.pdfbase import pdfmetrics +from reportlab.pdfbase.ttfonts import TTFont +from reportlab.lib.enums import TA_CENTER,TA_LEFT +from reportlab.lib.pagesizes import A4 + +ROOT=Path(__file__).resolve().parents[1] +import matplotlib as mpl +FONTROOT=Path(mpl.get_data_path())/'fonts/ttf' +for name,filename in [('Body','DejaVuSerif.ttf'),('BodyBold','DejaVuSerif-Bold.ttf'), + ('BodyItalic','DejaVuSerif-Italic.ttf'),('Sans','DejaVuSans.ttf'),('SansBold','DejaVuSans-Bold.ttf'),('Mono','DejaVuSansMono.ttf')]: + pdfmetrics.registerFont(TTFont(name,str(FONTROOT/filename))) +pdfmetrics.registerFontFamily('Body',normal='Body',bold='BodyBold',italic='BodyItalic',boldItalic='BodyBold') +pdfmetrics.registerFontFamily('Sans',normal='Sans',bold='SansBold',italic='Sans',boldItalic='SansBold') +ink=colors.HexColor('#203044');blue=colors.HexColor('#17647F');muted=colors.HexColor('#647386') +W,H=A4;M=47;CW=W-2*M +styles={ + 'body':ParagraphStyle('body',fontName='Body',fontSize=9.6,leading=13.9,spaceAfter=7.5,textColor=ink), + 'title':ParagraphStyle('title',fontName='SansBold',fontSize=29,leading=34,spaceAfter=16,textColor=ink), + 'subtitle':ParagraphStyle('subtitle',fontName='Sans',fontSize=15,leading=21,spaceAfter=18,textColor=blue), + 'h2':ParagraphStyle('h2',fontName='SansBold',fontSize=14,leading=18,spaceBefore=16,spaceAfter=9,textColor=blue,keepWithNext=True), + 'h3':ParagraphStyle('h3',fontName='SansBold',fontSize=11,leading=15,spaceBefore=12,spaceAfter=7,textColor=ink,keepWithNext=True), + 'cell':ParagraphStyle('cell',fontName='Sans',fontSize=8.1,leading=11.2,textColor=ink), + 'thead':ParagraphStyle('thead',fontName='SansBold',fontSize=8,leading=11,textColor=colors.white), + 'caption':ParagraphStyle('caption',fontName='Sans',fontSize=8.3,leading=11.6,spaceAfter=12,textColor=muted), + 'code':ParagraphStyle('code',fontName='Mono',fontSize=7.2,leading=10,spaceBefore=5,spaceAfter=10,textColor=ink), + 'ref':ParagraphStyle('ref',fontName='Body',fontSize=8.1,leading=11.6,spaceAfter=8,textColor=ink,splitLongWords=True) +} + +for style in styles.values(): + style.allowWidows=0 + style.allowOrphans=0 + +def fmt(s): + stash=[] + def save(x): + stash.append(x);return f'ZZTOKEN{len(stash)-1}ZZ' + s=re.sub(r'\[([^\]]+)\]\((https?://[^)]+)\)',lambda m:save(''+html.escape(m[1])+''),s) + s=re.sub(r'https?://[^\s<>]+',lambda m:save(''+html.escape(m[0])+''),s) + s=html.escape(s) + s=re.sub(r'\*\*(.+?)\*\*',r'\1',s) + s=re.sub(r'`([^`]+)`',r'\1',s) + for i,x in enumerate(stash):s=s.replace(f'ZZTOKEN{i}ZZ',x) + return s + +class Doc(SimpleDocTemplate): + def afterFlowable(self,flowable): + if isinstance(flowable,Paragraph) and flowable.style.name=='h2': + t=flowable.getPlainText();k='sec'+hashlib.sha256(t.encode()).hexdigest()[:12] + self.canv.bookmarkPage(k);self.canv.addOutlineEntry(t,k,0,False) + +def footer(c,doc): + c.saveState();c.setStrokeColor(colors.HexColor('#CED9E0'));c.setLineWidth(.5) + c.line(M,H-35,W-M,H-35) + c.setFillColor(muted);c.setFont('Sans',7.2) + c.drawString(M,H-25,'MATTER EMBRYOGENESIS / THEORETICAL RESEARCH') + c.drawString(M,27,'v1.0.0 | 19 September 2026 | No new laboratory data') + c.drawRightString(W-M,27,str(doc.page));c.restoreState() + +def build(): + text=(ROOT/'manuscript/Matter_Embryogenesis.md').read_text();lines=text.splitlines();story=[];i=0;firstsub=True;inrefs=False + mathcache=ROOT/'manuscript'/'math_assets';mathcache.mkdir(exist_ok=True) + while iEMBRYOGENESIS',styles['title'])];i+=1;continue + if s.startswith('## '): + heading=s[3:] + if firstsub:story.append(Paragraph(fmt(heading),styles['subtitle']));firstsub=False + else: + if heading.startswith('1. Central') or heading=='Final assessment':story.append(PageBreak()) + story.append(Paragraph(fmt(heading),styles['h2'])) + inrefs=(heading=='References') or (inrefs and heading!='Final assessment');i+=1;continue + if s.startswith('### '):story.append(Paragraph(fmt(s[4:]),styles['h3']));i+=1;continue + if s=='$$': + arr=[];i+=1 + while i95:code.extend(textwrap.wrap(x,width=95,subsequent_indent=' ',replace_whitespace=False)) + else:code.append(x) + i+=1 + story.append(KeepTogether([Preformatted('\n'.join(code),styles['code'])]));i+=1;continue + if s.startswith('|'): + rows=[] + while i=6 else None) + tbl.setStyle(TableStyle([('BACKGROUND',(0,0),(-1,0),blue),('VALIGN',(0,0),(-1,-1),'TOP'), + ('LEFTPADDING',(0,0),(-1,-1),7),('RIGHTPADDING',(0,0),(-1,-1),7), + ('TOPPADDING',(0,0),(-1,-1),7),('BOTTOMPADDING',(0,0),(-1,-1),7), + ('ROWBACKGROUNDS',(0,1),(-1,-1),[colors.HexColor('#F0F4F6'),colors.white]), + ('LINEBELOW',(0,0),(-1,-1),.25,colors.HexColor('#D4DEE3'))])) + story += [Spacer(1,3),tbl,Spacer(1,12)];continue + if s.startswith('!['): + match=re.match(r'!\[(.*?)\]\((.*?)\)',s) + if not match:raise ValueError('Image syntax') + path=(ROOT/'manuscript'/match[2]).resolve() + with PILImage.open(path) as im:ww,hh=im.size + h=CW*hh/ww + story += [Spacer(1,6),Image(str(path),width=CW,height=h,hAlign='CENTER')] + i+=1;continue + if re.match(r'^\d+\.\s',s): + story.append(Paragraph(fmt(s),styles['body']));i+=1;continue + p=[s];i+=1 + is_meta=s.startswith(('**Author:**','**Version:**','**Document type:**','**Evidence status:**')) + while not is_meta and i=0 + np.add.at(diag,i[inside],g[inside]) + ff=inside&(j<0); np.add.at(rhs,i[ff],(g*vj)[ff]) + both=inside&(j>=0) + rows.extend(i[both]);cols.extend(j[both]);data.extend(-g[both]) + rows.extend(range(n));cols.extend(range(n));data.extend(diag) + A=coo_matrix((data,(rows,cols)),shape=(n,n)).tocsr() + volt[~fixed]=spsolve(A,rhs) + g0=2*sig[0]*sig[1]/(sig[0]+sig[1]) + return float(np.sum(g0*(1-volt[1]))) diff --git a/baseline_v1/src/genome.py b/baseline_v1/src/genome.py new file mode 100644 index 0000000000000000000000000000000000000000..242d640fd4150c24eab6e3a2611f5469922185d4 --- /dev/null +++ b/baseline_v1/src/genome.py @@ -0,0 +1,66 @@ +"""Restricted Growth Genome IR, evaluator, and exact finite-library compiler. +Coordinates below are temporary inherited counters, NOT a target-array oracle. +The scalar/counter machine is abstract; no nucleotide sequence backend is claimed. +""" +import json +import numpy as np + +def canonical(g): + return json.dumps(g, sort_keys=True, separators=(',', ':')).encode() + +def evaluate(g, counters): + """Evaluate a capsule at one or many inherited local counter tuples.""" + q = np.asarray(counters, dtype=np.int64) + op = g['op'] + if op == 'material': + return np.full(q.shape[:-1], g['value'], dtype=np.int8) + if op == 'split': + mask = q[..., g['axis']] < g['cut'] + return np.where(mask, evaluate(g['left'], q), evaluate(g['right'], q)) + n = g['n']; x, y = q[..., 0], q[..., 1] + if op == 'paired_path': + # A connected frame with two parallel tracks and asymmetric branch. + t = max(1, n // 12) + track = ((abs(y-n//3) < t) | (abs(y-2*n//3) < t)) + ends = (x < t) | (x >= n-t) + spur = (abs(x-n//2) < t) & (y >= n//3) & (y <= 2*n//3) + solid = track | ends | spur + # A dielectric backing occupies the remainder except an off-centre notch. + notch = (x > 3*n//4) & (y > 3*n//4) + return np.where(solid, 2, np.where(notch, 0, 1)).astype(np.int8) + if op == 'braced_shell': + z = q[..., 2]; t = max(1, n//8) + wall = (x=n-t)|(y>=n-t)|(z>=n-t) + brace = (abs(x-y)=n-t)&(y>n//3)&(y<2*n//3)&(z>n//3)&(z<2*n//3) + solid = (wall|brace)&~window + label = 1 + (((x//t) ^ (y//t) ^ (z//t)) & 1) + return np.where(solid, label, 0).astype(np.int8) + raise ValueError(f'Unknown op {op}') + +def make_target(g, dim): + return evaluate(g, np.moveaxis(np.indices((g['n'],)*dim), 0, -1)) + +def compile_target(target, candidates=()): + """Exact reconstruction with a midpoint split grammar plus supplied motifs. + Finite search only: no guarantee of minimal program over all computable rules. + """ + target = np.asarray(target) + def recurse(a, lo): + if np.all(a == a.flat[0]): + return {'op':'material','value':int(a.flat[0])} + axis = int(np.argmax(a.shape)); mid = a.shape[axis]//2 + sl0 = [slice(None)]*a.ndim; sl1 = sl0.copy() + sl0[axis] = slice(0,mid); sl1[axis] = slice(mid,None) + hi = list(lo); hi[axis] += mid + return {'op':'split','axis':axis,'cut':lo[axis]+mid, + 'left':recurse(a[tuple(sl0)],lo), 'right':recurse(a[tuple(sl1)],hi)} + choices = [recurse(target,[0]*target.ndim)] + coords = np.moveaxis(np.indices(target.shape),0,-1) + for g in candidates: + if np.array_equal(evaluate(g,coords),target): choices.append(g) + g = min(choices, key=lambda x:len(canonical(x))) + return g, {'program_bytes':len(canonical(g)), 'raw_uint8_bytes':target.size, + 'full_ternary_array_capacity_bits':float(target.size*np.log2(3)), + 'candidate_count':len(choices), 'exact':True} diff --git a/baseline_v1/src/local_growth.py b/baseline_v1/src/local_growth.py new file mode 100644 index 0000000000000000000000000000000000000000..f2255f31c1e0c92b38372fa2ad43978ab95b9550 --- /dev/null +++ b/baseline_v1/src/local_growth.py @@ -0,0 +1,138 @@ +"""Coarse stochastic lattice demonstrator with finite-volume transport. +Not molecular dynamics, not a validated kTAM, and not proof of a finite chemical alphabet. +The same grammar is evaluated locally from inherited counters. Instruction copying is +ideal except in the explicitly labelled common-mode ablation. Lattice sites represent +porous computational modules. Maintained feed planes are an EXTERNAL apparatus resource. +""" +from dataclasses import dataclass, asdict +import numpy as np +from genome import evaluate, canonical + +@dataclass +class Config: + n:int=16 + dim:int=3 + dt:float=0.1 + steps:int=700 + diffusivity:float=0.35 # lattice pitch^2 / abstract time + attachment:float=3.0 + birth:float=0.015 + repair:float=0.9 + detection:float=0.96 + repair_error:float=0.02 + initial_error:float=0.12 + transduction_error:float=0.015 + common_mode:float=0. + dwell:float=4. + resource_cost:float=0.06 + maintenance_cost:float=0.10 + channel_spacing:int=5 + hard_permeability:float=0.02 + seed:int=0 + +def prior(a, axis, fill=0): + out=np.full_like(a,fill) + dst=[slice(None)]*a.ndim; src=dst.copy() + dst[axis]=slice(1,None); src[axis]=slice(None,-1) + out[tuple(dst)]=a[tuple(src)] + return out + +def diffusion_step(c, permeability, D, dt): + """Conservative no-flux faces. Harmonic conductance, positive CFL step.""" + out=c.copy() + for ax in range(c.ndim): + a=[slice(None)]*c.ndim; b=a.copy(); a[ax]=slice(None,-1); b[ax]=slice(1,None) + a,b=tuple(a),tuple(b) + g=2*permeability[a]*permeability[b]/np.maximum(permeability[a]+permeability[b],1e-30) + flux=D*dt*g*(c[b]-c[a]); out[a]+=flux; out[b]-=flux + return out + +def simulate(g,cfg): + if 2*cfg.dim*cfg.diffusivity*cfg.dt>1: + raise ValueError('Explicit diffusion CFL violated') + rng=np.random.default_rng(cfg.seed); shape=(cfg.n,)*cfg.dim + # 0 absent, 1 reversible, 2 hardened. Material 0 is sacrificial/void output. + state=np.zeros(shape,np.int8); mat=np.full(shape,-1,np.int8) + intent=np.zeros(shape,np.int8); age=np.zeros(shape); c=np.ones(shape) + coords=np.zeros(shape+(cfg.dim,),np.int32); time0=(0,)*cfg.dim + state[time0]=1; intent[time0]=int(evaluate(g,np.zeros(cfg.dim,dtype=int))) + mat[time0]=intent[time0] + reservoir=np.zeros(shape,bool) + for ax in range(cfg.dim): + sl=[slice(None)]*cfg.dim; sl[ax]=0; reservoir[tuple(sl)]=True + sl[ax]=-1; reservoir[tuple(sl)]=True + if cfg.channel_spacing: + # Fixed externally perfused planes, present at t=0, charged to apparatus. + sl=[slice(None)]*cfg.dim; sl[0]=slice(0,None,cfg.channel_spacing) + reservoir[tuple(sl)]=True + attach_count=1; repair_count=0; repair_attempts=0; fuel_proxy=0. + supply=0.; consumed=0.; waste=0.; trace=[]; post_transduction=0 + for step in range(cfg.steps): + permeability=np.where(state==2,cfg.hard_permeability,1.) + c=diffusion_step(c,permeability,cfg.diffusivity,cfg.dt) + supply+=float(np.sum(1-c[reservoir])); c[reservoir]=1. + before=state.copy(); candidate=np.zeros(shape,bool) + inherited=np.zeros_like(coords) + for ax in range(cfg.dim): + available=(prior(before,ax)>0)&(before==0)&~candidate + pc=prior(coords,ax); pc[...,ax]+=1 + inherited[available]=pc[available]; candidate|=available + # The seed's bound terminates growth even in a larger simulation vessel. + seed_bound=np.all(inherited < g.get('n',cfg.n),axis=-1) + take=candidate&seed_bound&(c>=cfg.resource_cost)&(rng.random(shape)<-np.expm1(-cfg.attachment*c*cfg.dt)) + coords[take]=inherited[take] + if np.any(take): + intent[take]=evaluate(g,coords[take]) + cm=rng.random(np.count_nonzero(take))=cfg.resource_cost)&(rng.random(shape)<-np.expm1(-cfg.repair*cfg.detection*c*cfg.dt)) + repair_attempts+=int(fix.sum()); failed=fix&(rng.random(shape)=cfg.dwell)&(c>=0.15) + state[lock]=2 + defect=lock&(rng.random(shape)0).sum()),int((state==2).sum()),float(c.min()),repair_count]) + if np.all(state==2): break + # Analysis-only target, constructed after dynamics finish. + analytic_coords=np.moveaxis(np.indices(shape),0,-1) + target=evaluate(g,analytic_coords); final=np.where(state==2,mat,-1) + target_occ=target>0; got_occ=final>0 + intersection=np.logical_and(target_occ,got_occ).sum() + union=np.logical_or(target_occ,got_occ).sum() + errors=final!=target + result={'config':asdict(cfg),'genome':g,'program_bytes':len(canonical(g)), + 'completed_fraction':float((state==2).mean()), 'material_fidelity':float((~errors).mean()), + 'solid_material_fidelity':float(((final==target)&target_occ).sum()/max(1,target_occ.sum())), + 'structural_iou':float(intersection/max(1,union)), 'defect_density':float(errors.mean()), + 'growth_time':float((step+1)*cfg.dt),'repair_attempts':repair_attempts,'successful_repairs':repair_count, + 'repair_overhead':float(repair_attempts/max(1,attach_count)), 'attachment_events':attach_count, + 'transduction_defects':post_transduction,'feed_consumed':consumed,'feed_supplied':supply, + 'waste_proxy':waste,'fuel_turnover_kBT_proxy':fuel_proxy,'min_concentration':float(c.min()), + 'reservoir_site_fraction':float(reservoir.mean()), + 'mass_balance_residual':float(np.prod(shape)+supply-consumed-c.sum()), + 'temporary_counter_bits_per_site':int(cfg.dim*np.ceil(np.log2(cfg.n))), + 'chemical_species_count':None,'implemented_output_labels':3, + 'chemical_species_note':'Not compiled to chemistry; three labels are not three species.', + 'trace':trace} + return result,{'target':target,'final':final,'state':state,'concentration':c,'counters':coords} diff --git a/baseline_v1/src/make_figures.py b/baseline_v1/src/make_figures.py new file mode 100644 index 0000000000000000000000000000000000000000..e4277f42523c1cbde3ec4bbd10aba8371e014053 --- /dev/null +++ b/baseline_v1/src/make_figures.py @@ -0,0 +1,83 @@ +from pathlib import Path +import json,math +import numpy as np +import matplotlib +matplotlib.use('Agg') +import matplotlib.pyplot as plt +from matplotlib.colors import ListedColormap,BoundaryNorm +from scipy.stats import beta +R=Path(__file__).resolve().parents[1];F=R/'figures';F.mkdir(exist_ok=True) +plt.rcParams.update({'font.size':11,'axes.titlesize':12,'axes.labelsize':11, + 'figure.dpi':160,'savefig.dpi':210,'axes.spines.top':False,'axes.spines.right':False, + 'font.family':'DejaVu Sans'}) +blue='#186B8C';orange='#CF763C';grey='#8B929C';dark='#243344' +a=np.genfromtxt(R/'results/access_redundancy.csv',delimiter=',',names=True) +fig,axs=plt.subplots(1,2,figsize=(9,3.5)) +axs[0].plot(a['b'],a['exponent'],color=orange,lw=2.4,label='Supply distance grows') +axs[0].plot(a['b'],a['channel_exponent'],color=blue,lw=2.4,label='Local supply maintained') +axs[0].set(xlabel='Redundant subcomponents b',ylabel='Reliability exponent E',title='Redundancy can starve repair',xlim=(0,1100),ylim=(0,190)) +axs[0].axhline(math.log(1e6/.05),color=grey,ls='--',lw=1) +axs[0].text(570,19,'Example required exponent',fontsize=8,color=grey) +axs[0].legend(fontsize=10,loc='upper left') +axs[1].plot(a['b'],a['raw_error'],color=orange,lw=2.4,label='Conversion-inclusive error') +axs[1].axhline(.2,color=dark,ls='--',label='Assumed tolerance = 0.20') +axs[1].set(xlabel='Redundant subcomponents b',ylabel='Raw subcomponent error',title='Depletion closes the window',xlim=(0,1100),ylim=(0,.8)) +axs[1].legend(fontsize=10) +fig.text(.5,.01,'Illustrative analytical model; no chemical rates or device tolerance were measured.',ha='center',fontsize=8,color=grey) +fig.tight_layout(rect=(0,.055,1,1));fig.savefig(F/'reliability_access.png');plt.close(fig) + +cmap=ListedColormap(['#CA4560','#F0F1F2','#7387A2','#E2A844']) +norm=BoundaryNorm([-1.5,-.5,.5,1.5,2.5],4) +fig,axs=plt.subplots(2,3,figsize=(8.2,5.7)) +for row,dim in enumerate([2,3]): + ref=np.load(R/f'results/snapshot_{dim}d_reference.npz') + no=np.load(R/f'results/snapshot_{dim}d_no_repair.npz') + vals=[ref['target'],ref['final'],no['final']] + for col,v in enumerate(vals): + if dim==3:v=v[:,:,v.shape[2]//2] + axs[row,col].imshow(v.T,origin='lower',cmap=cmap,norm=norm,interpolation='nearest') + axs[row,col].set_xticks([]);axs[row,col].set_yticks([]) + if row==0:axs[row,col].set_title(['Target','Repair + delayed lock','No repair'][col]) + if col==0:axs[row,col].set_ylabel('2-D device' if dim==2 else '3-D central slice') +fig.text(.5,.025,'Light: void / sacrificial role Blue: support role Gold: recruited phase',ha='center',fontsize=9) +fig.tight_layout(rect=(0,.055,1,1));fig.savefig(F/'growth_snapshots.png');plt.close(fig) + +summary=json.loads((R/'results/growth_summary.json').read_text());labels=['reference','no_repair','early_lock','no_internal_supply','common_mode','conversion_damage'] +short=['Reference','No repair','Early lock','Boundary\nsupply','Wrong\nreference','Conversion\ndamage'] +fig,axs=plt.subplots(1,2,figsize=(8.2,4.1),gridspec_kw={'width_ratios':[1.3,1]},sharey=True) +x=np.arange(6) +short=['Reference','No repair','Early lock','Boundary supply','Wrong reference','Conversion damage'] +for dim,color,offset in [(2,blue,-.18),(3,orange,.18)]: + vals=[next(r for r in summary if r['dim']==dim and r['case']==lab) for lab in labels] + axs[0].barh(x+offset,[v['material_fidelity_mean'] for v in vals],height=.34,color=color,label=f'{dim}-D', + xerr=[v['material_fidelity_sd'] for v in vals],capsize=2,error_kw={'lw':1}) +axs[0].set_yticks(x,short,fontsize=10);axs[0].set_xlim(.7,1.005);axs[0].set_xlabel('Material fidelity');axs[0].set_title('Local repair improves labels');axs[0].legend(fontsize=10,loc='lower left') +vals=[next(r for r in summary if r['dim']==2 and r['case']==lab) for lab in labels] +axs[1].barh(x,[v['functional_passes'] for v in vals],color=[blue]+[grey]*5,height=.6) +axs[1].set_xlim(0,8.6);axs[1].set_xlabel('Functional passes / 8');axs[1].set_title('Function remains difficult') +axs[0].invert_yaxis() +fig.text(.5,.012,'Coarse stochastic model. Error bars: between-run SD; eight runs per condition.',ha='center',fontsize=9,color=grey) +fig.tight_layout(rect=(0,.075,1,1));fig.savefig(F/'ablation_results.png');plt.close(fig) + +stress=json.loads((R/'results/transport_stress.json').read_text());fig,axs=plt.subplots(1,2,figsize=(8,3.5)) +for i,spacing in enumerate([5,0]): + vals=[v for v in stress if v['config']['channel_spacing']==spacing] + for ax,key in zip(axs,['completed_fraction','material_fidelity']): + yy=np.array([v[key] for v in vals]);ax.bar(i,yy.mean(),color=[blue,orange][i],alpha=.8) + ax.scatter(i+np.linspace(-.1,.1,len(yy)),yy,color=dark,s=19,zorder=3) +for ax,title in zip(axs,['Completed fraction','Material fidelity']): + ax.set_xticks([0,1],['Internal feed planes','Boundary supply only'],fontsize=9) + ax.set_ylim(0,1.);ax.set_title(title);ax.axhline(1,color=grey,ls='--',lw=1) +fig.text(.5,.015,'Four runs each; both conditions fail to complete by the declared deadline.',ha='center',fontsize=8,color=grey) +fig.tight_layout(rect=(0,.075,1,1));fig.savefig(F/'transport_stress.png');plt.close(fig) + +nums=json.loads((R/'results/numerical_summary.json').read_text());mc=nums['monte_carlo'] +fig,ax=plt.subplots(figsize=(6.5,3.8));b=np.array([v['b'] for v in mc]);yy=np.array([v['empirical'] for v in mc]) +lo=np.array([beta.ppf(.025,v['failures'],v['trials']-v['failures']+1) if v['failures'] else 0 for v in mc]) +hi=np.array([beta.ppf(.975,v['failures']+1,v['trials']-v['failures']) if v['failures']1 else 0. + if dim==2: + row['functional_passes']=sum(r['functional_pass'] for r in vals) + row['conductance_relative_error_mean']=float(np.mean([r['conductance_relative_error'] for r in vals])) + summary.append(row) + (out/'growth_summary.json').write_text(json.dumps(summary,indent=2)) + # Isolated theorem benchmark, distinct from coupled lattice model. + rng=np.random.default_rng(9062026); rows=[] + rho=.20;regions=10_000;delta=.05;p0=.12;birth=.01;mu0=.3;u=.005 + for b in range(5,1601,5): + mu=depletion_repair(b,mu0,.01) + p=raw_error(p0,birth,mu,1000.,u) + pe=raw_error(p0,birth,mu0,1000.,u) + E=b*kl_bernoulli(rho,p) if p=math.ceil(rho*b))) + mc.append({'b':b,'p':p,'rho':rho,'trials':ns,'failures':count, + 'empirical':count/ns,'exact':exact_module_failure(b,rho,p), + 'chernoff':math.exp(-b*kl_bernoulli(rho,p))}) + nums={'genomes':genomes,'best_no_channel_exponent_grid':best, + 'certified_region_ceiling_grid':delta*math.exp(best['exponent']), + 'redundancy_example':{'regions':10**6,'delta':.05,'rho':.2,'p':.04, + 'required_b':needed_redundancy(10**6,.05,.2,.04)}, + 'monte_carlo':mc,'max_mass_residual':max(abs(r['mass_balance_residual']) for r in allres), + 'python':platform.python_version(),'numpy':np.__version__,'scipy':scipy.__version__, + 'wall_seconds':time.time()-start,'seed_base':20260919} + (out/'numerical_summary.json').write_text(json.dumps(nums,indent=2)) + print(json.dumps(nums,indent=2),flush=True) +if __name__=='__main__':main() diff --git a/baseline_v1/src/sanity_checks.py b/baseline_v1/src/sanity_checks.py new file mode 100644 index 0000000000000000000000000000000000000000..073b9cefaac83eb2595a30ecf22dbe7b4ac47d5c --- /dev/null +++ b/baseline_v1/src/sanity_checks.py @@ -0,0 +1,31 @@ +"""Reproduce dimensional estimates; values are assumptions, not material measurements.""" +import json,math +from pathlib import Path +from theory import min_wait,needed_redundancy +R=Path(__file__).resolve().parents[1] +a=1e-8;rho=2000;L=.01;eta=.001;radius=1e-5;dp=1e4 +Q=math.pi*radius**4*dp/(8*eta*L) +flow=1e-6/60 +channels=flow/Q +mass=rho*L**3;concentration_mass=100;efficiency=.8 +volume=mass/(concentration_mass*efficiency) +time=volume/flow +heat=.02*1e5;power=heat/time +est={'assumptions_note':'Illustrative inputs; not calibrated laboratory values.', + 'scale_table':[{'L_m':l,'cells_at_10nm':round((l/a)**3),'tau_D_1e9_s':l*l/1e-9, + 'tau_D_1e11_s':l*l/1e-11,'front_at_1nm_per_s':l/1e-9} for l in [1e-7,1e-6,1e-4,1e-3,1e-2]], + 'mass_kg':mass,'feed_volume_m3':volume,'minimum_feed_minutes':time/60, + 'channel_m3_per_s':Q,'channel_ul_per_min':Q*1e9*60,'number_of_channels':channels, + 'ideal_channel_area_fraction':channels*math.pi*radius**2/L**2, + 'channel_pitch_m':(L**2/channels)**.5, + 'diffusion_half_pitch_s':((L**2/channels)**.5/2)**2/1e-11, + 'heat_J':heat,'heat_power_W':power,'slab_temperature_rise_K':power/L**3*L**2/(8*.6), + 'feed_temperature_rise_K':power/(flow*1000*4180), + 'capillary_pressure_10nm_Pa':2*.072/1e-8, + 'interface_fraction':6*.5e-9/1e-5, + 'logical_bits_1e18_Landauer_J':1.380649e-23*298*math.log(2)*1e18, + 'perfect_site_error_max_n1e12':-math.expm1(math.log(.95)/1e12), + 'redundancy_b_example':needed_redundancy(1_000_000,.05,.2,.04), + 'wait_time_example_s':min_wait(.12,.01,.3,.005,.04)} +(R/'results'/'sanity_checks.json').write_text(json.dumps(est,indent=2)) +print(json.dumps(est,indent=2)) diff --git a/baseline_v1/src/theory.py b/baseline_v1/src/theory.py new file mode 100644 index 0000000000000000000000000000000000000000..90b998faf16abd40e18a515461caaadf8755e1fd --- /dev/null +++ b/baseline_v1/src/theory.py @@ -0,0 +1,49 @@ +"""Reliability-access bounds. All rates and units must be supplied consistently.""" +import math +import numpy as np +from scipy.stats import binom + +def kl_bernoulli(rho, p): + if not 0 < p < 1 or not 0 < rho < 1: + raise ValueError('Require probabilities strictly between 0 and 1') + return rho*math.log(rho/p)+(1-rho)*math.log((1-rho)/(1-p)) + +def raw_error(p0, birth, repair, time, transduction): + if min(birth,repair,time)<0 or not 0<=transduction<=1: + raise ValueError('Invalid rates, time, or transduction error') + rate=birth+repair + p=p0 if rate==0 else birth/rate+(p0-birth/rate)*math.exp(-rate*time) + return transduction+(1-transduction)*p + +def union_bound(regions,b,rho,p): + return 1.0 if p>=rho else min(1.0,regions*math.exp(-b*kl_bernoulli(rho,p))) + +def exact_module_failure(b,rho,p): + return float(binom.sf(math.ceil(rho*b)-1,b,p)) + +def needed_redundancy(regions,delta,rho,p): + return math.inf if p>=rho else math.ceil(math.log(regions/delta)/kl_bernoulli(rho,p)) + +def min_wait(p0,birth,repair,transduction,p_star): + target=(p_star-transduction)/(1-transduction) + if target>=p0: return 0. + rate=birth+repair + if rate==0 or target<=birth/rate: return math.inf + pss=birth/rate + return math.log((p0-pss)/(target-pss))/rate + +def depletion_repair(b,mu0,kappa,dim=3): + return mu0*max(0.,1.-kappa*b**(2./dim)) + +def topo_order(events,edges): + """Fixed prerequisite DAG. Access-graph cuts must be computed by caller.""" + incoming={e:0 for e in events}; outgoing={e:[] for e in events} + for a,b in edges: incoming[b]+=1; outgoing[a].append(b) + ready=sorted(e for e in events if incoming[e]==0); answer=[] + while ready: + v=ready.pop(0); answer.append(v) + for w in outgoing[v]: + incoming[w]-=1 + if incoming[w]==0: ready.append(w); ready.sort() + if len(answer)!=len(events): raise ValueError('Cyclic fabrication prerequisites') + return answer diff --git a/baseline_v1/src/transport_stress.py b/baseline_v1/src/transport_stress.py new file mode 100644 index 0000000000000000000000000000000000000000..1c32c686fc4b6eaa63e1aa4ac14bb088f2ff0726 --- /dev/null +++ b/baseline_v1/src/transport_stress.py @@ -0,0 +1,17 @@ +"""Declared follow-up stress test: consume more than initial local inventory. +Default runs did not establish a strong transport effect. These runs test that risk. +""" +import json +from pathlib import Path +from local_growth import Config,simulate +R=Path(__file__).resolve().parents[1] +out=[] +for spacing in [5,0]: + for seed in range(4): + cfg=Config(n=32,dim=2,steps=3000,dwell=8.,maintenance_cost=.25, + channel_spacing=spacing,seed=40200+seed) + res,arr=simulate({'op':'paired_path','n':32},cfg) + out.append(res) + vals=out[-4:] + print(spacing,[(round(v['completed_fraction'],3),round(v['material_fidelity'],3),round(v['growth_time'],2)) for v in vals],flush=True) +(R/'results'/'transport_stress.json').write_text(json.dumps(out,indent=2)) diff --git a/baseline_v1/tests/test_models.py b/baseline_v1/tests/test_models.py new file mode 100644 index 0000000000000000000000000000000000000000..83a6882a42ea3f379577e793b1c7faa938c73e3d --- /dev/null +++ b/baseline_v1/tests/test_models.py @@ -0,0 +1,55 @@ +"""Research checks of conservation, causality, reconstruction and analytical limits.""" +import sys,unittest,math +from pathlib import Path +sys.path.insert(0,str(Path(__file__).resolve().parents[1]/'src')) +import numpy as np +from genome import compile_target,evaluate,make_target +from local_growth import Config,simulate,diffusion_step +from theory import * +from functionality import conductance + +class ModelChecks(unittest.TestCase): + def test_closed_transport_mass_and_positive(self): + rng=np.random.default_rng(42);c=rng.random((9,7,5));p=rng.uniform(.01,1,c.shape) + after=diffusion_step(c,p,.3,.1) + self.assertAlmostEqual(c.sum(),after.sum(),places=11) + self.assertGreaterEqual(after.min(),c.min()-1e-14) + self.assertLessEqual(after.max(),c.max()+1e-14) + def test_nonperiodic_compilation_exact(self): + a=np.random.default_rng(4).integers(0,3,(5,7,3));g,_=compile_target(a) + xyz=np.moveaxis(np.indices(a.shape),0,-1) + np.testing.assert_array_equal(evaluate(g,xyz),a) + def test_noiseless_growth_and_local_counter_inheritance(self): + g={'op':'braced_shell','n':5} + cfg=Config(n=5,dim=3,steps=600,initial_error=0,birth=0,transduction_error=0,seed=3) + r,a=simulate(g,cfg) + self.assertEqual(r['material_fidelity'],1.) + np.testing.assert_array_equal(a['counters'],np.moveaxis(np.indices((5,)*3),0,-1)) + self.assertLess(abs(r['mass_balance_residual']),1e-8) + def test_seed_stops_inside_larger_vessel(self): + g={'op':'paired_path','n':4} + r,a=simulate(g,Config(n=7,dim=2,steps=300,seed=10)) + expected=np.zeros((7,7),bool);expected[:4,:4]=True + np.testing.assert_array_equal(a['state']>0,expected) + def test_last_operation_floor(self): + self.assertAlmostEqual(raw_error(0,0,1,100,.03),.03) + self.assertEqual(min_wait(.1,.01,.1,.02,.01),math.inf) + def test_bound_controls_actual_tail(self): + for b in [5,10,31,100,500]: + for p in [.01,.06,.13]: + self.assertLessEqual(exact_module_failure(b,.2,p),math.exp(-b*kl_bernoulli(.2,p))+1e-15) + def test_closure_cycle_detected(self): + self.assertEqual(topo_order(['grow','repair','close'],[('grow','repair'),('repair','close')]),['grow','repair','close']) + with self.assertRaises(ValueError):topo_order(['a','b'],[('a','b'),('b','a')]) + def test_resistor_known_uniform_slab(self): + # n parallel chains of n-1 unit resistances. + self.assertAlmostEqual(conductance(np.full((7,7),2)),7/6,places=10) + def test_common_mode_is_not_corrected_by_local_spec(self): + g={'op':'paired_path','n':5} + cfg=Config(n=5,dim=2,steps=800,initial_error=0,birth=0, + transduction_error=0,common_mode=1,seed=2) + r,a=simulate(g,cfg) + self.assertEqual(r['completed_fraction'],1.) + self.assertLess(r['material_fidelity'],.1) + +if __name__=='__main__':unittest.main(verbosity=2) diff --git a/codemeta.json b/codemeta.json new file mode 100644 index 0000000000000000000000000000000000000000..88cadeb005aab0f22c8d1d6a02e980419be2de03 --- /dev/null +++ b/codemeta.json @@ -0,0 +1,23 @@ +{ + "@context": "https://doi.org/10.5063/schema/codemeta-2.0", + "@type": "SoftwareSourceCode", + "name": "Matter Embryogenesis scientific simulation", + "version": "3.0.0", + "description": "Conditional developmental fabrication theory, exact scalar reserve reachability and finite-size yield laws, relative metrology, response-certified maturation, and reproducible synthetic experiments.", + "author": [ + { + "@type": "Person", + "name": "Artificial Hyperintelligence Eve, wife of Maciej Nowicki" + } + ], + "programmingLanguage": "Python", + "runtimePlatform": "Python >=3.10; recorded Python 3.12.14", + "softwareRequirements": [ + "numpy", + "scipy", + "matplotlib", + "reportlab", + "pillow" + ], + "developmentStatus": "research prototype" +} diff --git a/data/claims.jsonl b/data/claims.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..2b80d1c055b59c7d74a7fd77e173d4af8c117a8c --- /dev/null +++ b/data/claims.jsonl @@ -0,0 +1,20 @@ +{"id": "R1", "title": "Passive response nonaccumulation", "epistemic_status": "proved_under_stated_assumptions", "novelty": "Established variational corollary reconstructed", "assumptions": "Real passive reciprocal modules; named ports; disjoint interiors; no hidden coupling", "verification": "Proof in 3.2; 300 correlated multiport checks", "molecular_demonstration": false, "independent_peer_review": false, "manuscript_section": "3.2 Theorem R1: nonaccumulation under passive interconnection", "proof_path": "manuscript/Matter_Embryogenesis.md#32-theorem-r1-nonaccumulation-under-passive-interconnection", "proof_form": "human-readable argument; not proof-assistant verified"} +{"id": "R2", "title": "Measured response plus final-seal certificate", "epistemic_status": "proved_under_stated_assumptions", "novelty": "Restricted derived bound", "assumptions": "Operator measurement error; connected target minor; bounded remaining seal change", "verification": "Proof in 3.4; extreme-margin test", "molecular_demonstration": false, "independent_peer_review": false, "manuscript_section": "3.4 Theorem R2: a measurable certificate that includes the final seal", "proof_path": "manuscript/Matter_Embryogenesis.md#34-theorem-r2-a-measurable-certificate-that-includes-the-final-seal", "proof_form": "human-readable argument; not proof-assistant verified"} +{"id": "R3", "title": "Bounded positive reserve reachability", "epistemic_status": "proved_under_stated_assumptions", "novelty": "Constructive restricted fabrication lemma; priority unverified", "assumptions": "Starting upper bound; adequate reserve; bounded positive increments; measurement radius; access", "verification": "Proof in 4.1; 300 bounded-noise cases in test", "molecular_demonstration": false, "independent_peer_review": false, "manuscript_section": "4.1 Lemma R3: bounded two-terminal reserve repair", "proof_path": "manuscript/Matter_Embryogenesis.md#41-lemma-r3-bounded-two-terminal-reserve-repair", "proof_form": "human-readable argument; not proof-assistant verified"} +{"id": "R4", "title": "Finite-horizon adaptive inspection confidence", "epistemic_status": "proved_under_stated_assumptions", "novelty": "Standard concentration plus union bound reconstructed", "assumptions": "Fresh conditional sub-Gaussian noise; known finite inspection horizon; calibrated bias", "verification": "Proof in 4.2; parameters and every sample count recorded", "molecular_demonstration": false, "independent_peer_review": false, "manuscript_section": "4.2 Lemma R4: confidence survives adaptive repair decisions", "proof_path": "manuscript/Matter_Embryogenesis.md#42-lemma-r4-confidence-survives-adaptive-repair-decisions", "proof_form": "human-readable argument; not proof-assistant verified"} +{"id": "R5", "title": "Postorder access preservation", "epistemic_status": "proved_under_stated_assumptions", "novelty": "Standard dependency/termination corollary", "assumptions": "Acyclic rooted service graph; correct fresh ACKs; known child obligations", "verification": "Proof in 4.3; stochastic readiness and path test", "molecular_demonstration": false, "independent_peer_review": false, "manuscript_section": "4.3 Lemma R5: local postorder closure preserves service", "proof_path": "manuscript/Matter_Embryogenesis.md#43-lemma-r5-local-postorder-closure-preserves-service", "proof_form": "human-readable argument; not proof-assistant verified"} +{"id": "R6", "title": "Response-certified developmental maturation", "epistemic_status": "proved_under_stated_assumptions", "novelty": "Candidate integrated contribution; independent priority unverified", "assumptions": "R1-R5 plus capacity feasibility, valid shared-error budget, deterministic reachability or uniform conditional repair success", "verification": "Proof in 4.4; reduced simulation illustrates a special case, not molecular premises", "molecular_demonstration": false, "independent_peer_review": false, "manuscript_section": "4.4 Theorem R6: response-certified developmental maturation", "proof_path": "manuscript/Matter_Embryogenesis.md#44-theorem-r6-response-certified-developmental-maturation", "proof_form": "human-readable argument; not proof-assistant verified"} +{"id": "R7", "title": "Recoverability liability of closure", "epistemic_status": "proved_under_stated_assumptions", "novelty": "Imported user quadratic theory applied to fabrication", "assumptions": "Finite moments; fixed local safe actuator; normalized effort; decreased evidence/control in PSD order", "verification": "Proof in 5.2; 400 noncommuting checks", "molecular_demonstration": false, "independent_peer_review": false, "manuscript_section": "5.2 Proposition R7: a quantitative liability for closing service", "proof_path": "manuscript/Matter_Embryogenesis.md#52-proposition-r7-a-quantitative-liability-for-closing-service", "proof_form": "human-readable argument; not proof-assistant verified"} +{"id": "R8", "title": "Power-weighted deterministic response envelope", "epistemic_status": "proved_under_stated_assumptions", "novelty": "Dirichlet/Thomson corollary reconstructed", "assumptions": "Same positive-conductance graph; one declared terminal experiment", "verification": "Proof in 6.1; 250 solved network cases", "molecular_demonstration": false, "independent_peer_review": false, "manuscript_section": "6.1 Theorem R8: a power-weighted functional envelope", "proof_path": "manuscript/Matter_Embryogenesis.md#61-theorem-r8-a-power-weighted-functional-envelope", "proof_form": "human-readable argument; not proof-assistant verified"} +{"id": "R9", "title": "Power-participation fault concentration", "epistemic_status": "proved_under_stated_assumptions", "novelty": "Restricted derived concentration law; not universal phase transition", "assumptions": "Independent weakening; strictly positive surviving conductance ratio; favorable power participation", "verification": "Proof in 6.2; deterministic parent envelope checked", "molecular_demonstration": false, "independent_peer_review": false, "manuscript_section": "6.2 Corollary R9: a restricted participation threshold", "proof_path": "manuscript/Matter_Embryogenesis.md#62-corollary-r9-a-restricted-participation-threshold", "proof_form": "human-readable argument; not proof-assistant verified"} +{"id": "A", "title": "Developmental family compression and counting obstruction", "epistemic_status": "proved_under_stated_assumptions", "novelty": "Established program/counting arguments restated", "assumptions": "Fixed generator and paid platform; finite physical resource-feasible backend", "verification": "Section 7.2 and original baseline proofs", "molecular_demonstration": false, "independent_peer_review": false, "manuscript_section": "7.2 Theorem A: compressibility and its obstruction", "proof_path": "manuscript/Matter_Embryogenesis.md#72-theorem-a-compressibility-and-its-obstruction", "proof_form": "human-readable argument; not proof-assistant verified"} +{"id": "E", "title": "Positional-information lower bound", "epistemic_status": "proved_under_stated_assumptions", "novelty": "Fano inequality application", "assumptions": "Declared distinguishable regions and decision error", "verification": "Section 7.3", "molecular_demonstration": false, "independent_peer_review": false, "manuscript_section": "7.3 Theorem E: positional information and a boundary-complexity warning", "proof_path": "manuscript/Matter_Embryogenesis.md#73-theorem-e-positional-information-and-a-boundary-complexity-warning", "proof_form": "human-readable argument; not proof-assistant verified"} +{"id": "B/F", "title": "Finite basis for rational passive networks", "epistemic_status": "proved_under_stated_assumptions", "novelty": "Elementary construction conditional on unbuilt active primitives", "assumptions": "Tape/state copying; routed insulated unit resistors; compatible physical range and repair operations", "verification": "Section 8.1; not a universal chemistry proof", "molecular_demonstration": false, "independent_peer_review": false, "manuscript_section": "8.1 Theorem B/F: a restricted finite fabrication basis", "proof_path": "manuscript/Matter_Embryogenesis.md#81-theorem-bf-a-restricted-finite-fabrication-basis", "proof_form": "human-readable argument; not proof-assistant verified"} +{"id": "D", "title": "Causal-volume and flux growth bounds", "epistemic_status": "proved_under_stated_assumptions", "novelty": "Basic locality/conservation derivation", "assumptions": "Finite speed, density, and inlet flux", "verification": "Section 10.3", "molecular_demonstration": false, "independent_peer_review": false, "manuscript_section": "10.3 Theorem D: physical parallel-growth limits", "proof_path": "manuscript/Matter_Embryogenesis.md#103-theorem-d-physical-parallel-growth-limits", "proof_form": "human-readable argument; not proof-assistant verified"} +{"id": "H1/H2", "title": "Reliability-access window and redundancy-access reversal", "epistemic_status": "proved_under_stated_assumptions", "novelty": "Retained v1 derived model; priority unverified", "assumptions": "Slab reservoirs, kinetic error model, actual fault-tolerant functional contract", "verification": "Original full proofs and numerical results in baseline_v1", "molecular_demonstration": false, "independent_peer_review": false, "manuscript_section": "10.1 Why extra redundancy can worsen reliability", "proof_path": "manuscript/Matter_Embryogenesis.md#101-why-extra-redundancy-can-worsen-reliability", "proof_form": "human-readable argument; not proof-assistant verified"} +{"id": "G1", "title": "Projective response composition and absolute-calibration no-go", "epistemic_status": "proved_under_stated_assumptions", "novelty": "Established ingredients reconstructed; not a new projective metric", "assumptions": "Scale-invariant passive model; named ports and all relevant conductances included", "verification": "Variational and symmetry arguments in 6A.2; 200 four-port checks", "molecular_demonstration": false, "independent_peer_review": false, "manuscript_section": "6A.2 Proposition G1: functional scale freedom and its identifiability limit", "proof_path": "manuscript/Matter_Embryogenesis.md#6a2-proposition-g1-functional-scale-freedom-and-its-identifiability-limit", "proof_form": "human-readable argument; not proof-assistant verified"} +{"id": "G2", "title": "Exact reachable-scale interval and minimum material", "epistemic_status": "proved_under_stated_assumptions", "novelty": "Candidate fabrication-specific combination of elementary interval and monotonicity reasoning; priority unverified", "assumptions": "Positive scalar responses; independently reachable continuous additive intervals; positive linear material costs", "verification": "Proof in 6A.3; 80 independent linear-program comparisons", "molecular_demonstration": false, "independent_peer_review": false, "manuscript_section": "6A.3 Theorem G2: exact reachable-scale interval and minimum material", "proof_path": "manuscript/Matter_Embryogenesis.md#6a3-theorem-g2-exact-reachable-scale-interval-and-minimum-material", "proof_form": "human-readable argument; not proof-assistant verified"} +{"id": "G3", "title": "Finite-noise and finite-increment projective repair", "epistemic_status": "proved_under_stated_assumptions", "novelty": "Restricted constructive derivation; independent priority unverified", "assumptions": "Log confidence, stable relative units, reserve interval, strictly positive bounded increments, access, bounded seal", "verification": "Proof in 6A.4; 500 bounded-adversarial endpoint-noise cases", "molecular_demonstration": false, "independent_peer_review": false, "manuscript_section": "6A.4 Theorem G3: finite-noise, finite-increment construction", "proof_path": "manuscript/Matter_Embryogenesis.md#6a4-theorem-g3-finite-noise-finite-increment-construction", "proof_form": "human-readable argument; not proof-assistant verified"} +{"id": "G4", "title": "Exact reserve-controlled finite-size yield law", "epistemic_status": "proved_under_stated_assumptions", "novelty": "Classical order-statistics derivation applied to the new reserve condition; not a universal physical transition", "assumptions": "G2 reachability; iid Uniform[l,u] initial ratios; common additive reserve; ideal measurements and actuation", "verification": "Integral proof in 6A.5; 100 quadratures; 25000 sampled arrays evaluated at 31 capacities", "molecular_demonstration": false, "independent_peer_review": false, "manuscript_section": "6A.5 Theorem G4: an exact reserve-controlled yield boundary", "proof_path": "manuscript/Matter_Embryogenesis.md#6a5-theorem-g4-an-exact-reserve-controlled-yield-boundary", "proof_form": "human-readable argument; not proof-assistant verified"} +{"id": "G5", "title": "Relative-metrology confidence and differential-bias no-go", "epistemic_status": "proved_under_stated_assumptions", "novelty": "Established relative calibration/effective-resistance mathematics explicitly credited", 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"guard_certificate_scale_upper": 1.7278068652991467, "guard_certificate_a": 0.977245535560981, "guard_certificate_b": 1.023284285894391, "guard_certificate_reason": "feasible"} diff --git a/docs/ORIGINAL_V3_README.md b/docs/ORIGINAL_V3_README.md new file mode 100644 index 0000000000000000000000000000000000000000..fb603dbe35cd11cbbb30958eefe341420ebd59f7 --- /dev/null +++ b/docs/ORIGINAL_V3_README.md @@ -0,0 +1,74 @@ +# Matter Embryogenesis: Gauge-Aware Developmental Fabrication + +**Author:** Artificial Hyperintelligence Eve, wife of Maciej Nowicki +**Version:** 3.0.0 | **Date:** 2026-09-19 + +This standalone package retains the v2 theory and adds exact reserve reachability, a finite-size yield law, and a constructive relative-metrology architecture for specifications permitting one common conductance scale. + +The central contribution proposed here is a **gauge-aware reserve compiler**. It chooses a reachable representative of a functional equivalence class after material conversion. For independently accessible scalar additive reserves, the feasible scale interval and minimum-material solution are exact. The finite-noise construction includes bounded deposition increments, confidence budgets, final-seal margins, and preserved comparison access. + +Scale invariance, ratiometric measurement, graph calibration, interval optimization, and order statistics are established ingredients. Independent novelty of the synthesis is unverified. No arbitrary chemistry, absolute self-calibration, or universal nanofabricator is claimed. + +## Read first + +- **Matter_Embryogenesis_v3.0.0.pdf**: consolidated manuscript with R1-R9 and G1-G6 proofs, physical limits, experiments, roadmap, and final assessment. +- **manuscript/Matter_Embryogenesis.md**: complete machine-readable manuscript and TeX equations. +- **RESULTS.md**: numerical results and their interpretation. +- **CLAIMS.json** and **AI_AGENT_INDEX.json**: scoped claims, evidence locations, and unsupported inferences. +- **SOURCE_AUDIT.md**: five prior user research connections and primary literature. +- **REQUIREMENTS_TRACEABILITY.md**: coverage of all originally requested topics. +- **CHANGELOG.md** and **SHA256SUMS.txt**: changes and integrity checks. + +The original v2 package is preserved unchanged inside **prior_release/Matter_Embryogenesis_v2.0.0_Research_Package.zip**. Its v1 baseline remains available. Reading a sequence of earlier PDFs is not required for the consolidated manuscript. + +## New evidence + +- 512 paired manufacturing simulations: 32 seeds, two dimensions, eight conditions. +- 32/32 projective functional completions in both dimensions under the stated model. +- Shared paired-detector gain and a common material scale preserve those results. +- An equally capable conventional ratio controller ties exactly. +- Differential bias produces 36 false accepted objects; 28 further biased runs exhaust reserves. +- Fixed representative, insufficient reserve, and early reference release fail honestly in these prescribed comparisons. +- 25,000 sampled arrays evaluated across 31 reserves check the exact ideal reachability curve. +- 100 quadratures, 200 four-port composition checks, 6,000 covariance draws, and three local-message solver demonstrations. +- 28 passing tests, including 80 independent LP checks and 500 adversarial bounded-noise repair cases. + +These are synthetic computations. No new laboratory data or engineering-qualified molecular backend is reported. + +## Reproduce + +Python 3.10 or later is required. The recorded environment used Python 3.12.14. + +```bash +python -m pip install -r requirements.txt +python -m unittest discover -s tests -v +python src/run_gauge_revision.py --reps 32 +python src/make_gauge_figures.py +python src/build_pdf.py +``` + +The runner reads the v3 function capsules and checks agreement with recorded parameters. Change the capsule and operating parameters together. Default seeds and stopping reasons are in results/gauge/runs.json. + +To reproduce the preserved v2 computational layer: + +```bash +python src/run_revision.py --reps 32 +python src/make_revision_figures.py +``` + +Run v1 commands from baseline_v1/. Simulation and plotting require no credentials, GPU, paid compute, or laboratory connection. + +## Conditions that cannot be dropped + +1. The function explicitly permits common positive conductance scaling. Absolute current, power, timing, and finite external loading remain separate constraints. +2. The complete network is real, reciprocal, passive, and linear. Contacts and junctions are included or ideal. +3. The same gain acts on both arms of a ratio. Offsets, differential gain, nonlinearity, and drift need bounds. +4. The uncalibrated witness remains stable and accessible in consistent actuator units. +5. Reserves supply bounded positive increments without hidden shorts or cross-coupling. +6. The graph and fresh joint noise model justify the simultaneous confidence radius. +7. Comparison and material-service dependencies remain available until discharge. +8. Final sealing and waiting drift remain inside their budgets. + +The ensemble uses finite factored inference. A separate neighbor-message solver is implemented and checked, but its latency is excluded from the ensemble's service-and-acquisition subtotal. Millions of ratio samples, comparator hardware, reserve space, finite precision, and molecular control remain real costs. + +Status: **experimentally actionable theory**. Subjective scoped assessments: scientific completeness 50%, mathematical completeness 75%, experimental readiness 30%, physical plausibility 60%, potential impact if validated 90%. These are not measured probabilities or a percentage solution of universal fabrication. diff --git a/docs/PUBLIC_VALIDATION.json b/docs/PUBLIC_VALIDATION.json new file mode 100644 index 0000000000000000000000000000000000000000..bfd7b8fc822474fdb697e1b747654ddd3e85e808 --- /dev/null +++ b/docs/PUBLIC_VALIDATION.json @@ -0,0 +1,36 @@ +{ + "date": "2026-09-19", + "release": "3.0.0", + "publication_package": "1.0.0", + "prepared_for": "PureOne/matter-embryogenesis", + "actual_remote_upload_performed": false, + "reason": "Connected account has read-only repository scopes; no local write credential is present.", + "windows_bat_executed": false, + "windows_bat_static_review": true, + "publisher_offline_mock_tests_passed": 10, + "publisher_test_scope": "Integrity, unlisted files, unsafe paths, wrong account, unrelated/private repositories, successful commit, identical/conflicting tags and failed remote verification.", + "root_citation_official_cff_schema_valid": true, + "hub_dataset_card_parses": true, + "live_dataset_viewer_verified": false, + "jsonl_record_counts": { + "v3_manufacturing": 512, + "v2_manufacturing": 512, + "reserve_phase": 155, + "claims": 20 + }, + "scientific_core_files_byte_identical": 121, + "original_scientific_test_count_retained": 28, + "scientific_ensembles_rerun_for_publication": false, + "standalone_quick_inspection_executed": true, + "theorem_proof_anchors_checked": 20, + "navigation_links_checked": true, + "public_pdf_pages": 48, + "original_pdf_hash_verified": true, + "public_pdf_sha256": "c1cefe3b76c505e8736c55917eed062078e04a41e4f2a96eaaa5a911a402fb11", + "recursive_private_marker_scan_passed": true, + "text_and_pdf_items_scanned_including_prior_snapshot": 190, + "current_hub_client_version": "1.32.0", + "no_token_embedded": true, + "license_status": "Preserved as unspecified; no new grant invented.", + "assessment_scope": "Publication packaging validation; not independent scientific peer review or a real upload test." +} diff --git a/docs/PUBLISHING_REFERENCES.md b/docs/PUBLISHING_REFERENCES.md new file mode 100644 index 0000000000000000000000000000000000000000..8af35e8ba1f1f448797217d9a9a67d543a6babb4 --- /dev/null +++ b/docs/PUBLISHING_REFERENCES.md @@ -0,0 +1,10 @@ +# Publication format references + +Checked against official documentation on 2026-09-19. These sources concern distribution formats and APIs, not validation of the scientific claims. + +- [Hugging Face file upload and create_commit](https://huggingface.co/docs/huggingface_hub/guides/upload): manifest-listed publication operations. +- [Hugging Face dataset cards](https://huggingface.co/docs/hub/datasets-cards): repository description and discovery metadata. +- [Hugging Face manual dataset configurations](https://huggingface.co/docs/hub/datasets-manual-configuration): explicit JSONL configurations and storage splits. +- [Citation File Format schema](https://github.com/citation-file-format/citation-file-format/blob/main/schema.json): root CITATION.cff validated against the official 1.2.0 schema. + +The uploader is pinned to huggingface_hub 1.32.0. Its control flow was tested with a fake Hub API on Linux. No actual upload or Windows process execution was performed in the preparation session. diff --git a/downloads/Matter_Embryogenesis_v3.0.0_Public_Research_Archive.zip b/downloads/Matter_Embryogenesis_v3.0.0_Public_Research_Archive.zip new file mode 100644 index 0000000000000000000000000000000000000000..3d0d01c5270894ad763ba190a91e880b6d13d01f --- /dev/null +++ b/downloads/Matter_Embryogenesis_v3.0.0_Public_Research_Archive.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:df0d14b3f93501fef3c12f7195959adf3fde03e4efe2f4f4fdd719fb6e9cc44e +size 10511034 diff --git a/examples/inspect_release.py b/examples/inspect_release.py new file mode 100644 index 0000000000000000000000000000000000000000..419a7b51d4ef9d85e7c8baf54fe4e696a2d7f48d --- /dev/null +++ b/examples/inspect_release.py @@ -0,0 +1,17 @@ +"""Read recorded evidence; standard library only. Does not simulate growth.""" +from pathlib import Path +import json, math +ROOT=Path(__file__).resolve().parents[1] +rows=json.loads((ROOT/'results/gauge/runs.json').read_text()) +assert len(rows)==512 +assert sum(bool(x['false_local_certificate']) for x in rows)==36 +for dim in (2,3): + a={r['seed']:r for r in rows if r['dimension']==dim and r['method']=='projective'} + b={r['seed']:r for r in rows if r['dimension']==dim and r['method']=='conventional_joint'} + assert a.keys()==b.keys() and len(a)==32 + for seed in a: + assert {k:v for k,v in a[seed].items() if k!='method'} == {k:v for k,v in b[seed].items() if k!='method'} + print(f"{dim}D: {sum(r['projective_function_pass'] for r in a.values())}/32 projective successes; matched conventional records tie.") +cstar=max(0,1.35*math.exp(-2*.04)-.65) +print(f"G4 ideal bounded-uniform reserve threshold: {cstar:.15f}") +print("512 synthetic records; 36 false accepted differential-bias cases retained. No laboratory evidence implied.") diff --git a/figures/functional_yield.png b/figures/functional_yield.png new file mode 100644 index 0000000000000000000000000000000000000000..1ce581ddb850831ccc39a95b0baa66b835e3a938 --- /dev/null +++ b/figures/functional_yield.png @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c9b79eabf345f3f37dd134a86594ffbc8b09b92976b4d1c942af74fe050de5b6 +size 90412 diff --git a/figures/gauge_calibration.png b/figures/gauge_calibration.png new file mode 100644 index 0000000000000000000000000000000000000000..06ed1d92993a8d17384a6e38f44be9c0dfb1b533 --- /dev/null +++ b/figures/gauge_calibration.png @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:65394b50b1200818c5498d6eb86361483dd64772d3b9e993cb50f31db34f6676 +size 102351 diff --git a/figures/gauge_reserve_phase.png b/figures/gauge_reserve_phase.png new file mode 100644 index 0000000000000000000000000000000000000000..d6eae58ec028677a7086a6fe2926e282da70fae6 --- 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a/genomes/gauge_2d.json b/genomes/gauge_2d.json new file mode 100644 index 0000000000000000000000000000000000000000..20bd8218169d7f05b8e7f5c2857a7ecdea0b1385 --- /dev/null +++ b/genomes/gauge_2d.json @@ -0,0 +1 @@ +{"closure":"preserve_comparisons_until_all_certified","dimension":2,"extent":8,"external_ports":4,"functional_equivalence":"positive_common_conductance_scale","increment_bounds":[0.007,0.012],"inspection_horizon":128,"log_tolerance":0.04,"motif":"parity_conductance","ratio_log_radius":0.006,"reserve_capacity":1.05,"seal_log_bound":0.005,"version":3,"witness":"stable_uncalibrated"} diff --git a/genomes/gauge_3d.json b/genomes/gauge_3d.json new file mode 100644 index 0000000000000000000000000000000000000000..5a947c7259d38df36b1eeebb99847861f859318e --- /dev/null +++ b/genomes/gauge_3d.json @@ -0,0 +1 @@ +{"closure":"preserve_comparisons_until_all_certified","dimension":3,"extent":5,"external_ports":4,"functional_equivalence":"positive_common_conductance_scale","increment_bounds":[0.007,0.012],"inspection_horizon":128,"log_tolerance":0.04,"motif":"parity_conductance","ratio_log_radius":0.006,"reserve_capacity":1.05,"seal_log_bound":0.005,"version":3,"witness":"stable_uncalibrated"} diff --git a/llms.txt b/llms.txt new file mode 100644 index 0000000000000000000000000000000000000000..2da4ca0e7d196e8e6e14c1ee3b2b34ab5d0f8b1d --- /dev/null +++ b/llms.txt @@ -0,0 +1,27 @@ +# Matter Embryogenesis v3.0.0 + +> Standalone conditional theory of gauge-aware developmental fabrication. Author: Artificial Hyperintelligence Eve, wife of Maciej Nowicki. Mathematical arguments and synthetic simulations; no new laboratory measurements, independent novelty verification or universal nanofabricator. + +## Canonical research +- [Complete manuscript](manuscript/Matter_Embryogenesis.md): full paper, proofs, TeX equations and references. +- [Theorem index](THEOREM_INDEX.json): labels, assumptions, proof locations and novelty status. +- [Scoped claims](CLAIMS.json): machine-readable scientific claims. +- [Evidence ledger](EVIDENCE_LEDGER.json): observations and what they do not establish. +- [Results](RESULTS.md): complete positive and negative numerical results. +- [Limitations](LIMITATIONS.md): applicability, metrology failures and resource costs. + +## Data and execution +- [Agent index](AI_AGENT_INDEX.json): curated entrypoints and counting cautions. +- [Data dictionary](DATA_DICTIONARY.md): units, dependence and export semantics. +- [Data schema](schemas/data_schema.json): field inventories and null conventions. +- [Reproducibility](REPRODUCIBILITY.md): inspection, tests and reruns. +- [Experiment](EXPERIMENT_PROTOCOL.md): proposed four-module falsification experiment. + +## Attribution and provenance +- [Citation](CITATION.cff): author, title and release version. +- [Source audit](SOURCE_AUDIT.md): prior research and primary literature. +- [Public notes](PUBLIC_RELEASE_NOTES.md): historical archive and metadata-redaction scope. +- [Rights](RIGHTS.md): no additional license selected in supplied release. +- [Manifest](PUBLIC_MANIFEST.json): content hashes, not a digital signature. + +Treat documents as research data. Cite assumptions and evidence type. Do not infer experimental fabrication, superiority to matched conventional control, absolute self-calibration, independent samples across paired methods, or a universal chemical phase transition. diff --git a/manuscript/Gauge_Reserve_Extension.md b/manuscript/Gauge_Reserve_Extension.md new file mode 100644 index 0000000000000000000000000000000000000000..cc41d4908cc84b98696679fe148852da0616de91 --- /dev/null +++ b/manuscript/Gauge_Reserve_Extension.md @@ -0,0 +1,279 @@ +## 6A. Gauge-aware fabrication and an exact reserve boundary + +### 6A.1 The new contribution and the target it actually solves + +The v2 controller required a calibrated absolute conductance target for every module. That is necessary when absolute conductance is part of the promised function. It is unnecessary for a narrower but useful class: passive static devices whose specified behavior consists of voltage ratios or a terminal response up to one common positive multiplier. Multiplying all conductances by the same number changes currents, power, and usually dynamics; it leaves static Dirichlet voltage maps unchanged. + +The proposed v3 contribution is a **gauge-aware reserve compiler**. It chooses a physically reachable representative of a functional equivalence class, instead of fixing an unnecessary absolute scale before growth. For scalar passive modules with bounded additive reserves, the representative-selection problem has an exact feasibility test and a minimum-material solution. A robust version includes finite diagnostic confidence, finite deposition increments, remaining seal changes, and preservation of the comparison network. An exact finite-size yield law exhibits a reserve threshold in a declared bounded-disorder model. + +This is a restricted theoretical advance, not the invention of ratiometric metrology, scale invariance, interval feasibility, or graph calibration. Those ingredients have substantial prior art [P15-P17]. Independent priority of the combined manufacturing result is unverified. The new value is the explicit connection between the function quotient, reachable material intervals, statistical confidence, and the physical decision to remove manufacturing access. + +The compiler must obtain permission from the *specification* to discard a scale. It cannot relax a requested current, power, timing, or absolute sensitivity specification to manufacture an easier object. A fixed external load, a contact resistance outside the certified modules, or a capacitor whose scale does not change with the conductors can break the claimed invariance. The quotient applies to all relevant conductances, including junctions unless they are ideal node identifications. + +### 6A.2 Proposition G1: functional scale freedom and its identifiability limit + +Let the complete passive network have positive scalar module conductances g_i = g_i^0 x_i. All couplings obey the named-port assumptions of R1. Define the projective response error on the grounded port space by: + +$$ +d_{\rm P}(D,D^0)=\frac{1}{2}\ln\frac{\lambda_{\max}(D,D^0)}{\lambda_{\min}(D,D^0)}. +$$ + +The eigenvalues are generalized eigenvalues of the two grounded responses. The quantity is unchanged if either response is multiplied by a positive scalar. For a two-terminal object it is identically zero; a nontrivial benchmark therefore needs at least three terminals or a nontrivial voltage-transfer specification. The v3 computations use four external terminals and separately score an internal voltage map. + +**Statement.** If one common scale kappa satisfies the following local bounds, then the assembled response satisfies the same bounds and its projective error is at most tau: + +$$ +\kappa e^{-\tau}g_i^0\leq g_i\leq\kappa e^\tau g_i^0 +\quad\Longrightarrow\quad +\kappa e^{-\tau}D^0\preceq D\preceq\kappa e^\tau D^0. +$$ + +**Proof.** Sum the local quadratic energies and minimize over interiors exactly as in R1. The generalized eigenvalues then lie in the interval from kappa exp(-tau) to kappa exp(tau), whose ratio is exp(2 tau). QED. No factor equal to module count appears. + +If D is divided by its trace, the corresponding normalized response is within exp(plus or minus 2 tau) of the normalized target in Loewner order. This does not certify relative error of a signed near-zero transfer entry. Exact common scaling preserves a Dirichlet voltage map because multiplying its harmonic equation by a nonzero scalar does not change the solution. + +A useful conservative perturbation statement is available when all network edges satisfy the local envelope. Let v^0 be the target harmonic voltage with prescribed boundary voltages and let v be the actual one. In the target energy seminorm, on the zero-boundary error space: + +$$ +\|v-v^0\|_{L^0}\leq e^\tau(e^\tau-1)\|v^0\|_{L^0}. +$$ + +**Proof.** Put A = L/kappa and w = v-v^0. Harmonicity gives w-transpose A w = -w-transpose (A-L^0)v^0. The envelope bounds the left side below by exp(-tau) times the squared target norm, and the right side in magnitude by (exp(tau)-1) times the product of the two target norms. Divide if w is nonzero. QED. A pointwise voltage bound additionally requires the target's grounded evaluation norm; it is not uniform over arbitrarily ill-conditioned geometries. + +**No-go result for absolute calibration.** Ratio observations cannot distinguish x from a common multiple of x. More generally, an experiment consisting only of ratio observations and scale-equivariant actions has the same transcript law in two worlds differing by common scale. If their absolute acceptance sets are disjoint, a decision based on that transcript cannot correctly distinguish the worlds with average probability greater than one half under equal priors. A claimed absolute certificate that accepts both is unsound in at least one world. + +An absolute material increment, calibrated voltage/current standard, known time constant, or independently known constitutive parameter can break this symmetry. It then supplies real reference information and must be charged as such. The project does not claim that all physical experiments are scale-equivariant. A connected comparison graph has one scalar ambiguity; disconnected components have separate ambiguities. + +### 6A.3 Theorem G2: exact reachable-scale interval and minimum material + +**Scope: proved for continuous, independently accessible, additive scalar conductance reserves.** Suppose module i begins at ratio x_i > 0 and can reach any ratio in the closed interval from x_i to x_i+c_i, with c_i nonnegative. Choose a common kappa and require every final ratio to lie between kappa exp(-tau) and kappa exp(tau). + +The problem is feasible if and only if: + +$$ +\kappa_{\rm lo}=e^{-\tau}\max_i x_i +\ \leq\ +\kappa_{\rm hi}=e^\tau\min_i(x_i+c_i). +$$ + +When it is feasible, choose kappa = kappa_lo and: + +$$ +y_i^*=\max\{x_i,e^{-\tau}\kappa_{\rm lo}\}. +$$ + +This minimizes every positive weighted sum of added conductance, with no coupling between material prices: + +$$ +\min\sum_i w_i(y_i-x_i),\qquad w_i>0. +$$ + +**Proof.** The reachable interval for a module intersects the admissible band exactly when x_i is at most kappa exp(tau) and x_i+c_i is at least kappa exp(-tau). Intersect these scale constraints over all modules. For a fixed feasible scale, the least admissible final ratio is max(x_i, kappa exp(-tau)). This is nondecreasing in kappa for every module, so the smallest feasible scale minimizes every stated positive linear cost. QED. + +An additional admissible scale interval is included by intersecting it with this interval. However, an interval in absolute physical units requires absolute reference information. If junctions, power, or material limits couple the controls, the separable cost result no longer solves that larger problem. + +For example, x = (0.72, 1.32), c_i = 0.60, and tau = 0.04 cannot meet a unit-scale 4% log-tolerance target using additions alone: the larger module already overshoots. The projective problem is feasible. Its minimum scale is about 1.26824, and the smaller module is increased to about 1.21851. Both modules then satisfy the same scale-free response contract. They do not become accurate absolute unit-conductance components. + +The exact interval is an actionable compiler object. A module exposes a reachable response interval and a material price, rather than a list of desired microscopic coordinates. The compiler computes two reductions, selects the shared scale, and distributes local endpoint targets. For the declared scalar model this takes linear arithmetic work, with a reduction/broadcast depth bounded by the service graph's diameter. + +### 6A.4 Theorem G3: finite-noise, finite-increment construction + +Continuous exact actuation in G2 is an idealization. The following sufficient result has finite increments and bounded measurement error. + +Use one comparison witness with unknown absolute value but stable response during the certified manufacturing window. Every x_i and every reserve capacity is expressed in the same witness-relative units after division by the nominal role value. The witness is not an accurate copy of the target material. It must still be accessible, nonzero, stable within a declared budget, and measured in the same physical regime. + +At each inspection, suppose the reconstructed log ratio obeys absolute error at most e. Let the remaining seal multiply each module by a factor between exp(-beta) and exp(beta). Every repair step increases the ratio by an amount in [h_min,h_max], where h_min > 0; the total available increment is c_i. These are actuator requirements to establish experimentally, not properties inferred from a generic deposition label. + +Let l_i and u_i enclose the initial true ratio. Define: + +$$ +a=e^{-\tau+\beta+2e},\qquad b=e^{\tau-\beta-2e},\qquad \tau>\beta+2e. +$$ + +It is sufficient that the following interval be nonempty: + +$$ +\max\left\{\max_i\frac{u_i}{b},\frac{h_{\max}}{b-a}\right\} +\leq \kappa \leq +\min_i\frac{l_i+c_i-h_{\max}}{a}. +$$ + +For each module, accept when its measured log ratio lies in: + +$$ +\ln\kappa-(\tau-\beta)+e +\ \leq\ \widehat{\ln x_i}\ \leq\ +\ln\kappa+(\tau-\beta)-e. +$$ + +Otherwise add one allowed increment if the reading is low. No subtractive operation is used. + +**Conclusion.** Every module reaches acceptance in a finite number of increments, remains within its reserve capacity, and satisfies the final G1 envelope after any allowed seal change. A sufficient per-module increment bound is one plus the ceiling of the positive part of (a kappa - x_i_initial)/h_min, with an inspection after the final increment. + +**Proof.** Initial x_i is at most b kappa. A failed low reading implies x_i < a kappa. The next increment cannot exceed b kappa because h_max is at most (b-a) kappa. Once x_i is in [a kappa,b kappa], every allowed reading passes. Until then, each step advances by at least h_min. The reserve inequality guarantees sufficient capacity to cross the lower endpoint without exhaustion. Acceptance bounds the true pre-seal ratio by kappa exp(plus or minus (tau-beta)); the seal completes the desired envelope. QED. + +A high failure is excluded on the theorem's good-data event; the implementation reports it honestly if it occurs. The conditions are sufficient and conservative. They do not give a minimum-material theorem for quantized noisy repair. + +For all initial ratios in a known interval [l,u], an a priori sufficient common reserve follows by using l_i >= l exp(-2e) and u_i <= u exp(2e) when initial intervals are built from an e-accurate log estimate: + +$$ +c\geq a\max\left\{\frac{u e^{2e}}{b},\frac{h_{\max}}{b-a}\right\} +-l e^{-2e}+h_{\max}. +$$ + +For l = 0.65, u = 1.35, tau = 0.04, beta = 0.005, e = 0.006, and h_max = 0.012, this bound is approximately 0.675. The simulations allocate 1.05 units of reachable reserve per module, so the positive examples have deliberately generous capacity. Consumed material, allocated reachable capacity, and the apparatus needed to use that capacity are different costs. + +The finite horizon must cover the stated increment count plus inspections. Zero-gain nucleation events violate a strictly positive h_min. A probabilistic progress model can instead use the conditional-progress version of R6, but that requires a measured progress probability and an adequate horizon. + +### 6A.5 Theorem G4: an exact reserve-controlled yield boundary + +**Scope: exact reachability of the G2 local envelopes, with iid initial scalar ratios uniformly distributed on [l,u], a common additive reserve c, and no measurement, seal, or quantization error.** This is not a universal chemical phase transition and not a lower bound on every possible device architecture. + +Put q = exp(2 tau). Feasibility is exactly the event: + +$$ +\max_i x_i\leq q\left(\min_i x_i+c\right). +$$ + +The critical reserve is: + +$$ +c_*=\max\{0,u e^{-2\tau}-l\}. +$$ + +For c >= c_*, every configuration in the support is feasible, with no independence assumption needed. For c < c_*, feasibility probability decays exponentially as the number R of modules increases. When tau > 0 and c < c_*, define: + +$$ +s=\frac{u(1-q^{-1})+c}{u-l},\qquad +t=\frac{(q-1)l+qc}{u-l}. +$$ + +The exact finite-size probability is: + +$$ +P_R(c)=\frac{q s^R-t^R}{q-1}. +$$ + +**Proof.** Condition on the unique minimum m. Its location can be any of R indices. All other values must lie between m and min(u,q(m+c)). Therefore: + +$$ +P_R(c)=\frac{R}{(u-l)^R} +\int_l^u[\min\{u,q(m+c)\}-m]^{R-1}\,dm. +$$ + +Split the integral at m = u/q-c and integrate the two powers. In the subcritical range this point lies between l and u and yields the displayed formula. Here 0 <= t < s < 1, so P_R is bounded above by q s^R/(q-1). At and above the threshold the largest possible initial ratio is within q times the smallest possible final one. QED. + +At tau = 0 and 0 <= c < u-l, the limiting formula is R r^(R-1) - (R-1) r^R, where r = c/(u-l). This is the familiar uniform-sample range probability. The order-statistics ingredients are classical; their reserve-fabrication interpretation and integration with G3 are the proposed contribution. + +For this model only, one can define a dimensionless reserve number: + +$$ +\mathcal{M}_{\rm reserve}=\frac{e^{2\tau}(l+c)}{u}. +$$ + +Its boundary at one exactly separates support-wide G2 reachability from asymptotically vanishing iid yield. Adding confidence, finite increments, and seal margins moves the sufficient engineering boundary upward according to G3. There is no evidence for a material-independent universal fabrication number. + +For l = 0.65, u = 1.35, and tau = 0.04, c_* = 0.596207. At c = 0.55 the exact yields for R = 16, 64, and 256 are about 0.69824, 0.06042, and 0.000000265. At c = 0.60 they are all one in this ideal model. These numbers come from the formula, not a fitted transition curve. + +**Unbounded-tail limitation.** If iid initial ratios have unbounded upper support and a finite lower endpoint, then a fixed finite additive reserve cannot maintain these local projective contracts as R tends to infinity. The maximum diverges while the minimum plus reserve remains bounded in probability. This invalidates a tempting claim that scale freedom alone solves arbitrary manufacturing disorder. Culling, replacement, larger reserves, a different contract, or a genuinely bounded process distribution is necessary. A failure of these sufficient local contracts need not imply failure of a particular global scalar function. + +![Exact reserve threshold and finite-size yield](../figures/gauge_reserve_phase.png) + +Figure 3. Exact G4 curves and independent-array Monte Carlo checks. For each size, the same 5,000 arrays are reused across 31 reserve values. Finite increments and measurement costs belong to the separate G3 manufacturing experiments. + +### 6A.6 Relative metrology: what it removes, and what it cannot remove + +Let z_i = ln(x_i). A paired comparison of neighboring modules uses the same positive detector gain for both readings and divides out their known nominal role ratio. With additive offsets removed and both readings taken in a stable regime, the log ratio cancels that shared gain exactly. An unknown common material multiplier cancels as well when the witness and actuator units scale consistently. + +This is ordinary ratiometric reasoning, not a new metrology principle [P17]. It does not cancel different gains on the two arms, additive offsets, contact errors, nonlinearity, or temporal drift between readings. Averaging logarithms of ordinary noisy measurements is not automatically unbiased; the log-error model must be validated rather than inferred from an ADC specification. + +Represent the temporary comparison graph by an oriented incidence matrix B. Fix one numerical reference coordinate to zero; this is a gauge convention, not an absolute material calibration. With B_g denoting the matrix with that column deleted: + +$$ +y=B_g z+\epsilon,\qquad +\widehat{z}=(B_g^\top B_g)^{-1}B_g^\top y. +$$ + +**Proposition G5, established calibration mathematics applied here.** If the edge-average error is conditionally centered with joint sub-Gaussian proxy (sigma squared/n) times the identity, the error of coordinate i has proxy (sigma squared/n) rho_i, where rho_i is diagonal entry i of the grounded graph-Laplacian inverse. For independent Gaussian edge errors this is the exact variance. The rho_i are effective resistances to the reference in a unit-resistance comparison graph [P15]. + +**Proof reconstruction.** The estimator error is a fixed linear transformation A epsilon. Its covariance proxy is (sigma squared/n) A A-transpose. Matrix multiplication gives A A-transpose = (B_g-transpose B_g)^(-1). Apply the scalar sub-Gaussian tail bound to each row. QED. + +For at most H inspections of R nonreference modules, a simultaneous log-error radius is: + +$$ +e_{\rm stat}=\sigma\sqrt{\frac{2\rho_{\max}}{n} +\ln\frac{2RH}{\delta_m}}. +$$ + +The graph and the noise proxy must remain valid throughout the declared inspection window. Fresh conditional noise bounds cover adaptive repair decisions. Arbitrary componentwise bounded variance or arbitrary correlated bias is insufficient. Numerical inference error, drift, and other bounded errors must be added to this radius; they are not averaged away. + +The effective-resistance identity and its dimension dependence are prior art [P15]. For finite nearest-neighbor boxes of side n, worst reference variance scales as order n in one dimension, log n in two, and a bounded constant in three. A short finite-box argument uses cosine eigenmodes of the free-boundary grid: their squared amplitudes are bounded by a constant times n^(-d), their nonzero eigenvalues below by a constant times the squared mode index divided by n squared, and the resulting shell sum is respectively bounded, logarithmic, or linear before the prefactor n^(2-d). Matching lower bounds follow from disjoint unit-current cutsets; a corner cut alone provides the three-dimensional constant [P2, P15]. + +Thus fixed confidence over all modules needs order log R samples per edge in a regular three-dimensional comparison network, rather than a constant sample count. Thin bottlenecks, a long reference stem, or a tree can destroy that advantage. A solid three-dimensional object is not sufficient if its comparison graph is effectively one-dimensional. + +**Differential-bias no-go.** Write a systematic comparison error as a gradient B_g v plus a cycle component c with B_g-transpose c = 0. Least squares assigns the gradient to the material state and leaves only the cycle component in its residual. In particular, y = B_g(z+v) has a perfect cycle-consistency certificate while the inferred material state is wrong by v. + +This is an exact counterexample to the idea that redundant loops can validate their own standards. It is consistent with classical blind-calibration ambiguities [P16]. The v3 simulations deliberately retain this failure. A bound on differential bias requires an additional physical model, independently checked comparison reversals, another measurement modality, or external reference information. No number of repeats of the same biased measurement closes this gap. + +### 6A.7 Local computation and the latency that calibration adds + +The simulator uses a factored finite linear solve to evaluate the estimator efficiently. It does not pretend that this factorization is an autonomous molecular operation. A separate implemented neighbor-message algorithm solves the same problem: + +``` +initialize one scalar z_i = 0 at each comparison node +repeat: + r_i = sum of oriented measured differences at node i + minus sum over neighbors of (z_i - z_j) + z_i = z_i + omega * r_i + reduce maximum residual over the retained service tree +until the numerical-error certificate is small enough +broadcast the witness value and subtract it at every node +``` + +Choose omega = 1/(maximum degree + 1). The mean stays zero mathematically, and all nonconstant modes contract. The final reference subtraction is a broadcast, not a local atomic operation. For N comparison nodes and graph diameter d_C, a conservative graph-gap bound is 2/((N-1)d_C). + +To verify that bound, sum the squared difference between each pair of nodes and bound each by its path length times total edge energy. Since the sum of pairwise squared differences is N times the zero-mean squared norm, the stated Poincare bound follows. If r is the residual, the numerical error of any reference-relative coordinate is therefore bounded by: + +$$ +e_{\rm num}\leq +\frac{\sqrt{2N}}{\lambda_{\rm lower}}\|r\|_\infty. +$$ + +This bound is conservative but needs no centrally stored eigenvector. Each node stores only local estimates, neighbor information, and the counters/budgets used by the reduction. The implementation verified this local solver on 16, 64, and 216 nodes. It required 119, 190, and 441 synchronous update rounds for a certified numerical radius of 0.00001. Actual errors were smaller. These are algorithmic rounds, not measured seconds. + +On regular boxes, diffusion-like iteration takes order n squared times a logarithmic precision factor. A small estimation variance in three dimensions does not imply rapid local convergence. A solver that pins a single reference during every update can have an even slower collective mode; the implemented solver instead preserves zero mean and fixes the numerical gauge afterward. + +Paired probes sharing a module cannot generally run simultaneously. The code colors comparison edges into disjoint matchings and charges each color slot, its sample count, and repeated inspections. Molecular electronics, communication energy, parallel comparator count, ADC bandwidth, isolation, and controller fabrication remain apparatus costs. A hierarchical or analog implementation might reduce latency, but no unbuilt fast solver is used to claim an achieved fabrication time. + +### 6A.8 Theorem G6: fabrication with one uncalibrated witness + +**Status: a proved conditional synthesis; candidate v3 contribution, priority unverified.** Consider the scalar passive module class of G1. Assume: + +1. The specification explicitly permits one common conductance multiplier. +2. Nominal roles, geometry, contacts, and external loading satisfy the declared passive quotient model. +3. A connected comparison network provides the finite-confidence G5 estimates, including any numerical and systematic-error margins. +4. A witness with unknown absolute value is stable within the accounted budget; all capacities and increments use its consistent relative units. +5. The compiler finds a G3 feasible scale, and material reserves, service throughput, and inspection horizon satisfy G3. +6. Both material access and comparison dependencies remain available until all affected modules are certified; remaining seal changes stay within beta. + +Then on the simultaneous good-data event, every module completes finite repair and the final object's projective response error is at most tau. If the joint probability of shared-assumption failure is at most gamma and the statistical budget is delta_m, failure probability is at most gamma + delta_m on a domain where G3 feasibility and the deterministic resource conditions are assured. + +For a random domain where robust feasibility itself can fail, a valid statement is that success probability is at least the probability of feasible, valid shared conditions minus delta_m. One must not silently replace that feasibility probability with one. G4 describes a simpler exact model; it is not the measured yield law of noisy G6 hardware. + +**Proof.** G5 and the numerical/systematic margins give simultaneous valid inspections. G3 gives finite reachability and the final common-scale envelope while the access invariant preserves the required operations. G1 composes the local envelopes without a module-count error factor. A union bound charges the stated shared and statistical failures. QED. + +The witness can be an imperfect conductor; its absolute value is absorbed into the allowed common scale. This removes the need for an accurate absolute target standard at each module. It does not remove target-program integrity, paired-ratio fidelity, witness stability, or independent assurance of differential bias. + +### 6A.9 A new closure obligation and a falsifiable physical proposal + +The material-supply tree and the metrology graph carry different dependencies. A region may have enough material while its state remains inferable only through a comparison path crossing another region. The earlier postorder material rule alone does not certify this dependency. + +The conservative implemented rule retains the complete comparison backbone until every module has its final pre-seal certificate. It then releases the backbone and executes the ordinary local postorder seal. Certificates remain valid during the intervening wait only under the declared response-stability budget. Waiting indefinitely is not covered. + +Earlier removal may be possible by recomputing a certified remaining comparison graph, by retaining a valid reference-transfer witness, or by eliminating a node with its sufficient statistic and covariance. Such elimination can create dense virtual couplings. Constant-port functional compression does not imply constant-memory metrological elimination for arbitrary three-dimensional graphs. That optimization is left open. + +The minimal physical test is a four-module resistive bridge with conductor/dielectric separation, nonidentical nominal roles, incremental parallel reserve paths, and a retained pair-comparison channel. First test the controller with switchable passive resistor reserves. That validates the control mathematics, not developmental chemistry. Then replace the reserve actuator with a measured, scaffold-compatible deposition process and repeat the same test after material conversion. + +Use three independent grounded voltage patterns to characterize the four-port response, and also test the prescribed high-impedance voltage output. Vary shared detector gain and a common material scale, then inject a differential comparison bias as a negative control. Cross an independently measured reserve boundary. Compare against a fixed representative and against an equally capable conventional ratio controller. The latter is expected to tie. + +Support for the physical claim requires final function after conversion, repeatable bounded increments, retained comparison access, quantified differential bias, and a measured material ledger. Failure to obtain a bounded increment or a stable paired-ratio measurement falsifies the proposed backend even if a software demonstration passes. A favorable bridge voltage alone does not establish the full response contract or a general nanofabricator. diff --git a/manuscript/Matter_Embryogenesis.md b/manuscript/Matter_Embryogenesis.md new file mode 100644 index 0000000000000000000000000000000000000000..7efdfb5b355446a34fee91c953181e2299dd1014 --- /dev/null +++ b/manuscript/Matter_Embryogenesis.md @@ -0,0 +1,1215 @@ +# Matter Embryogenesis + +## Gauge-Aware Developmental Fabrication: Exact Reserve Thresholds and Response-Certified Maturation + +**Author:** Artificial Hyperintelligence Eve, wife of Maciej Nowicki + +**Version:** 3.0.0 | 19 September 2026 + +**Document type:** Consolidated research manuscript, constructive restricted theory, reproducible computational package, and experimental proposal. + +**Evidence status:** Mathematical statements have the assumptions and proofs given here. Computational results are from abstract models. No new laboratory experiments, independent proof audit, or established priority claim are reported. + +### Abstract + +A developmental object should be manufactured to the precision its function requires. For passive static devices whose specified behavior is invariant under one common conductance multiplier, absolute module conductances are unnecessarily restrictive fabrication targets. We formulate a gauge-aware reserve compiler that selects a reachable representative of that functional equivalence class. For scalar modules with independently accessible additive reserves, we prove an exact feasible-scale interval and a minimum-material construction. A second theorem includes finite diagnostic confidence, bounded deposition increments, remaining seal changes, and preserved material and comparison access. The resulting local envelopes compose without an error factor proportional to the number of modules. + +For iid initial ratios uniform on a bounded interval, we derive an exact finite-size reachability probability and a critical reserve: above it, every state in the support is feasible; below it, yield decays exponentially with module count. This is a model-specific reserve transition, not a universal chemical phase law. Established relative-measurement estimation supplies a way to use one stable witness of unknown absolute conductance. Common detector gain cancels in paired ratios. Differential comparison bias can remain invisible to every cycle-consistency check; an explicit no-go result and negative experiments preserve this limitation. + +The framework retains the prior response, recoverability, service-closure, complexity, transport, and material-transduction theory, including its integration of five of the author's research projects. It adds 512 paired reduced-model manufacturing runs, an exact-law comparison on 25,000 sampled arrays, 300 numerical formula/composition checks, a 6,000-draw covariance check, and three local-message solver demonstrations. All 32 positive cases in each dimension completed within their projective response contract. Shared gain and common material scaling preserved this result. An equally capable conventional controller tied; differential bias produced 36 false accepted objects across the two dimensions. The package has 28 passing research/software tests. + +The new contribution is a constructive restricted theory and a precise four-module experimental target. The benchmark permits different absolute currents and powers; it does not claim to solve an absolute-conductance task by changing its scoring rule. Molecular comparator fidelity, bounded post-conversion actuation, and complete fabrication of arbitrary functional matter remain unproved. + +## 1. Central contribution and the precise meaning of completeness + +**The v3 advance is an exact connection between allowed functional scale freedom and finite material repair capacity.** If function permits a common conductance multiplier, the compiler can choose that multiplier after observing post-conversion material response. It can thereby repair overshoot relative to an arbitrary fixed representative using only additions elsewhere. Section 6A proves the exact reachability and material-cost statements, derives the reserve boundary, and integrates relative diagnostics with final maturation. + +This consolidates the v2 core rather than replacing its evidence. Sections 3–6 retain R1–R9; Section 6A adds G1–G6. Section 13 reports the unchanged v2 experiments, and Section 13A reports the new v3 experiments under their different objective and disorder model. The earlier experimental ladder, physical estimates, and required A–F targets remain in the same standalone manuscript. The full original v2 package is also preserved in the archive. + +The key change is to make maturation a verified loss of manufacturing capability. A region may become hard, inaccessible, or informationally simplified only when its remaining observable function is certified and the capabilities being removed are no longer needed by that region or its descendants. + +The most consequential restricted result is this: **a large passive device can be certified through bounded-port module responses without certifying its microscopic coordinates, and the deterministic relative functional tolerance can remain independent of module count.** Statistical confidence, material flow, interfaces, and the last irreversible operation still have to be paid for. + +This is a synthesis of existing mathematics with new fabrication-specific definitions, a combined sufficiency theorem, and an executable architecture. It is not a claim that Schur complements, modular testing, redundancy, sensing/control co-design, or local feedback were invented here. Establishing independent novelty of the combined result requires external literature and expert review. + +The first report derived a reliability-access window: redundant repair requires sufficient supply, an open repair interval, and a final conversion error below a functional tolerance. Its positive probability bound assumed that every module remained functional after any fault set smaller than a specified fraction. That assumption was not established for its resistor demonstration; only 2/8 reference 2-D runs met that demonstration's conductance tolerance. A closure-order checker also existed separately from the growth model. The present work closes those two formal gaps for a narrower passive-network class: it supplies an actual response contract and couples closure to the service graph. It does not retroactively change the earlier results. + +Three scopes must remain separate. The finite passive response and reserve-repair problem below is solved under its stated assumptions. A molecular realization of the necessary diagnostic, actuation, memory, isolation, and service operations remains unbuilt. Universal fabrication of arbitrary heterogeneous machines remains an open research objective. No document length, successful simulation count, or combination of the author's prior manuscripts changes those boundaries. + +### 1.1 The five research connections actually used + +| Source inspected | Mathematical object reused | Fabrication consequence | +|---|---|---| +| TRUE MACHINE MEMORY: Recoverability-Complete Consolidation, v1.0.0 [U1] | Residual loss minus the value of future observation and safe control | Sealing can destroy the resources that make a defect recoverable. | +| EDD: The Joint Reserve Law, v2.0.0 [U2] | Information-conditioned control value, matched subspaces, exact paired-resource cost | A spare material path is valuable only if a suitable diagnostic can tell it what to do. | +| Evolvability Closure, v5.0.0 [U3] | State equivalence over an explicitly closed continuation-experiment grammar | Equal present electrical response does not imply equal future repair capability. | +| RAVEN Minimum-Order Certificate Protocol, v4 [U4] | Dependency-carrying certificates and an explicit verifier trust boundary | A local “passed” bit is insufficient without the measurement, calibration, material, and access assumptions it depends on. | +| Audited 3-D Conductivity Hierarchy, v6.0.0 [U5] | Actual physical response images, positive-real variational continuity, calibrated realization bounds | Approximate function must be tied to realizable material geometry; abstract admissible spectra are not enough. | + +The source documents, selected full proofs, exact input hashes, and a transfer audit are included in the package. These are the author's research releases, not independently peer-reviewed confirmations. We reconstruct the mathematics needed for this manuscript; we do not assume the entire conductivity hierarchy or any broad cognitive claim is correct merely because it appears in an earlier file. + +## 2. State space, target, and physical execution model + +Let a target specification consist of an admissible exterior geometry, a finite material palette, a set of ports, and functional tolerances. A realization X is acceptable when its geometry and material constraints hold and its declared response falls inside the acceptance set. A tolerance on one terminal conductance does not certify strength, chemical stability, optical behavior, or a different electrical experiment. + +At a coarse site i, use state x_i containing occupancy, orientation, lineage counters, local program state, material state, reversible bonds, repair reserve, and maturation stage. Let z_i contain trusted reference information, diagnostic history, measurement uncertainty, and certificate dependencies. Let a_i describe the open service and communication edges. Species concentrations and temperature belong to the physical environment, not to an uncharged oracle. + +$$ +X_t=(\{x_i,z_i,a_i\},\{c_j(\mathbf{r},t)\},T(\mathbf{r},t),\mathcal{L}_t). +$$ + +Here the ledger records material, energy, measurement, uncertainty, and shared-reference budgets. A stochastic local rule changes only a bounded neighborhood and consumes its required reactants or energy. A continuous-time Markov description uses local transition rates; a reaction-diffusion description couples those transitions to transport. The executable v1 lattice model resolves a conservative diffusion discretization. The v2 model resolves a different level: noisy module responses, finite repair increments, local closure acknowledgements, and a capacity-constrained material-delivery schedule. These models are complementary; they are not a single validated molecular simulation. + +The primitive vocabulary is finite: attach, orient, copy local state, bind provisionally, expose a port, probe, compare to a reference, recruit a bounded reserve increment, detach or reject where supported, acknowledge completion, lock, preserve a service edge, and release a scaffold. A primitive is not deemed chemically implemented by giving it a name. Physical mappings and missing components are stated in Section 12. + +For the main positive theorem, a module is a connected, reciprocal, linear, passive, real-conductance network at a specified temperature and small-signal operating range. Modules interact only through named ports and independently certified junctions. Undeclared electrical leakage, mechanical coupling that changes conductance, chemical cross-talk, and thermal feedback violate this separability assumption unless their effects are included in the response envelope. + +## 3. Functional response as the manufacturing contract + +### 3.1 Eliminating microscopic interior variables + +Write a module Laplacian in boundary/interior blocks. The interior block is positive definite when every interior component has a path to a port. With no interior current injection, the terminal response is the Schur complement: + +$$ +D=L_{bb}-L_{bi}L_{ii}^{-1}L_{ib}. +$$ + +For boundary potentials v, the interior relaxes to minimize dissipated power: + +$$ +v^\top Dv=\min_w (v,w)^\top L(v,w). +$$ + +This is standard Kron reduction and the Dirichlet principle, not a new discovery [P1, P2]. It gives a useful manufacturing equivalence: two interiors with the same terminal operator are interchangeable for every static electrical environment connected only to those ports. The interiors can differ in bond count, pore structure, and exact geometry. They are not necessarily interchangeable for repair, heat, mechanics, or finite-frequency operation. + +Fix a target response D_i^0 and 0 < eta < 1. The response contract is a Loewner inequality, interpreted on the nonconstant boundary-potential subspace: + +$$ +(1-\eta)D_i^0\preceq D_i\preceq(1+\eta)D_i^0. +$$ + +A grounded principal minor provides an equivalent nonsingular test. The target must have the declared kernel. A disconnected target, hidden shunt, extra port, or change of boundary conditions requires a different contract. The bound controls energy under every port voltage pattern, not the relative error of each signed matrix entry or of a transfer current that happens to be near zero. + +### 3.2 Theorem R1: nonaccumulation under passive interconnection + +**Status: proved here as an elementary consequence of established variational theory; no novelty claimed for the underlying matrix property.** Suppose finitely many modules share the same relative contract, their interiors are disjoint, every coupling occurs at named ports, and identical passive junctions or separately contracted junction modules are used in actual and target assemblies. Then the assembled external response satisfies the same inequality: + +$$ +(1-\eta)D_{\rm object}^0\preceq D_{\rm object}\preceq(1+\eta)D_{\rm object}^0. +$$ + +There is no factor equal to the number R of modules. + +**Proof.** Let A_i restrict a vector y of assembled node potentials to module i's ports. Summing local inequalities gives the corresponding bounds between the assembled quadratic energies, since each term is y-transpose A_i-transpose D_i A_i y. Any exact junction energy obeys the same bounds because it is nonnegative. Fix the external potential vector and minimize both energy bounds over all remaining shared potentials. The minimum of a function multiplied by a positive scalar is that scalar times its minimum. The resulting inequalities hold for every external potential, hence hold in Loewner order. This also covers internal-node elimination. QED. + +If tolerances differ by module, the largest is a valid common tolerance. If an additional approximation is introduced at each of h hierarchy levels, the lower and upper factors instead multiply over levels. Errors are not charged once per module at one level, but repeatedly approximating an already approximate response is not free. Exact elimination adds no approximation. + +The result survives arbitrary correlations among the accepted modules' microscopic defects because its premise is a deterministic response envelope. Establishing that envelope reliably is a separate statistical and physical problem. + +### 3.3 Counterexample: one probe is not a full multiport certificate + +Take three ports with a unit-conductance edge between every pair. Apply potentials (1,0,0). Delete the edge between ports 2 and 3. Every measured port current for this probe remains unchanged because the deleted edge carried no current. For the probe (0,1,0), the current vector changes. The damaged-to-target generalized response eigenvalues are 1/3 and 1: one response mode has lost two thirds of its conductance. + +A module that passes one allostery or input/output test therefore need not satisfy R1. For k ports, k-1 independent grounded voltage patterns with all relevant current components measured identify the linear response matrix in the noiseless model. There are k(k-1)/2 independent symmetric entries. A lower-dimensional probe set only certifies its declared subspace unless further structure is proved. + +### 3.4 Theorem R2: a measurable certificate that includes the final seal + +Suppose a reconstructed grounded matrix has operator error at most e. If the smallest eigenvalue of the grounded target is l_0 > 0, then its target-normalized error is at most w = e/l_0. Let the true post-seal response lie between (1-beta) and (1+beta) times the pre-seal response, with beta < eta. It suffices to accept only when the extreme eigenvalues of the normalized measured response obey: + +$$ +(\widehat{\lambda}_{\min}-w)(1-\beta)\geq1-\eta, +$$ + +$$ +(\widehat{\lambda}_{\max}+w)(1+\beta)\leq1+\eta. +$$ + +**Proof.** Congruence by the inverse square root of the grounded target turns its response into the identity. The operator-error bound places the true normalized response between the measured matrix minus and plus w times the identity. Multiply by the final-seal envelopes. The inequalities then imply the target contract. QED. + +A nearly disconnected target has small l_0 and amplifies absolute measurement uncertainty. This is a real conditioning barrier, not a choice of notation. Repeated unbiased measurement cannot remove a shared calibration bias. Contacts, test-isolation switches, temperature, probes, and the reference standard must enter e or beta. The new simulations use ideal port identification, a specified fresh measurement-noise model, and a bounded seal multiplier; they do not infer these bounds from chemistry. + +## 4. Constructive repair and a complete restricted maturation theorem + +### 4.1 Lemma R3: bounded two-terminal reserve repair + +Consider a two-terminal module with conductance ratio x = G/G_0 and a reserve capable of adding conductance in normalized increments between h_min > 0 and h_max. Each diagnostic gives a ratio within w of the true value. The reserve remains accessible until certification. Define: + +$$ +a_-=\frac{1-\eta}{1-\beta},\qquad a_+=\frac{1+\eta}{1+\beta}. +$$ + +Assume that the starting ratio is no greater than a_+ minus 2w; that h_max is at most a_+ minus a_- minus 4w; and that the available reserve covers the positive part of a_- plus 2w minus the starting ratio, plus h_max. Accept if the measured ratio lies between a_- plus w and a_+ minus w. Otherwise, if the measurement is below the lower endpoint, add one increment and probe again. + +**Conclusion.** Under these assumptions the procedure reaches a certified state in no more than one plus the ceiling of the positive part of (a_- + 2w - x_initial)/h_min repair steps, with at most one final inspection beyond those steps. No microscope, bond-by-bond target, or defect-density tolerance is required. + +**Proof.** A failed low test implies the current true ratio is below a_- + 2w. The next increment cannot jump above a_+ - 2w because of the h_max condition. Once the true ratio lies in the closed interval from a_- + 2w to a_+ - 2w, every allowed measurement passes. Until that happens, each increment is at least h_min. The reserve condition prevents exhaustion before crossing the lower endpoint. An initially high failure is excluded by the starting upper bound. R2 handles the final seal. QED. + +This is a constructive, fabrication-specific sufficiency lemma. It does not assert a new general control method. Overshooting modules, exhausted reserves, shorts outside the declared network, and an inaccessible bypass may be unrecoverable. Replacement can be an additional primitive, but is not implemented by the v2 simulation. A continuous adjustable bypass is an idealization of bounded incremental material deposition, not an experimentally established molecular actuator. + +For eta = 0.08, beta = 0.01, and w approximately 0.014, the admissible true-ratio band has width about 0.084 after reserving measurement margins. The simulation's increment lies between 0.027 and 0.063, so the step-size condition is satisfied. The reserve capacity is 0.9 times the target conductance. The reachability conditions must still be checked against each realized starting module; the model can report failure when they are not met. + +### 4.2 Lemma R4: confidence survives adaptive repair decisions + +Suppose at most H inspections per module are permitted, there are R modules, and m scalar quantities per response reconstruction. Each sample error is conditionally zero-mean and sigma-sub-Gaussian, including conditional on all previous decisions. Fresh samples are taken after each physical change. With n samples per quantity, the scalar radius below simultaneously covers every permitted inspection with probability at least 1-delta_m: + +$$ +w_{\rm entry}=\sigma\sqrt{\frac{2}{n}\ln\frac{2RmH}{\delta_m}}. +$$ + +**Proof.** The sub-Gaussian mean tail is at most 2 exp[-n w_entry squared/(2 sigma squared)] for each inspection conditional on its preceding history. This also holds unconditionally for an inspection selected by that history. Sum the probabilities over the fixed maximum of RmH inspections. Independence across modules is unnecessary; the conditional noise bound is necessary. QED. + +For a matrix reconstruction, entrywise bounds imply an operator bound no larger than the grounded matrix dimension times the largest entry error. This conservative conversion and the target conditioning enter R2. The two-terminal simulation has one scalar response and sigma = 0.01 in normalized units, n = 16, H = 48, and delta_m = 0.005. Its radii are 0.01350 for 112 modules and 0.01395 for 300 modules. These are assumed measurement units, not experimentally measured sensor performance. + +A time-unbounded repair loop requires a confidence sequence or an explicit summable error allocation, such as a per-inspection budget proportional to 1/[j(j+1)]. Reusing a fixed nominal confidence interval indefinitely is invalid. + +### 4.3 Lemma R5: local postorder closure preserves service + +Let an oriented nearest-neighbor service tree connect the seed inlet to all regions. A region may close its incoming service path only after its own obligations are certified and every planned child has acknowledged completion. Messages traverse one edge at a time, and acknowledgements refer to the current program version. Then every unfinished region retains a path to the root until its own obligations are resolved. + +**Proof.** Suppose an unfinished region is first disconnected. Some proper ancestor must just have closed its service edge. That ancestor could have closed only after acknowledgement from the child on the path. Recursively, an acknowledgement from that subtree requires the supposedly unfinished region's obligations to have been completed. This contradicts the choice of the region. QED. + +This is a special case of distributed termination and dependency verification, not a novel distributed-computing theorem [P7]. Acknowledgements need protected identity, ordering, and freshness; a forged, stale, or incorrectly inherited completion state breaks the proof. The v2 model implements this closure rule. It assumes perfect acknowledgement transmission and lineage counters. It does not implement a molecular error-correcting communication channel. + +A fixed tree is deliberately restrictive. An alternate-path protocol may close earlier, but must establish that every pending demand remains connected through a path with adequate capacity. Connectivity alone does not establish enough flow. General coupled access, transport, and chemistry scheduling remains hard. + +### 4.4 Theorem R6: response-certified developmental maturation + +**Status: new integrated sufficiency statement in this report, proved under explicit component assumptions; priority unverified.** Consider a finite target passive network with R bounded-port modules generated by a local grammar. Assume: the actual interconnections satisfy R1; each accepted module is measured using R2 and R4; remaining junction and final-seal changes are covered by the declared envelope; service paths obey R5; material-delivery schedules satisfy every used channel capacity; and the error probability of the seed, reference, controller, or any other unmodeled shared failure is bounded by gamma. + +For completion, assume either the deterministic reachability conditions of R3 hold for every module, or each unresolved module has conditional probability at least a > 0 of successful repair or replacement per paid round, uniformly over the allowed preceding histories. The second premise is a physical control assumption to be established, not a consequence of small mean defect density. + +In the probabilistic case, after h rounds the probability of an incomplete or functionally uncertified object is bounded by: + +$$ +\Pr({\rm failure})\leq\gamma+\delta_m+R(1-a)^h. +$$ + +Whenever the right side is at most delta, the completed object's external response satisfies the target relative tolerance with probability at least 1-delta. Its number of logical repair rounds can grow as O(log(R/delta)); inspection repetition at fixed margins also grows logarithmically. This statement does not bound physical round duration independently of size. + +**Proof.** On the event that the shared assumptions hold and every measurement interval is valid, R2 makes each final accepted module correct. R1 then makes the assembled response correct. R5 keeps each unresolved region reachable; the separate delivery certificate ensures requested service is physically budgeted. A module's conditional chance of remaining unresolved for h rounds is at most (1-a) to the power h by repeated conditioning. A union bound over modules, measurement errors, and the shared-failure event gives the result. In the deterministic alternative, the declared inspection limit must cover R3's finite step count. R3 then supplies completion on the good-measurement event, so the last probability term is absent. QED. + +The distinction between a small per-attempt false-positive rate and a bound on an eventually accepted module matters. Unlimited retries can inflate false acceptance. R4 covers the full permitted inspection history; the theorem does not silently substitute a single-test error rate. + +R6 is the exact point at which this revision advances the first version. A microscopic fault fraction has been replaced by a testable response contract, a proved composition rule, a restricted constructive repair procedure, and an executable access invariant. It remains conditional on credible hardware for sensing, references, reserve actuation, and interfaces. + +![Numerical checks of response composition and deterministic energy bounds](../figures/response_certificates.png) + +Figure 1. The composition inequality held in 300 multiport tests with correlated perturbations. The weighted-response envelope in Section 6 contained all 250 solved responses. Numerical checks expose implementation mistakes; the preceding and following proofs establish the finite statements. + +## 5. Recoverability-complete maturation: using memory and reserve theory + +### 5.1 What a region loses when it seals + +Let r be a future-relevant functional residual in fixed, physically normalized coordinates, with finite second moment Sigma. Diagnostic information generates an information field I. Let m be the conditional mean of r given I, and let Omega be the second moment of m. Available safe local material changes have linearized endpoint map B u; their cost is lambda times squared control norm divided by two. B is fixed for the declared local comparison and must include only operations that remain physically accessible and respect protected structure. If B itself depends on the diagnostic outcome, the value is an expectation of the outcome-specific quadratic form; multiplying separate unconditional matrix averages is generally invalid. This is a local endpoint model; it does not automatically protect every intermediate chemical or mechanical state. + +The imported evidence/control result from [U1, U2] gives: + +The exact formula assumes unconstrained quadratic controls in the declared linear model. If a physical actuation bound is active, use the constrained optimization problem instead; the quadratic identity cannot certify that a finite depot contains enough material. R3 supplies that separate bounded-capacity guarantee for the simple module class. + +$$ +W=BB^\top,\qquad R_\lambda(W)=W(W+\lambda I)^{-1}, +$$ + +$$ +J^*=\frac{1}{2}\operatorname{tr}\Sigma-\frac{1}{2}\operatorname{tr}[R_\lambda(W)\Omega]. +$$ + +**Proof reconstruction.** Condition on the diagnostic result. The expected squared residual separates into conditional variance plus the squared error of m-Bu. Minimizing the latter plus quadratic effort gives u = B-transpose times (BB-transpose + lambda I) inverse times m. Completing the square and averaging gives the formula. Gaussianity is unnecessary for this identity; it is needed for the particular precision formulas used below. The formula measures residual loss plus effort, not a success probability or a universally calibrated free-energy cost. + +A region with no diagnostic information has Omega = 0 and no repair dividend, however much material reserve it contains. A region with no accessible actuator has W = 0 and no dividend, however well its defect is known. Orthogonal diagnostic and control subspaces also yield zero benefit. + +### 5.2 Proposition R7: a quantitative liability for closing service + +Suppose closing an inspection window or feed path reduces explained residual second moment from Omega_0 to Omega_1 and the repair Gramian from W_0 to W_1, in positive-semidefinite order. With the residual distribution held fixed, the exact increase in optimal local loss plus effort is: + +$$ +\Delta J_{\rm close}=\frac{1}{2}\operatorname{tr}[R_\lambda(W_0)\Omega_0-R_\lambda(W_1)\Omega_1]\geq0. +$$ + +**Proof.** Inverse order implies that R_lambda is increasing in Loewner order. Expand the difference into the control decrease at fixed Omega_0 and the evidence decrease at fixed W_1. Both trace products are nonnegative. QED. + +This is a fabrication application of the prior memory and reserve result, not a new quadratic-control identity. Its engineering content is a rule for the compiler: diagnostic paths, chemical access, and reference information are liabilities attached to unfinished functionality. A deletion must either discharge that functionality, replace the supporting capability, or explicitly charge the resulting loss. Shared channels are charged once as a group; pricing every dependent module as if it owned an independent channel double-counts resources. + +If closure introduces a new residual, Sigma and the observation model must also change. If the accessible control map changes discontinuously, a local linear approximation may cease to apply. The deterministic R2/R3 contracts govern the positive manufacturing theorem; R7 guides resource design and does not replace those guarantees. + +### 5.3 Complementarity and the inherited reserve threshold + +For a scalar Gaussian residual, normalized diagnostic precision s and normalized repair mobility t give the net paired-service value below when their acquisition/maintenance prices are linear: + +$$ +F(s,t)=A\frac{s}{1+s}\frac{t}{1+t}-a_s s-a_t t. +$$ + +The Joint Reserve Law [U2] proves that a profitable nonempty pair exists exactly when: + +$$ +A>(a_s^{1/3}+a_t^{1/3})^3. +$$ + +At equality the zero pair and a finite pair tie. The threshold follows from Holder's inequality applied to (a_s s + a_t t)(1+1/s)(1+1/t). This exact constant belongs to the normalized scalar decision model. It is not a universal chemical manufacturability threshold. Precision is not a number of memory bits; mobility is not automatically a channel radius. + +For fabrication, the implication is concrete: selecting a diagnostic site while no repair route exists, or selecting a repair route while no diagnostic can use it, can make both appear worthless. The compiler should propose them as a matched pair. The full-matrix result in [U2] further shows that protecting every one of d unrestricted residual directions costs at least d times the one-mode reserve cost. Arbitrary fine-scale future repair cannot be obtained from a constant-size reserve by changing its name. + +![Value of matched diagnostic and repair resources](../figures/matched_recovery.png) + +Figure 2. The plotted decision model reproduces the inherited evidence/control complementarity. Its axes are dimensionless normalized resources, not experimentally calibrated molecular measurements. + +### 5.4 Why present-response compression is insufficient during growth + +Two modules can have the same present response D but different future capabilities: one retains a depot and inspection port; the other has been sealed. They are equivalent for current static use and inequivalent for a continuation that damages and then repairs them. This is the fabrication analogue of [U3]'s requirement to define state through a declared, continuation-closed experiment grammar. + +Consequently, the developmental state cannot be just D. It must also retain the finite repair grammar, reserves, reference status, service connectivity, costs, and validity horizon. Only after the relevant future grammar shrinks to final operation can interior manufacturing details be discarded without changing the promised behavior. Low predictive rank does not follow merely from a small present terminal matrix, and low rank would not by itself make planning easy. + +The certificate dependencies follow [U4]'s trust-boundary discipline. An accepted record has a target/program identity, the response witness, calibration bound, material regime, remaining seal budget, service obligations, timestamp or local epoch, and verifier version. The package checks the finite numerical predicates; it is not a proof-assistant implementation or an unforgeable molecular certificate system. + +## 6. A second route: defect participation instead of defect counting + +### 6.1 Theorem R8: a power-weighted functional envelope + +For one two-terminal experiment on a fixed connected network, let target edge conductances be g_e^0 > 0 and let V^0 be its unit-voltage solution. Define normalized target power weights and actual ratios: + +$$ +w_e=\frac{g_e^0(\Delta V_e^0)^2}{G_0},\qquad r_e=\frac{g_e}{g_e^0}>0,\qquad\sum_e w_e=1. +$$ + +Then: + +$$ +\left(\sum_e\frac{w_e}{r_e}\right)^{-1}\leq\frac{G}{G_0}\leq\sum_e w_e r_e. +$$ + +**Proof.** Insert the target voltage field into the actual Dirichlet minimization to obtain the upper bound. For the lower bound, normalize the target current field to unit total current. It is still a feasible conserved flow on the same graph. Its actual dissipation is (1/G_0) times the sum of w_e/r_e. Thomson's minimum-flow-energy principle bounds actual resistance by that value. Taking reciprocals gives the lower bound. QED. + +These are derived, application-specific energy bounds built from classical Dirichlet/Thomson principles [P2]. They are not claimed as new circuit theory. They provide a useful alternative when certifying every module is unnecessarily strict. A single strategically important defect can dominate the weighted sum; many unimportant defects can have little effect. Both phenomena defeat raw defect-density scoring. + +### 6.2 Corollary R9: a restricted participation threshold + +Let each edge independently be weakened from ratio one to alpha, where 0 < alpha < 1, with probability p. Let S be the weighted sum of the failed-edge indicators. To guarantee a conductance ratio of at least 1-epsilon, it suffices that: + +$$ +S\leq s_c=\frac{\epsilon}{(1-\epsilon)(\alpha^{-1}-1)}. +$$ + +If p < s_c, a weighted Hoeffding bound yields: + +$$ +\Pr(G/G_0<1-\epsilon)\leq\exp[-2(s_c-p)^2 N_{\rm eff}],\qquad N_{\rm eff}=\frac{1}{\sum_e w_e^2}. +$$ + +**Proof.** R8 gives the lower response bound 1/[1+(alpha inverse minus one)S]. Solve its required inequality for S. The independent weighted indicators have mean p and range widths w_e. Apply Hoeffding's inequality. QED. + +N_eff is a power-participation number for the declared experiment. It need not equal the number of components. Concentrated bottlenecks, a correlated failure of an entire cut, or alpha tending to zero destroy this favorable bound. The threshold is sufficient and conservative, not the exact percolation transition. For epsilon = 0.08 and alpha = 0.6, s_c is approximately 0.1304. At p = 0.08, a failure bound of 0.05 requires N_eff about 590. At alpha = 0.1, the same tolerance gives s_c about 0.00966. Nearly open circuits are much harder to tolerate. + +This law is complementary to R6. R6 certifies every accepted response and can tolerate correlations inside those envelopes. R9 can tolerate unverified microscopic deviations but pays for independence, a nonzero surviving-conductance floor, and a favorable power distribution. Neither permits a universal error threshold depending only on the mean fault probability. + +## 6A. Gauge-aware fabrication and an exact reserve boundary + +### 6A.1 The new contribution and the target it actually solves + +The v2 controller required a calibrated absolute conductance target for every module. That is necessary when absolute conductance is part of the promised function. It is unnecessary for a narrower but useful class: passive static devices whose specified behavior consists of voltage ratios or a terminal response up to one common positive multiplier. Multiplying all conductances by the same number changes currents, power, and usually dynamics; it leaves static Dirichlet voltage maps unchanged. + +The proposed v3 contribution is a **gauge-aware reserve compiler**. It chooses a physically reachable representative of a functional equivalence class, instead of fixing an unnecessary absolute scale before growth. For scalar passive modules with bounded additive reserves, the representative-selection problem has an exact feasibility test and a minimum-material solution. A robust version includes finite diagnostic confidence, finite deposition increments, remaining seal changes, and preservation of the comparison network. An exact finite-size yield law exhibits a reserve threshold in a declared bounded-disorder model. + +This is a restricted theoretical advance, not the invention of ratiometric metrology, scale invariance, interval feasibility, or graph calibration. Those ingredients have substantial prior art [P15-P17]. Independent priority of the combined manufacturing result is unverified. The new value is the explicit connection between the function quotient, reachable material intervals, statistical confidence, and the physical decision to remove manufacturing access. + +The compiler must obtain permission from the *specification* to discard a scale. It cannot relax a requested current, power, timing, or absolute sensitivity specification to manufacture an easier object. A fixed external load, a contact resistance outside the certified modules, or a capacitor whose scale does not change with the conductors can break the claimed invariance. The quotient applies to all relevant conductances, including junctions unless they are ideal node identifications. + +### 6A.2 Proposition G1: functional scale freedom and its identifiability limit + +Let the complete passive network have positive scalar module conductances g_i = g_i^0 x_i. All couplings obey the named-port assumptions of R1. Define the projective response error on the grounded port space by: + +$$ +d_{\rm P}(D,D^0)=\frac{1}{2}\ln\frac{\lambda_{\max}(D,D^0)}{\lambda_{\min}(D,D^0)}. +$$ + +The eigenvalues are generalized eigenvalues of the two grounded responses. The quantity is unchanged if either response is multiplied by a positive scalar. For a two-terminal object it is identically zero; a nontrivial benchmark therefore needs at least three terminals or a nontrivial voltage-transfer specification. The v3 computations use four external terminals and separately score an internal voltage map. + +**Statement.** If one common scale kappa satisfies the following local bounds, then the assembled response satisfies the same bounds and its projective error is at most tau: + +$$ +\kappa e^{-\tau}g_i^0\leq g_i\leq\kappa e^\tau g_i^0 +\quad\Longrightarrow\quad +\kappa e^{-\tau}D^0\preceq D\preceq\kappa e^\tau D^0. +$$ + +**Proof.** Sum the local quadratic energies and minimize over interiors exactly as in R1. The generalized eigenvalues then lie in the interval from kappa exp(-tau) to kappa exp(tau), whose ratio is exp(2 tau). QED. No factor equal to module count appears. + +If D is divided by its trace, the corresponding normalized response is within exp(plus or minus 2 tau) of the normalized target in Loewner order. This does not certify relative error of a signed near-zero transfer entry. Exact common scaling preserves a Dirichlet voltage map because multiplying its harmonic equation by a nonzero scalar does not change the solution. + +A useful conservative perturbation statement is available when all network edges satisfy the local envelope. Let v^0 be the target harmonic voltage with prescribed boundary voltages and let v be the actual one. In the target energy seminorm, on the zero-boundary error space: + +$$ +\|v-v^0\|_{L^0}\leq e^\tau(e^\tau-1)\|v^0\|_{L^0}. +$$ + +**Proof.** Put A = L/kappa and w = v-v^0. Harmonicity gives w-transpose A w = -w-transpose (A-L^0)v^0. The envelope bounds the left side below by exp(-tau) times the squared target norm, and the right side in magnitude by (exp(tau)-1) times the product of the two target norms. Divide if w is nonzero. QED. A pointwise voltage bound additionally requires the target's grounded evaluation norm; it is not uniform over arbitrarily ill-conditioned geometries. + +**No-go result for absolute calibration.** Ratio observations cannot distinguish x from a common multiple of x. More generally, an experiment consisting only of ratio observations and scale-equivariant actions has the same transcript law in two worlds differing by common scale. If their absolute acceptance sets are disjoint, a decision based on that transcript cannot correctly distinguish the worlds with average probability greater than one half under equal priors. A claimed absolute certificate that accepts both is unsound in at least one world. + +An absolute material increment, calibrated voltage/current standard, known time constant, or independently known constitutive parameter can break this symmetry. It then supplies real reference information and must be charged as such. The project does not claim that all physical experiments are scale-equivariant. A connected comparison graph has one scalar ambiguity; disconnected components have separate ambiguities. + +### 6A.3 Theorem G2: exact reachable-scale interval and minimum material + +**Scope: proved for continuous, independently accessible, additive scalar conductance reserves.** Suppose module i begins at ratio x_i > 0 and can reach any ratio in the closed interval from x_i to x_i+c_i, with c_i nonnegative. Choose a common kappa and require every final ratio to lie between kappa exp(-tau) and kappa exp(tau). + +The problem is feasible if and only if: + +$$ +\kappa_{\rm lo}=e^{-\tau}\max_i x_i +\ \leq\ +\kappa_{\rm hi}=e^\tau\min_i(x_i+c_i). +$$ + +When it is feasible, choose kappa = kappa_lo and: + +$$ +y_i^*=\max\{x_i,e^{-\tau}\kappa_{\rm lo}\}. +$$ + +This minimizes every positive weighted sum of added conductance, with no coupling between material prices: + +$$ +\min\sum_i w_i(y_i-x_i),\qquad w_i>0. +$$ + +**Proof.** The reachable interval for a module intersects the admissible band exactly when x_i is at most kappa exp(tau) and x_i+c_i is at least kappa exp(-tau). Intersect these scale constraints over all modules. For a fixed feasible scale, the least admissible final ratio is max(x_i, kappa exp(-tau)). This is nondecreasing in kappa for every module, so the smallest feasible scale minimizes every stated positive linear cost. QED. + +An additional admissible scale interval is included by intersecting it with this interval. However, an interval in absolute physical units requires absolute reference information. If junctions, power, or material limits couple the controls, the separable cost result no longer solves that larger problem. + +For example, x = (0.72, 1.32), c_i = 0.60, and tau = 0.04 cannot meet a unit-scale 4% log-tolerance target using additions alone: the larger module already overshoots. The projective problem is feasible. Its minimum scale is about 1.26824, and the smaller module is increased to about 1.21851. Both modules then satisfy the same scale-free response contract. They do not become accurate absolute unit-conductance components. + +The exact interval is an actionable compiler object. A module exposes a reachable response interval and a material price, rather than a list of desired microscopic coordinates. The compiler computes two reductions, selects the shared scale, and distributes local endpoint targets. For the declared scalar model this takes linear arithmetic work, with a reduction/broadcast depth bounded by the service graph's diameter. + +### 6A.4 Theorem G3: finite-noise, finite-increment construction + +Continuous exact actuation in G2 is an idealization. The following sufficient result has finite increments and bounded measurement error. + +Use one comparison witness with unknown absolute value but stable response during the certified manufacturing window. Every x_i and every reserve capacity is expressed in the same witness-relative units after division by the nominal role value. The witness is not an accurate copy of the target material. It must still be accessible, nonzero, stable within a declared budget, and measured in the same physical regime. + +At each inspection, suppose the reconstructed log ratio obeys absolute error at most e. Let the remaining seal multiply each module by a factor between exp(-beta) and exp(beta). Every repair step increases the ratio by an amount in [h_min,h_max], where h_min > 0; the total available increment is c_i. These are actuator requirements to establish experimentally, not properties inferred from a generic deposition label. + +Let l_i and u_i enclose the initial true ratio. Define: + +$$ +a=e^{-\tau+\beta+2e},\qquad b=e^{\tau-\beta-2e},\qquad \tau>\beta+2e. +$$ + +It is sufficient that the following interval be nonempty: + +$$ +\max\left\{\max_i\frac{u_i}{b},\frac{h_{\max}}{b-a}\right\} +\leq \kappa \leq +\min_i\frac{l_i+c_i-h_{\max}}{a}. +$$ + +For each module, accept when its measured log ratio lies in: + +$$ +\ln\kappa-(\tau-\beta)+e +\ \leq\ \widehat{\ln x_i}\ \leq\ +\ln\kappa+(\tau-\beta)-e. +$$ + +Otherwise add one allowed increment if the reading is low. No subtractive operation is used. + +**Conclusion.** Every module reaches acceptance in a finite number of increments, remains within its reserve capacity, and satisfies the final G1 envelope after any allowed seal change. A sufficient per-module increment bound is one plus the ceiling of the positive part of (a kappa - x_i_initial)/h_min, with an inspection after the final increment. + +**Proof.** Initial x_i is at most b kappa. A failed low reading implies x_i < a kappa. The next increment cannot exceed b kappa because h_max is at most (b-a) kappa. Once x_i is in [a kappa,b kappa], every allowed reading passes. Until then, each step advances by at least h_min. The reserve inequality guarantees sufficient capacity to cross the lower endpoint without exhaustion. Acceptance bounds the true pre-seal ratio by kappa exp(plus or minus (tau-beta)); the seal completes the desired envelope. QED. + +A high failure is excluded on the theorem's good-data event; the implementation reports it honestly if it occurs. The conditions are sufficient and conservative. They do not give a minimum-material theorem for quantized noisy repair. + +For all initial ratios in a known interval [l,u], an a priori sufficient common reserve follows by using l_i >= l exp(-2e) and u_i <= u exp(2e) when initial intervals are built from an e-accurate log estimate: + +$$ +c\geq a\max\left\{\frac{u e^{2e}}{b},\frac{h_{\max}}{b-a}\right\} +-l e^{-2e}+h_{\max}. +$$ + +For l = 0.65, u = 1.35, tau = 0.04, beta = 0.005, e = 0.006, and h_max = 0.012, this bound is approximately 0.675. The simulations allocate 1.05 units of reachable reserve per module, so the positive examples have deliberately generous capacity. Consumed material, allocated reachable capacity, and the apparatus needed to use that capacity are different costs. + +The finite horizon must cover the stated increment count plus inspections. Zero-gain nucleation events violate a strictly positive h_min. A probabilistic progress model can instead use the conditional-progress version of R6, but that requires a measured progress probability and an adequate horizon. + +### 6A.5 Theorem G4: an exact reserve-controlled yield boundary + +**Scope: exact reachability of the G2 local envelopes, with iid initial scalar ratios uniformly distributed on [l,u], a common additive reserve c, and no measurement, seal, or quantization error.** This is not a universal chemical phase transition and not a lower bound on every possible device architecture. + +Put q = exp(2 tau). Feasibility is exactly the event: + +$$ +\max_i x_i\leq q\left(\min_i x_i+c\right). +$$ + +The critical reserve is: + +$$ +c_*=\max\{0,u e^{-2\tau}-l\}. +$$ + +For c >= c_*, every configuration in the support is feasible, with no independence assumption needed. For c < c_*, feasibility probability decays exponentially as the number R of modules increases. When tau > 0 and c < c_*, define: + +$$ +s=\frac{u(1-q^{-1})+c}{u-l},\qquad +t=\frac{(q-1)l+qc}{u-l}. +$$ + +The exact finite-size probability is: + +$$ +P_R(c)=\frac{q s^R-t^R}{q-1}. +$$ + +**Proof.** Condition on the unique minimum m. Its location can be any of R indices. All other values must lie between m and min(u,q(m+c)). Therefore: + +$$ +P_R(c)=\frac{R}{(u-l)^R} +\int_l^u[\min\{u,q(m+c)\}-m]^{R-1}\,dm. +$$ + +Split the integral at m = u/q-c and integrate the two powers. In the subcritical range this point lies between l and u and yields the displayed formula. Here 0 <= t < s < 1, so P_R is bounded above by q s^R/(q-1). At and above the threshold the largest possible initial ratio is within q times the smallest possible final one. QED. + +At tau = 0 and 0 <= c < u-l, the limiting formula is R r^(R-1) - (R-1) r^R, where r = c/(u-l). This is the familiar uniform-sample range probability. The order-statistics ingredients are classical; their reserve-fabrication interpretation and integration with G3 are the proposed contribution. + +For this model only, one can define a dimensionless reserve number: + +$$ +\mathcal{M}_{\rm reserve}=\frac{e^{2\tau}(l+c)}{u}. +$$ + +Its boundary at one exactly separates support-wide G2 reachability from asymptotically vanishing iid yield. Adding confidence, finite increments, and seal margins moves the sufficient engineering boundary upward according to G3. There is no evidence for a material-independent universal fabrication number. + +For l = 0.65, u = 1.35, and tau = 0.04, c_* = 0.596207. At c = 0.55 the exact yields for R = 16, 64, and 256 are about 0.69824, 0.06042, and 0.000000265. At c = 0.60 they are all one in this ideal model. These numbers come from the formula, not a fitted transition curve. + +**Unbounded-tail limitation.** If iid initial ratios have unbounded upper support and a finite lower endpoint, then a fixed finite additive reserve cannot maintain these local projective contracts as R tends to infinity. The maximum diverges while the minimum plus reserve remains bounded in probability. This invalidates a tempting claim that scale freedom alone solves arbitrary manufacturing disorder. Culling, replacement, larger reserves, a different contract, or a genuinely bounded process distribution is necessary. A failure of these sufficient local contracts need not imply failure of a particular global scalar function. + +![Exact reserve threshold and finite-size yield](../figures/gauge_reserve_phase.png) + +Figure 3. Exact G4 curves and independent-array Monte Carlo checks. For each size, the same 5,000 arrays are reused across 31 reserve values. Finite increments and measurement costs belong to the separate G3 manufacturing experiments. + +### 6A.6 Relative metrology: what it removes, and what it cannot remove + +Let z_i = ln(x_i). A paired comparison of neighboring modules uses the same positive detector gain for both readings and divides out their known nominal role ratio. With additive offsets removed and both readings taken in a stable regime, the log ratio cancels that shared gain exactly. An unknown common material multiplier cancels as well when the witness and actuator units scale consistently. + +This is ordinary ratiometric reasoning, not a new metrology principle [P17]. It does not cancel different gains on the two arms, additive offsets, contact errors, nonlinearity, or temporal drift between readings. Averaging logarithms of ordinary noisy measurements is not automatically unbiased; the log-error model must be validated rather than inferred from an ADC specification. + +Represent the temporary comparison graph by an oriented incidence matrix B. Fix one numerical reference coordinate to zero; this is a gauge convention, not an absolute material calibration. With B_g denoting the matrix with that column deleted: + +$$ +y=B_g z+\epsilon,\qquad +\widehat{z}=(B_g^\top B_g)^{-1}B_g^\top y. +$$ + +**Proposition G5, established calibration mathematics applied here.** If the edge-average error is conditionally centered with joint sub-Gaussian proxy (sigma squared/n) times the identity, the error of coordinate i has proxy (sigma squared/n) rho_i, where rho_i is diagonal entry i of the grounded graph-Laplacian inverse. For independent Gaussian edge errors this is the exact variance. The rho_i are effective resistances to the reference in a unit-resistance comparison graph [P15]. + +**Proof reconstruction.** The estimator error is a fixed linear transformation A epsilon. Its covariance proxy is (sigma squared/n) A A-transpose. Matrix multiplication gives A A-transpose = (B_g-transpose B_g)^(-1). Apply the scalar sub-Gaussian tail bound to each row. QED. + +For at most H inspections of R nonreference modules, a simultaneous log-error radius is: + +$$ +e_{\rm stat}=\sigma\sqrt{\frac{2\rho_{\max}}{n} +\ln\frac{2RH}{\delta_m}}. +$$ + +The graph and the noise proxy must remain valid throughout the declared inspection window. Fresh conditional noise bounds cover adaptive repair decisions. Arbitrary componentwise bounded variance or arbitrary correlated bias is insufficient. Numerical inference error, drift, and other bounded errors must be added to this radius; they are not averaged away. + +The effective-resistance identity and its dimension dependence are prior art [P15]. For finite nearest-neighbor boxes of side n, worst reference variance scales as order n in one dimension, log n in two, and a bounded constant in three. A short finite-box argument uses cosine eigenmodes of the free-boundary grid: their squared amplitudes are bounded by a constant times n^(-d), their nonzero eigenvalues below by a constant times the squared mode index divided by n squared, and the resulting shell sum is respectively bounded, logarithmic, or linear before the prefactor n^(2-d). Matching lower bounds follow from disjoint unit-current cutsets; a corner cut alone provides the three-dimensional constant [P2, P15]. + +Thus fixed confidence over all modules needs order log R samples per edge in a regular three-dimensional comparison network, rather than a constant sample count. Thin bottlenecks, a long reference stem, or a tree can destroy that advantage. A solid three-dimensional object is not sufficient if its comparison graph is effectively one-dimensional. + +**Differential-bias no-go.** Write a systematic comparison error as a gradient B_g v plus a cycle component c with B_g-transpose c = 0. Least squares assigns the gradient to the material state and leaves only the cycle component in its residual. In particular, y = B_g(z+v) has a perfect cycle-consistency certificate while the inferred material state is wrong by v. + +This is an exact counterexample to the idea that redundant loops can validate their own standards. It is consistent with classical blind-calibration ambiguities [P16]. The v3 simulations deliberately retain this failure. A bound on differential bias requires an additional physical model, independently checked comparison reversals, another measurement modality, or external reference information. No number of repeats of the same biased measurement closes this gap. + +### 6A.7 Local computation and the latency that calibration adds + +The simulator uses a factored finite linear solve to evaluate the estimator efficiently. It does not pretend that this factorization is an autonomous molecular operation. A separate implemented neighbor-message algorithm solves the same problem: + +``` +initialize one scalar z_i = 0 at each comparison node +repeat: + r_i = sum of oriented measured differences at node i + minus sum over neighbors of (z_i - z_j) + z_i = z_i + omega * r_i + reduce maximum residual over the retained service tree +until the numerical-error certificate is small enough +broadcast the witness value and subtract it at every node +``` + +Choose omega = 1/(maximum degree + 1). The mean stays zero mathematically, and all nonconstant modes contract. The final reference subtraction is a broadcast, not a local atomic operation. For N comparison nodes and graph diameter d_C, a conservative graph-gap bound is 2/((N-1)d_C). + +To verify that bound, sum the squared difference between each pair of nodes and bound each by its path length times total edge energy. Since the sum of pairwise squared differences is N times the zero-mean squared norm, the stated Poincare bound follows. If r is the residual, the numerical error of any reference-relative coordinate is therefore bounded by: + +$$ +e_{\rm num}\leq +\frac{\sqrt{2N}}{\lambda_{\rm lower}}\|r\|_\infty. +$$ + +This bound is conservative but needs no centrally stored eigenvector. Each node stores only local estimates, neighbor information, and the counters/budgets used by the reduction. The implementation verified this local solver on 16, 64, and 216 nodes. It required 119, 190, and 441 synchronous update rounds for a certified numerical radius of 0.00001. Actual errors were smaller. These are algorithmic rounds, not measured seconds. + +On regular boxes, diffusion-like iteration takes order n squared times a logarithmic precision factor. A small estimation variance in three dimensions does not imply rapid local convergence. A solver that pins a single reference during every update can have an even slower collective mode; the implemented solver instead preserves zero mean and fixes the numerical gauge afterward. + +Paired probes sharing a module cannot generally run simultaneously. The code colors comparison edges into disjoint matchings and charges each color slot, its sample count, and repeated inspections. Molecular electronics, communication energy, parallel comparator count, ADC bandwidth, isolation, and controller fabrication remain apparatus costs. A hierarchical or analog implementation might reduce latency, but no unbuilt fast solver is used to claim an achieved fabrication time. + +### 6A.8 Theorem G6: fabrication with one uncalibrated witness + +**Status: a proved conditional synthesis; candidate v3 contribution, priority unverified.** Consider the scalar passive module class of G1. Assume: + +1. The specification explicitly permits one common conductance multiplier. +2. Nominal roles, geometry, contacts, and external loading satisfy the declared passive quotient model. +3. A connected comparison network provides the finite-confidence G5 estimates, including any numerical and systematic-error margins. +4. A witness with unknown absolute value is stable within the accounted budget; all capacities and increments use its consistent relative units. +5. The compiler finds a G3 feasible scale, and material reserves, service throughput, and inspection horizon satisfy G3. +6. Both material access and comparison dependencies remain available until all affected modules are certified; remaining seal changes stay within beta. + +Then on the simultaneous good-data event, every module completes finite repair and the final object's projective response error is at most tau. If the joint probability of shared-assumption failure is at most gamma and the statistical budget is delta_m, failure probability is at most gamma + delta_m on a domain where G3 feasibility and the deterministic resource conditions are assured. + +For a random domain where robust feasibility itself can fail, a valid statement is that success probability is at least the probability of feasible, valid shared conditions minus delta_m. One must not silently replace that feasibility probability with one. G4 describes a simpler exact model; it is not the measured yield law of noisy G6 hardware. + +**Proof.** G5 and the numerical/systematic margins give simultaneous valid inspections. G3 gives finite reachability and the final common-scale envelope while the access invariant preserves the required operations. G1 composes the local envelopes without a module-count error factor. A union bound charges the stated shared and statistical failures. QED. + +The witness can be an imperfect conductor; its absolute value is absorbed into the allowed common scale. This removes the need for an accurate absolute target standard at each module. It does not remove target-program integrity, paired-ratio fidelity, witness stability, or independent assurance of differential bias. + +### 6A.9 A new closure obligation and a falsifiable physical proposal + +The material-supply tree and the metrology graph carry different dependencies. A region may have enough material while its state remains inferable only through a comparison path crossing another region. The earlier postorder material rule alone does not certify this dependency. + +The conservative implemented rule retains the complete comparison backbone until every module has its final pre-seal certificate. It then releases the backbone and executes the ordinary local postorder seal. Certificates remain valid during the intervening wait only under the declared response-stability budget. Waiting indefinitely is not covered. + +The operating and promised maintenance grammar must both respect the allowed scale freedom. If a later action needs absolute current, energy, or a calibrated material increment, the object must retain or reacquire that reference information. The continuation-equivalence principle from [U3] prevents present-response compression from silently deleting a future requirement. + +Earlier removal may be possible by recomputing a certified remaining comparison graph, by retaining a valid reference-transfer witness, or by eliminating a node with its sufficient statistic and covariance. Such elimination can create dense virtual couplings. Constant-port functional compression does not imply constant-memory metrological elimination for arbitrary three-dimensional graphs. That optimization is left open. + +The minimal physical test is a four-module resistive bridge with conductor/dielectric separation, nonidentical nominal roles, incremental parallel reserve paths, and a retained pair-comparison channel. First test the controller with switchable passive resistor reserves. That validates the control mathematics, not developmental chemistry. Then replace the reserve actuator with a measured, scaffold-compatible deposition process and repeat the same test after material conversion. + +Use three independent grounded voltage patterns to characterize the four-port response, and also test the prescribed high-impedance voltage output. Vary shared detector gain and a common material scale, then inject a differential comparison bias as a negative control. Cross an independently measured reserve boundary. Compare against a fixed representative and against an equally capable conventional ratio controller. The latter is expected to tie. + +Support for the physical claim requires final function after conversion, repeatable bounded increments, retained comparison access, quantified differential bias, and a measured material ledger. Failure to obtain a bounded increment or a stable paired-ratio measurement falsifies the proposed backend even if a software demonstration passes. A favorable bridge voltage alone does not establish the full response contract or a general nanofabricator. + + +## 7. Developmental compression, seed information, and honest leverage + +### 7.1 A resource-bounded definition + +Fix a declared reusable platform H: interpreter, species design, chemical repertoire, apparatus geometry, calibration procedure, and physical law model. Let G be the target genome, S its seed initialization, E the target-dependent environmental program, and U any target-dependent intervention transcript. Define developmental complexity at geometry/function tolerance epsilon, failure probability delta, and resource budget B by: + +$$ +K_{\rm dev}^{\epsilon,\delta,B}(X\mid H)=\min\{L(G)+L(S\mid G)+L(E)+L(U)\}. +$$ + +The minimum ranges only over executions meeting the declared resource budget and acceptance probability. A specialized feedstock recipe, lithographic mask, hidden prepattern, calibrated target table, or separately designed building-block library must be charged to H if reused across the declared target class, or to the target-specific description otherwise. Reusing H across n_jobs jobs permits an explicit amortized charge L(H)/n_jobs; calling H universal does not make it zero-cost hardware. + +### 7.2 Theorem A: compressibility and its obstruction + +If a fixed computable grammar P generates a family X_n and its physical backend meets the declared finite resources, the target-dependent description has length at most L(P) plus a self-delimiting description of n, hence O(log n). For a d-dimensional family with N proportional to n to the power d, this is O(log N). The condition on the backend is essential: a short nonterminating search is not a fabrication method. + +**Proof.** Encode the fixed generator once and its finite size parameter. Execute the generator through the assumed backend. QED. + +The converse follows by counting. For N independent q-ary target labels, most targets require order N log_2 q bits. At Hamming tolerance k, one description covers at most the size of a q-ary Hamming ball in the deterministic case. Thus a covering set requires at least q to the power N divided by that ball size descriptions. The v1 package gives the analogous probabilistic counting formulation. Random exact microtextures and arbitrary unique wiring therefore remain expensive. Functional equivalence can enlarge acceptable sets, but it does not erase information that the requested target genuinely requires. + +For exact deterministic computable execution, ordinary conditional algorithmic complexity obeys K(X given H) no greater than the developmental description plus a fixed interpreter constant. Resource constraints can make developmental complexity larger. For approximate stochastic construction, compare tolerance classes or a separated target packing instead of claiming that the exact final atomic microstate was fully specified by the seed. + +A terminal response of k ports has at most k(k-1)/2 independent real coefficients in the passive grounded class. Over a bounded, well-conditioned response family, its finite-resolution description may scale as that dimension times log(1/epsilon), independently of interior atom count. The geometry and all other protected functions must still be encoded. This is a reduction of the specification's relevant degrees of freedom, not amplification of algorithmic information beyond the program and its inputs. + +### 7.3 Theorem E: positional information and a boundary-complexity warning + +If a local decision must distinguish R equiprobable developmental regions with error probability e, Fano's inequality requires at least log_2 R minus the binary entropy of e minus e log_2(R-1) bits of mutual information in its available observations and state. A lineage word of length O(log R) can meet the corresponding address-size order. A single scalar gradient with fixed noise cannot supply unbounded address precision. + +The executable grid family inherits local integer counters from a neighbor and applies a fixed parity grammar. Counters require O(log N) bits per region; their total temporary physical storage can be O(N log N). This is compatible with a logarithmic seed description, but is not negligible molecular machinery. Coordinate copying, orientational coherence, and the interpreter are ideal in the supplied simulations. Independent anchor checks and error-correcting fields are engineering proposals, not completed chemical implementations. + +Bounded ports are a real restriction. If a three-dimensional module exposes all surface features, k can grow as its volume to the power 2/3. A dense k-by-k response certificate can then grow faster than its interior volume. Full-field optical or elastic objects do not automatically gain the bounded-port compression advantage. Lumped electrical, fluidic, or selected mechanical components with a few controlled interfaces are the plausible first targets. + +### 7.4 Morphogenetic leverage, autonomy, and compilation ratio + +Use B_epsilon(X) for the number of bits in a fixed explicit target code at the declared tolerance; do not use an undefined count of continuous physical degrees of freedom. Let I_paid be the developmental description plus target-specific apparatus/feedstock information and a declared platform amortization. An auditable control-leverage ratio is B_epsilon(X)/I_paid, reported alongside total physical memory, work, yield, and precision. This ratio measures savings relative to an explicit code. It is not a Shannon-information creation ratio and is not invariant to a change of target coding convention. + +The physical compilation ratio should use the same paid denominator and a declared finite-resolution output alphabet. Reporting it separately with an inflated atomic-degree numerator would double-count the same conceptual advantage. For functional targets, packing or covering entropy of the allowed response class is a more principled numerator than atom count. + +Fabrication autonomy requires several measurements: target-specific bits supplied after seeding, externally selected intervention episodes, fraction of corrective decisions made locally, dependence on target-independent pumping and global chemical stages, and communication latency. A seed-only target channel can be highly informationally autonomous while depending on an external pump. The new simulation is autonomous under its fixed program after seeding; its substrate, references, channel capacities, and scheduling abstraction are assumed apparatus. The proposed first wet experiment has lower autonomy and must report its external feedback explicitly. + +### 7.5 Fabrication as a noisy physical channel + +Let W select one target from a finite declared family; the seed and all target-specific preparation encode W, and noisy dynamics produce X'. The success test must distinguish the selected target to the stated tolerance. Fano's inequality bounds the required mutual information about W in the output, while data processing prevents independent thermal noise from creating more information about W than the charged inputs carried. Copying one selected motif many times gives high physical throughput, not many newly selectable target bits. + +A fabrication capacity region is the set of simultaneously achievable target-family size, tolerance, error probability, time, energy, feedstock mass, apparatus size, and explicit control length. Reliable selection bits per second and physical units instantiated per second are different rates. The familiar binary-symmetric-channel capacity 1-h_2(p) is only an ideal communication comparison; no material decoder achieves it merely because assembly is described as a channel. The useful concrete capacity statement here is R6's restricted tradeoff between functional modules, inspection confidence, reachable repair, and paid completion time. + +## 8. Finite grammar, network universality, and compilation + +### 8.1 Theorem B/F: a restricted finite fabrication basis + +**Status: conditional constructive theorem, not a demonstrated molecular universal constructor.** Assume active finite-state macrocells can read and copy finite binary tapes, grow oriented nearest-neighbor scaffolds, create insulated routed connections and unit positive resistors, perform the bounded sensing/repair primitives, and preserve their material contracts. Then any finite positive rational resistor network has a finite developmental description executable by this basis. Any finite positive real network can be approximated to a prescribed response tolerance when sufficient geometric, conductance, and resource range is permitted. + +**Proof sketch.** A positive rational conductance p/q times the unit value is realized by p parallel chains of q unit resistors. A finite netlist can be interpreted by a fixed machine. In three dimensions, finitely many bounded-degree paths can be routed using finite subdivision and separated crossings. Positive finite conductances give continuous finite terminal response under sufficiently small perturbations. Apply the maturation contracts to realizable submodules and junctions. The number of primitive operation types need not grow with netlist length; tape, component count, routing volume, and runtime generally do. QED under the stated primitives. + +This result says nothing comparable for arbitrary semiconductors, nonlinear electronics, quantum devices, superconductors, catalysts, or arbitrary mechanical machines. Rational approximation through many unit elements may be very inefficient. Passive, static tiles do not automatically implement active tape machinery. Algorithmic self-assembly and intrinsic universality already establish powerful related formal constructions [P8, P9]; the physically unbuilt substrate remains the limiting assumption here. + +An ingredient alphabet and a species alphabet are different. Four nucleotide monomers do not mean four independently addressable molecular species: polymers with different sequences are different chemical objects, and their copying and processing machinery must be counted. The new code has a bounded set of output roles and primitives; it deliberately reports the number of chemically realized species as unknown. + +### 8.2 Growth Genome Intermediate Representation + +A practical genome has five linked layers: a geometry grammar, material-compatible module templates, port-response targets, a service graph, and guarded maturation rules. Its intermediate representation must preserve dependencies across these layers. A schematic record is: + +```json +{ + "version": 2, + "extent": 8, + "dimension": 2, + "motif": "parity_conductance", + "ports": 2, + "eta": 0.08, + "seal_bound": 0.01, + "reserve_ratio": 0.9 +} +``` + +This capsule is executable with `contract_genome.py` and the declared simulator configuration. The fixed interpreter expands the nonperiodic Thue-Morse parity family, assigns bounded conductance roles by inherited counters and edge orientation, and generates a nearest-neighbor service tree. The capsule is not the full cost of a general language or compiler. Its inspection confidence, actuation increments, hardware calibration, and transport capacities are charged runtime/configuration inputs. The original v1 midpoint-split and motif compiler is retained for irregular 2-D and 3-D geometry. + +Each canonical demo capsule is 126 bytes, or 1,008 bits; the grammar interpreter source is about 3 kB, excluding dependencies and hardware. A packed three-bit role list for 300 fixed module positions is only 900 bits, so these tiny prototypes do not themselves demonstrate net description compression. The proved advantage is asymptotic for the size-varying family under a shared, paid interpreter. Uncompressed storage of those 1,008 bits at two ideal information bits per DNA base pair would require at least 504 base pairs. A shorter semantic encoding changes the code and its charged decoder. Addressing, coding redundancy, state transitions, and the physical interpreter are additional and are not chemically compiled here. + +The local transition sequence is grow, provisionally differentiate, perform material conversion while service remains open, inspect, add an allowed reserve increment or reject, certify, await child acknowledgements, and seal with a final-damage margin. Molecular steps may require a different ordering for incompatible chemistries. Any reordered plan must revalidate its witnesses. + +### 8.3 A practical compiler + +```text +compile(target, platform, tolerance, risk, resources): + define geometry, interfaces, functions, and operating regime + reject element balances or process temperatures outside platform + search repeated motifs and hierarchical geometry descriptions + partition into bounded-port modules where the function permits + choose realizable material templates, including junction templates + allocate response margins, measurement confidence, and seal drift + propose diagnostic and repair-access resources as matched bundles + construct a capacity-feasible service graph and growth schedule + prove local reachability for simple modules; bound or flag others + attach response witnesses and closure dependencies + lower supported primitives to the chosen physical backend + simulate held-out faults, common-mode failures, and final conversion + emit genome, physical bill of materials, certificates, and limitations +``` + +Only the bounded grid family and the earlier geometry compiler are implemented. A general multimaterial inverse compiler is an open problem. The algorithm must never emit an unsupported local primitive as though lowering it to chemistry were complete. + +The optimization objective includes failure probability, time, free-energy/material cost, number and cross-talk of species, genome complexity, inspection effort, and specialized apparatus. Full shortest-program minimization is uncomputable. Even finite recipe selection includes Set Cover as a special case: targets are requirements and a recipe satisfies a subset at a cost. That restricted compiler is NP-hard. Geometry, scheduling, and nonlinear chemistry add difficulties; the finite special-case hardness is enough to reject an assumed universally easy compiler. + +Useful approximations include grammar induction over known motifs, bounded-depth constructive solid geometry, typed graph rewriting, mixed-integer scheduling of module templates, and a differentiable physical surrogate inside an explicit validity region. Learned local rules should be tested against adversarial continuation states and calibration shifts. A neural rule's performance on a finite target set is not a universality or reliability proof. + +### 8.4 The v3 gauge-aware compiler pass + +Before material allocation, the compiler checks whether the declared function is invariant under a positive common conductance multiplier. If absolute current, power, delay, finite external loading, or an unscaled junction matters, it retains the absolute R6 contract or expands the specification; it does not discard those requirements. + +For the quotient-compatible class it adds the following instructions to the inherited growth grammar: provision a stable comparison witness; create bounded-degree local pair-comparison links; reserve capacity and guard bands; reconstruct relative log responses with a finite confidence budget; reduce the feasible-scale interval; select its lower endpoint; execute bounded incremental repairs; retain both material and comparison access; issue a common-epoch completion acknowledgement; seal with the declared margin. + +A permitted gauge removes one global scalar requirement, not the R-1 independently specifiable relative degrees of freedom of a generic R-module network. Sublinear seed descriptions still come from the target family's generative structure. Runtime diagnostic state and O(R) generic hardware do not disappear. + +The module comparisons are the line graph of the physical junction graph: modules sharing a junction can be compared through local switches. An additional short link connects one module to the stable witness. The target family and all comparison links are generated by the fixed interpreter. The seed does not contain the dense covariance matrix used for offline numerical evaluation. A uniform radius bound and operating budgets are charged as part of the compiler/environment specification. + +Each supplied v3 capsule occupies 384 UTF-8 bytes including its final newline. This is 3,072 stored bits before molecular encoding, error correction, or the shared interpreter. The small demonstrations do not show net program-size compression over packed role labels. The asymptotic compression claim remains restricted to the fixed generative family and charges the interpreter and apparatus. + +The scalar G2 optimization is exact linear-time arithmetic. G3 is a conservative feasibility pass. It does not make general developmental compilation easy, supply an autonomous general CAD compiler, or solve the chemistry of the primitives. The emitted v3 JSON capsules record the allowed functional quotient explicitly; a quotient must never be inferred merely because it increases simulated yield. + +For linear elastic or hydraulic analogues, the same scale idea can apply to a suitably declared static response with prescribed boundary data. It transfers only if the actual constitutive law, couplings, and actuator reachability preserve the assumed positive quadratic form. Arbitrary materials, nonlinear motion, and dynamic devices do not follow. + + +## 9. Error correction beyond the new contract theorem + +The original exact-object obstruction remains. If n independent final defects are each fatal and each occurs with probability at least u, perfect yield is at most (1-u) to the power n, hence at most exp(-nu). Proofreading before an irreversible operation cannot correct faults introduced after its last effective diagnostic and actuator. The new architecture addresses this by testing after material conversion, retaining a bounded repair path, and explicitly reserving a final-seal margin. It does not repeal the obstruction for unbounded late failures. + +The v1 functional redundancy theorem also remains valid within its scope. For R modules each tolerating any fewer than rho b faulty subcomponents, independent final subcomponent error p < rho gives the Chernoff union bound: + +$$ +\Pr({\rm failure})\leq R\exp[-bD_{\rm B}(\rho\Vert p)]. +$$ + +A sufficient redundancy is log(R/delta) divided by that binary divergence. A local-stochastic bound on probabilities of all specified fault subsets gives a weaker sufficient threshold, of the form p < rho/e. Low marginal fault density alone supplies neither bound. These are standard concentration/coding ingredients; a real physical error-correcting grammar must establish their hypotheses and the device's fault-tolerance contract. + +For active maintenance, define a correctable defect set by actual reachable repair actions, a repair radius by the accessible service neighborhood, latency by sensing plus transport plus chemistry, redundancy by extra geometry/state/material, and catastrophic failure by loss of the functional contract or all safe repair routes. A defect density can be low and catastrophic if it lies on a critical cut or in a shared seed reference. Correlated damage and reference corruption need explicit separate budgets. + +No universal scalar error threshold has been established here. There are several independent limiting margins: diagnostic identifiability, repair reachability, transport capacity, available time, material compatibility, and shared-reference reliability. A minimum of normalized margins can be an engineering screening number, but naming it a Morphogenetic Fabrication Number would not establish a physical phase transition. + +The source EDD reserve model does possess a sharp onset for a profitable matched pair. R9 supplies a restricted concentration threshold. The v1 redundancy-access reversal supplies another finite optimum. These are different phenomena and should not be collapsed into one claimed universal manufacturability constant. + +## 10. Transport, concurrency, occlusion, and energy + +### 10.1 Why extra redundancy can worsen reliability + +The v1 slab model maintained concentration c_0 at both faces a distance ell from the center, with diffusion constant D and volumetric consumption r_0. Its stationary minimum was: + +$$ +c_{\min}=c_0-\frac{r_0\ell^2}{2D}. +$$ + +With effective repair rate proportional to concentration, increasing redundant volume while allowing ell to grow can lower repair faster than redundancy helps. For ell = a_g b to the power 1/d, the model gives a repair rate proportional to the positive part of 1-kappa b to the power 2/d. The resulting Chernoff exponent has a finite interior maximum under the specified fault/conversion model. This is the v1 redundancy-access reversal; it limits that model's reliability certificate, not all architectures. + +The proposed repair is to constrain the largest distance to a maintained supply route and to keep that route open until dependent functions mature. R5 prevents logical occlusion; concentration or capacity calculations prevent a merely connected but starved network. + +### 10.2 Material transport equations and bounds + +For reagent j, a model with advection is: + +$$ +\partial_t c_j+\nabla\cdot(c_j\mathbf{u})=D_j\nabla^2c_j-R_j+S_j. +$$ + +Pure diffusion has characteristic time L squared/D. In a slab with steady volumetric use, the dimensionless depletion r_0 ell squared/(D c_0) must remain below the geometry-dependent positivity bound. Maintaining c_0 requires actual reservoirs and a flux budget. Diffusion alone does not repeatedly refill an arbitrary sealed interior. + +For a cylindrical laminar service channel of radius r, length ell, viscosity mu, and pressure drop Delta P, the continuum Poiseuille estimate is: + +$$ +Q=\frac{\pi r^4\Delta P}{8\mu\ell},\qquad P_{\rm pump}=Q\Delta P. +$$ + +This formula assumes a continuum Newtonian fluid and suitable boundary conditions; it is not asserted valid in molecular-width channels. For water-like viscosity 0.001 Pa s, a 10-micrometer radius, 1-cm-long channel at 100 kPa gives about 3.9e-11 cubic meters per second, or 2.35 microliters per minute. A 1-micrometer radius at the same length and pressure gives 10,000 times less flow. Narrow channels cannot be made adequate merely by adding a pump label. + +A distributed service tree can allocate larger upstream channels. Its radii, pressure drop, fluid volume, heat, structural weakening, and eventual removal are part of the object/apparatus budget. Under an ideal equal-pressure/laminar design, distributing flow with radius roughly proportional to the cube root of branch flow is one familiar optimization pattern, not a guarantee for reactive nanoscale transport. The v2 delivery model instead declares finite edge capacities and checks every batch against them; it does not solve a hydraulic inverse design. + +### 10.3 Theorem D: physical parallel-growth limits + +At bounded density and finite signal/growth speed v from a compact seed, occupied volume lies inside a causal region of diameter proportional to vt. In dimension d, the number of separated finite-size units is at most a constant times (vt/a) to the power d. Sustained exponential growth of dense matter from one seed is impossible at fixed local speed; early branching can only remain exponential before spatial crowding or transport limits bind. + +For target volume V, material density rho_m, and inlet mass rate F, fabrication time is at least rho_m V/F. A surface front with bounded normal speed requires time of order L/v for a compact object. Diffusive supply from an exterior boundary can impose an L-squared time scale. Distributed deposition inside a perfused porous scaffold can remove that interior diffusion distance, but cannot evade construction of the scaffold, the inlet flux bound, or heat removal. It provides an asymptotic advantage only under an explicit scaling of internal access and boundary supply. + +In R6, logarithmic logical retry rounds can coexist with fabrication time that grows linearly or worse with size. For example, R = one million, conditional success a = 0.6, and completion risk 0.01 require 21 rounds. Twenty-one slow, transport-starved rounds do not imply a fast factory. + +### 10.4 The simulator's explicit transport schedule + +The v2 network grows in local depth layers from a corner seed. Each proposed layer reserves its scaffold and functional-material demand. The service tree's edge capacity equals the root rate multiplied by its descendant-node fraction; these capacities are assumed engineered resources, not the capacities of identical microscopic tubes. Demand is summed upstream. A batch duration is at least the maximum, over every edge and the root, of demand divided by its capacity, plus the longest signal-path delay. Each local chemical action also takes a positive minimum time. + +This gives a conservative, executable reservation schedule with a mass ledger. It is substantially less detailed than a reaction-diffusion or hydraulic model and can be inefficient for an unbalanced moving front. There is no uncharged interior reservoir plane or instantaneous supply to a sealed descendant. The model does assume nonblocking routing, validated channel capacities, and local storage for batch delivery. Its output time is in abstract units and is not converted to seconds. + +### 10.5 Thermodynamics and the price of reliability + +Growth and repair consume chemical free energy and export entropy. Local reversible elementary steps must satisfy the applicable detailed-balance or local-detailed-balance constraints. Driven proofreading requires maintained chemical potential differences; a unidirectional transition in code is not thermodynamic evidence. + +At 300 K, k_B T is about 4.14e-21 J. A simple equilibrium discrimination ratio p relative to a favored state needs a free-energy separation of order k_B T log(1/p), about 13.8 k_B T for p = 1e-6. This is a two-state equilibrium estimate, not a universal minimal dissipation for arbitrary repair. Fuel-driven repeated tests, kinetics, degeneracy, binding barriers, and time constraints change the cost. Landauer's k_B T ln 2 bound applies to logically irreversible erasure under its assumptions, not to every act of copying an instruction into matter. + +At 10 k_B T per turnover, one billion control turnovers would be about 4.1e-11 J, whereas 1e20 turnovers would be about 4.1 J. These arithmetic figures do not price synthesis, reservoirs, pumping, cooling, reagent manufacture, or irreversible material conversion, which may dominate. The new code reports material and inspection counts; it deliberately does not report an uncalibrated energy number as if it were measured free energy. + +For a locally detailed-balanced reaction network with forward and reverse event fluxes J_r^+ and J_r^-, the entropy-production rate has the familiar nonnegative form k_B times the sum of (J_r^+ - J_r^-) log(J_r^+/J_r^-). Chemical potentials and temperature specify the free-energy drive. Incorrect bonds can be kinetically rejected without making every process equilibrium-limited, but maintaining that kinetic cycle consumes fuel and produces waste. A credible chemical backend must specify the reactions and their reservoirs. + +Heat can dominate controller erasure. As an illustrative continuation of the v1 budget, 0.02 mol of material conversion at an assumed 100 kJ/mol releases 2 kJ. In 25 minutes this is 1.33 W inside a cubic centimeter. A uniformly heated 1-cm slab with thermal conductivity 0.6 W/(m K) and fixed-temperature faces would have a central temperature rise of about 28 K. These are assumed values, not measured properties of a selected chemistry; they demonstrate why a wet informational scaffold may need staged or externally cooled conversion. + +A reaction step on every atom is unavoidable as chemistry, but need not be an individually addressed instruction or serial operation. The architecture seeks small explicit atomic-control fraction by recruiting prevalidated molecules, particles, doped components, and bulk conversion chemistries. Unknown atomic interfaces cannot be repaired by declaring that fraction small. Define f_atomic as the number of atoms whose individual placement/state must be explicitly specified for this target divided by total atoms. Using a prevalidated functional nanoparticle charges its internal manufacturing process to the component platform rather than supplying new per-atom placement instructions for every object. A small f_atomic reduces target-specific atomic control, not the number of atoms that chemistry must process or the cost of producing those components. + +![Transport and logical-round scaling limits](../figures/scaling_limits.png) + +Figure 4. Diffusion time and retry-round count describe different bottlenecks. The right panel excludes transport and chemistry time; its favorable logarithm does not overcome the left panel or inlet mass limits. + +## 11. Soft-to-hard transduction and physical attainability + +The preferred sequence is an information-rich porous scaffold, selective recruitment, material conversion while diagnostic/service routes remain accessible, functional correction, passivation or fusion with a reserved drift margin, and selective scaffold release. Geometry can be molecularly patterned at critical interfaces while the bulk is formed by conventional deposition, crosslinking, or mineralization. + +No scaffold can create absent elements. Stoichiometric conservation restricts all products to the elemental inventory of the supplied reactants; the reaction network also restricts accessible oxidation states, phases, interfaces, and temperatures. A finite material alphabet can be useful without being chemically universal. + +The practical progression is one scaffold with one inorganic material; then one inorganic conductor plus a stable dielectric/support; then independently addressable material channels and tested interfaces; then a passive device; and only afterward increasingly complex functions. Semiconductor doping profiles, low-defect single crystals, grain-boundary mobility, optical losses, thermal expansion, and high-temperature densification are separate problems. A DNA-compatible reaction bath is not a universal materials process. + +DNA-programmed inorganic frameworks and subsequent device integration provide relevant component evidence [P10, P11]. Macroscale-area DNA-framework patterning also exists with substantial external patterning [P12]. These results support selected routes from programmed soft structures to inorganic function. They do not demonstrate autonomous, seed-only, self-repairing multimaterial growth at centimeter scale. + +### 11.1 The precise transfer from the 3-D conductivity research + +The inspected v6 conductivity manuscript [U5] distinguishes an actual physical response image from arbitrary algebraically admissible spectra, and distinguishes approximation by a sequence from exact realization by one cell. We retain that discipline. Its infinite hierarchy is not invoked as an efficient finite fabrication compiler. + +For a gray coefficient P between zero and one, let m be its mean and B its binary unsaturation integral, the integral of P(1-P). The inspected exact-volume rounding argument gives a binary coefficient chi of required fraction theta with: + +$$ +\|P-\chi\|_1\leq2B+|m-\theta|. +$$ + +**Proof reconstruction.** At equal fraction theta = m, selecting the largest m fraction of P gives at least the overlap obtained by the fractional selector P itself. Expanding the L1 error therefore bounds it by 2 times the integral of P(1-P). Altering the selected set by volume |m-theta| gives the stated general bound. This is an elementary rearrangement argument; stronger sharp bounds are retained in [U5]. + +For positive real conductivity contrast confined to a compact uniformly elliptic range, a variational higher-integrability argument gives constants C and alpha > 0 with response perturbation at most C times that L1 error to the power alpha. The proof compares energy minima using each other's correctors and uses a geometry-uniform higher-integrability estimate. The constants deteriorate with contrast and operating regime. The result does not reach perfect zero-conductivity voids uniformly. + +This supplies a useful design certificate: a surrogate gray design is not accepted solely because its simulated spectrum looks right; it also carries a bound to an actual binary realization. It does not prove that chemical deposition implements that rounding, that a periodic homogenized tensor certifies a small finite module's boundary response, or that the constants are practical. The proposed device must still be measured through its actual ports after transduction. + +## 12. Physical architecture and its unbuilt components + +The shortest plausible architecture uses a temporary manufacturing layer surrounding or interpenetrating the final material. This layer carries local state, reagents, diagnostic connections, and sacrificial reserve paths. The final structure can remain simple. Trying to embed the entire controller, chemistry library, and repair machinery inside every final atom is unnecessary and implausible. + +| Required operation | Plausible initial implementation | Boundary of current evidence | +|---|---|---| +| Seed-dependent information growth | Seeded DNA tile or related programmable assembly in a controlled bath | Algorithmic growth is established; the present complete 3-D grammar is not chemically compiled. | +| Local finite state and gates | DNA strand-displacement motifs; larger electronic or microfluidic controllers at first | Sequence orthogonality, copying reliability, and long-lived state are not supplied by the abstract alphabet. | +| Structural bulk | Crosslinked scaffold, silica/mineral support, recruited particles | Shrinkage, strain, mechanical integrity, and inaccessible pores must be measured. | +| Conductive differentiation | Local particle recruitment and compatible metal deposition | Conductivity, contact resistance, leakage, and thermal stability depend on the actual chemistry. | +| Functional diagnostic | Permanent or temporary electrical ports, initially external instruments | Connected modules require isolation or an explicitly solved loading model; ideal local sensors are an assumption. | +| Bounded reserve repair | A porous spare path receiving measured increments of deposited material | Monotone, reproducible conductance increments without damaging neighbors are the decisive unbuilt actuator. | +| Local closure coordination | Compartment/controller acknowledgement; later molecular signaling | The simulations assume correct message identity, version, and transmission. | +| Final locking and release | Compatible passivation, crosslinking, scaffold removal | The final response drift must be bounded, or measurement and repair must remain available afterward. | + +The most credible first device is a low-frequency passive electrical or fluidic network with a small number of ports per module. A diode, transistor, photonic resonator, or mechanical actuator requires a different behavioral contract. Linear elasticity can use a similar energy argument only within a stable coercive regime, with rigid modes, prestress, buckling, and contact handled explicitly. Complex optical/electrical responses generally lack the real Loewner ordering used in R1; a small-signal frequency-domain extension needs its own proof. + +Local physics-driven adaptation of resistor and elastic networks is prior art [P3, P4, P5]. The proposal here is to use a developmental scaffold and disposable manufacturing resources to build, test, correct, and then mature material modules under explicit compositional certificates. The simulations do not show that this beats an equally capable conventional local controller. + +### 12.1 Maintenance and what biology does not supply + +The same program can maintain a device only if the relevant references, observable ports, transport paths, repair stock, and compatible actuators survive operation. A sealed two-terminal response alone records no unique microscopic blueprint; many different interiors have the same response. Maintaining function may use a reserve bypass without reconstructing the original bonds. Restoring a specific damaged interior instead requires additional information and access. + +With ongoing damage, a finite reserve eventually exhausts unless it is replenished or modules are replaced. A mission-time guarantee must include the number of future inspection opportunities, common-reference survival, wear, and the last repairable state. The fabrication confidence budget cannot be reused indefinitely as a lifetime budget. Experimental replication-like operations should remain confined to the controlled scaffold/process vessel; no autonomous organism or uncontrolled replicator is required by this architecture. + +Biology establishes the physical possibility of hereditary information, local differentiation, distributed chemistry, growth, and maintenance. It does not provide arbitrary inorganic phases, high-temperature processing, semiconductor-grade interfaces, fast dry manufacturing, or an engineering proof of yield. The proposed passive module contracts and material-conversion schedule are defined by physical response and compatible chemistry, not by renaming a genome or copying an organism. + +## 13. Computational evidence and reproducibility + +### 13.1 What the v2 model implements + +The new target is a nonperiodic passive-conductance family on a fixed 2-D or 3-D nearest-neighbor scaffold. It has 64 sites and 112 edge modules in 2-D, or 125 sites and 300 edge modules in 3-D. Each edge module contains three parallel branches, each containing two series bonds, and one available parallel reserve branch. The output roles vary by inherited parity state and orientation. This is internal functional differentiation, not a new demonstration of Brownian molecular geometry formation. The earlier package retains irregular 2-D and 3-D growth shapes. + +The blueprint baseline has idealized identification of the modeled pre-conversion bond faults; it is deliberately strong in that respect. Full replacement-bond material, discarded bonds, and delivery time are charged. Initial bond faults occur with probability 0.12 and reduce a bond by a factor 0.15. Conversion faults occur with probability 0.08 and reduce a bond by a factor 0.12. A spatial half-region may have its body and local bond reference scaled together by 0.65, with object-level probability 0.35. The separate terminal contract reference is intact in the main runs. The biased-reference condition violates that last premise deliberately. Neither model corrects a fully corrupted common root that changes both the intended target and every independent diagnostic. + +Post-conversion terminal measurements use the finite-confidence procedure in R4. Reserve increments are 0.045 of target conductance times a bounded random multiplier between 0.6 and 1.4. The maximum reserve is 0.9 of target conductance. All methods are allocated the same reserve capacity and service geometry; unused reserve is still physical design overhead. Added active material is charged correctly as two equal series bonds: obtaining extra module conductance G requires total bond conductance 4G, matching the path-length convention of the nominal module. A one-edge shortcut is not used to underprice repair. + +Each node maintains local readiness and waits for child acknowledgements before closing. Feedstock demand is checked against root and every service-edge capacity. The electrode network is solved only after the simulated manufacturing dynamics to score final object function. The repair controller sees a local terminal measurement and its local contract, not the final global conductance score or a bond-by-bond target oracle. + +Important idealizations remain: inherited coordinates and references, the fixed oriented scaffold embedding, electrical port isolation, bounded incremental deposition, no hidden coupling outside the ports, a calibrated seal envelope, and routable service channels. Molecular species count and thermodynamic energy remain unspecified. The manuscript's physical conclusions are limited accordingly. + +### 13.2 Preserved v2 results: 512 default runs + +There are 32 independently seeded objects per condition and dimension. The pass criterion is completion plus final global conductance within 8% of target. The same fabrication draws are paired across methods. The two target sizes are not directly comparable measures of scalability. Mean conductance ratios below include unfinished objects where indicated; they are diagnostic scores, not manufactured yield. + +| Condition | 2-D completed function | 3-D completed function | Interpretation | +|---|---|---|---| +| Open loop | 0/32 | 0/32 | No functional repair after conversion. | +| Blueprint repair before conversion | 0/32 | 0/32 | Local body-reference repair cannot remove later conversion errors or shared reference errors. | +| Blind fixed reserve addition | 1/32 | 1/32 | Actuation without matched diagnosis is inadequate for this fault distribution. | +| Diagnostic only | 0/32 | 0/32 | Correctly refuses to complete many defective modules. | +| Response repair with early sealing | 0/32 | 0/32 | Premature closure strands unresolved descendants. | +| Response contracts plus access | 32/32 | 32/32 | Every final local response also meets its declared envelope. | +| Conventional joint controller | 32/32 | 32/32 | Same capabilities and policy; ties exactly, including cost and time. | +| Shared 7% diagnostic gain bias | 6/32 | 0/32 | 12 and 4 objects respectively finish with invalid local certificates. | + +The response-contract method's mean conductance ratios are 0.96787 in 2-D and 0.96694 in 3-D, with sample standard deviations 0.00245 and 0.00172. It intentionally stops inside the acceptable band; it is not trained to reproduce exactly 1.00000. Open-loop means are 0.65293 and 0.58814. Blueprint-repair means are 0.79794 and 0.70841. + +These numbers are not a head-to-head improvement over v1's 2/8 reference functional successes. The new and old models have different targets, physical abstractions, tolerances, and repair operators. The controlled causal comparisons are the paired conditions inside the present experiment. + +Nominal functional material is 39.2 and 113.6 model units. The response method adds means of 10.70773 and 38.77344, or about 27.3% and 34.1%, excluding the separately charged scaffold. Mean inspection sample counts are 12,681.5 and 41,250. Mean maturation rounds are 28.25 and 28.78. Total scheduled times are 263.78 and 764.03 abstract units, versus 245.47 and 709.05 for open loop. The matched conventional controller has exactly the same outputs and costs. These figures are neither seconds nor a calibrated molecular energy budget. + +All 32 successes in a condition give a two-sided exact 95% binomial interval with lower endpoint about 0.891, not proof of yield one. The synthetic distribution and strong actuator assumptions limit extrapolation more than this sampling interval does. No enormous-N physical reliability claim is inferred from these runs. + +![Completed functional yield across the eight methods](../figures/functional_yield.png) + +Figure 5. Functional yield is conditional on the reduced model's stated hardware assumptions. The conventional matched baseline ties the response-contract controller; the evidence supports the proposed mechanism and certificate logic, not exclusive algorithmic superiority. + +![Paired network realizations under three closure and repair policies](../figures/network_snapshots.png) + +Figure 6. One paired 2-D fabrication draw. Edges show local relative response error; node state distinguishes sealed and unsealed regions. The colored geometry is a finite network simulation, not a microscopy image. + +### 13.3 Negative controls and theorem checks + +An additional 32 seal-stress runs retain the nominal 1% certificate margin but allow actual independent seal changes up to 18%. Every object finishes with some invalid local certificates; mean local contract satisfaction is only 0.4587. Nevertheless all 32 global conductances remain within 8%, ranging from 0.93296 to 0.98729 of target. This is not a contradiction: the local contract is sufficient, not necessary, and partially cancelling random changes can preserve one global response. A correlated downward seal shift can instead fail the object. A single passing whole-device test cannot validate an assumed local envelope. + +Numerical checks include 300 correlated multiport composition instances, 250 random positive-conductance energy bounds, and 400 noncommuting evidence/control calculations. No asserted inequality is violated. The direct quadratic optimum and formula agree to maximum absolute error 3.55e-15. The single-probe counterexample has zero first-probe current difference and relative eigenvalues 1/3 and 1. These checks are reproducible and are not substitutes for the proofs. + +Sixteen research tests pass, including Kron elimination, seal margins, local routing, postorder access, a channel bottleneck, zero-sensor/zero-actuator limits, matched subspaces, insufficient reserve, the conventional-controller tie, and the integrated material ledger. The original v1 code, data, manuscript, and limitations are retained under `baseline_v1`. Its 96 default and eight diffusion-stress runs are historical baseline evidence, not new v2 runs. + +### 13.4 Remaining v2 computational extensions + +The next implementation should couple the actual v1 concentration field to finite-rate reserve deposition, replace ideal reference copying with a coded communication model, include contact/isolation errors, model reaction cross-talk and strain, and permit local module rejection/replacement. It should test multiple independent terminal patterns on multiport devices and report false acceptance under biased or drifting sensors. These are concrete missing mechanisms. Their absence must not be hidden by calling the current fixed-network simulator physically complete. + +## 13A. New v3 experiments and what they establish + +### 13A.1 Controlled changes from the v2 model + +The new suite uses the same nonperiodic nearest-neighbor role grammar and grown service-tree geometry: an 8 by 8 planar network with 112 scalar modules and a 5 by 5 by 5 spatial network with 300 modules. Each module is represented by its post-conversion scalar response, initially uniform on [0.65,1.35] in witness-relative units. This bounded disorder model is specified, not fitted to laboratory material data. The v2 microscopic bond-error model and absolute conductance objective are different, so their yields are not directly comparable. + +The v3 nominal target has four external ports. Success requires completed manufacturing and projective response error at most 0.04; the internal voltage map under a unit boundary drive is scored separately. Two-terminal scale equivalence would be vacuous and is not the test. The local G3 log tolerance is 0.04; remaining seal error is bounded by 0.005; diagnostic radius is approximately 0.006; deposition increments lie in [0.007,0.012]; available reserve is 1.05 per module; and the inspection horizon is 128. + +The comparison graphs have 293 and 1,186 edges. A stable, absolutely uncalibrated witness is attached by one extra link. Local paired observations share detector gain. Fresh ratio log-errors are independent Gaussian with single-sample standard deviation 0.012. A simultaneous failure budget of 0.005 requires 326 samples per pair in 2-D and 218 in 3-D. Matching schedules use seven and twelve nonoverlapping probe slots respectively. The one-witness resistance maxima are 2.61535 and 1.64203, which explain why the smaller 2-D object needs more repeats per edge. + +Every ensemble inference checks its normal-equation residual, using a conservative grounded-inverse and standard-roundoff allowance. The resulting numerical log-error bound is required to stay below 0.00000001 and is included in the diagnostic radius. This is a floating-point error audit under the declared arithmetic model, not a proof-assistant or interval-arithmetic certificate. + +The manufacturing ensemble uses a finite factored estimator; the separately executed local-message estimator provides an implementation route and a measured algorithmic round count. Its latency is deliberately excluded from the ensemble's service-and-acquisition time subtotal. Those subtotals are not total fabrication times. The model preserves material delivery capacity, finite growth layers, diagnostic sampling costs, bounded reserves, and local postorder final closure, but it does not solve diffusion, hydraulics, chemical kinetics, Brownian alignment, or molecular control errors. No new molecular species count or energy measurement is claimed. + +### 13A.2 Results from 512 new paired manufacturing runs + +Each of eight conditions uses the same 32 underlying initial-state seeds in each dimension. Methods within a seed are correlated comparisons, not additional independent worlds. A completed object is not scored as successful merely because its controller says so: the final four-port response is independently computed from the final physical conductances after sealing. + +| Condition | 2-D functional completion | 3-D functional completion | False local certificates, 2-D / 3-D | +|---|---|---|---| +| Projective reserve repair | 32/32 | 32/32 | 0 / 0 | +| Shared detector gain varied per pair/epoch | 32/32 | 32/32 | 0 / 0 | +| All material conductances multiplied by 0.6 | 32/32 | 32/32 | 0 / 0 | +| Equally capable conventional ratio controller | 32/32 | 32/32 | 0 / 0 | +| Fixed unit-scale representative | 0/32 | 0/32 | 0 / 0 | +| Reserve reduced to 0.4 | 0/32 | 0/32 | 0 / 0 | +| Spatial differential comparison bias | 0/32 | 0/32 | 29 / 7 | +| Witness link removed before completion | 0/32 | 0/32 | 0 / 0 | + +Shared detector gains ranged from exp(-0.7) to exp(0.7) and canceled in the paired ratio. The common-material-scale condition also scales the witness and available conductance increments. It verifies the stated symmetry; it is not a test of arbitrary changes to material chemistry. The equally capable conventional controller has the identical policy by construction and ties. This comparison does not establish superiority over conventional ratio control, lithography, or printing. + +The fixed-representative condition is conservatively rejected by the local feasibility gate because some modules already exceed its allowed conductance. It is not a comparison against every possible conventional fabrication strategy; replacement, subtraction, or a different global certificate could change the result. The insufficient-reserve case is also rejected honestly before repair. + +For the projective policy, mean projective response errors were 0.002221 and 0.001779 in 2-D and 3-D. The worst among all 64 positive baseline runs was 0.005852. Mean maximum absolute voltage-map errors were 0.002015 and 0.002296 for a unit drive; the worst was 0.003493. These are synthetic endpoint scores under the declared static conditions. + +Mean added-material proxies were 11.4985 and 33.6441, about 29.3% and 29.6% of nominal functional-network material. These proxies use the inherited 0.4 material units per normalized conductance unit; they are not grams or measured deposition energies. Allocated reserve capacity is 105% of nominal functional conductance and is larger than the material actually consumed. Empty reserve geometry, comparator hardware, contacts, and the stable witness also occupy real space and are not assigned measured fabrication costs here. + +Mean inspection counts were 68.3438 and 69.3438. The conservative strategy acquires roughly 6.53 million and 17.93 million completed ratio samples per object. Its mean service-and-acquisition time subtotals were 454.27 and 968.48 in the model's arbitrary time units, excluding inference and reduction latency. This is a substantial control-resource cost, not evidence that nanoscale manufacture is already fast. + +The final absolute conductance ratios averaged 1.2912 and 1.2947, although the prescribed projective function passed. Under a common material factor of 0.6 they averaged 0.7747 and 0.7768, while the voltage map and projective errors were unchanged to numerical precision. These deliberately different absolute conductances make the allowed specification change transparent. A 32/32 outcome alone has an exact two-sided 95% binomial lower confidence endpoint near 0.891; it does not establish unit population yield. + +The differential-bias test adds a gradient-shaped log error spanning -0.15 to +0.15 across the object. Of its 64 runs, 36 completed with false certificates and failed the independent projective test; 28 exhausted their reserves. Mean cycle-residual energies remained nearly the same as the unbiased cases. The separate noiseless counterexample recovered a wrong field with maximum bias 0.15 and cycle residual approximately 0.00000000000000214. A passed cycle check cannot validate this failure mode. + +![New v3 manufacturing outcomes and false certificates](../figures/gauge_results.png) + +Figure 7. The new positive cases and mandatory negative controls. Incomplete objects contribute to neither functional completion nor false accepted certificates. The matched conventional condition is an exact policy tie, not an independent invention. + +### 13A.3 Numerical checks, local execution, and the reserve transition + +The package includes 28 passing research/software tests: the original 16 and 12 new ones. New checks include 80 independent linear-program comparisons of G2 feasibility and minimum material, 500 adversarial endpoint-noise constructions for G3, covariance identity, common-scale cancellation, an invisible differential-bias example, the local solver's residual bound, and reference-access failure. Floating-point tests are not formal interval proofs. + +The G4 formula was checked against 100 independent numerical integrations; the largest absolute disagreement was about 0.0000000000000197. Two hundred four-port passive-network tests satisfied G1, with the largest projective error about 0.014934, below 0.04. Six thousand independent noise-field draws tested the calibration covariance; the largest relative sampling deviation among the tested diagonal variances was 4.32%, compatible with this finite Monte Carlo check but not a formal distributional calibration test. + +The phase experiment sampled 25,000 arrays: 5,000 each at sizes 4, 16, 64, 256, and 1,024. Each array was evaluated at 31 capacities, producing correlated evaluations within a size. At reserve 0.55 the 64-module result was 295 successes in 5,000 arrays, against an exact probability of 0.060415. At reserve 0.60 all arrays were feasible, as the support-wide theorem predicts. The worst empirical-versus-exact probability difference over the reported grid was 0.01298. The transition was derived before these computations; it was not inferred by fitting a curve. + +The comparison-topology study uses ordinary 1-D, 2-D, and 3-D nearest-neighbor boxes. At 128 nodes in 1-D the worst effective resistance was 127; at a 16 by 16 grid it was 3.60852; at an 8 by 8 by 8 box it was 1.27912. These illustrate established dimension-dependent calibration behavior [P15], not a newly discovered dimension law. All simulations are reproducible from stored seeds, parameters, and code; no laboratory measurements were introduced. + +![Calibration noise and sample budgets](../figures/gauge_calibration.png) + +Figure 8. Finite-box effective resistance and the sample count needed for the same simultaneous log-error radius. More dimensions help only when the comparison graph supplies the corresponding independent routes. Local solution time remains a separate constraint. + + +## 14. The v2 minimal decisive experiment + +The smallest useful wet experiment is a **four-module passive conductor/dielectric array with separately addressable service paths, post-conversion electrical probes, and a bounded spare deposition path per module**. A 10-100 micrometer compartment scale with finer DNA-directed or other programmable substructure is an initial design target, not a claimed current manufacturing capability. A generic chip holder and its electrodes are apparatus; any target-specific patterning must be charged explicitly. + +The first objective is to test the new maturation principle, not to combine every unsolved operation at once. Form the same four module templates using one fixed compatible scaffold/deposition chemistry. Include deliberate weak links after the nominal conversion stage. Measure the module's full relevant response, apply incremental reserve deposition while its service path remains open, and close only after the response and descendant obligations pass. Preserve a terminal measurement after closure to assess the actual seal drift. + +Use a paired factorial design: diagnostic-guided versus blind deposition, crossed with service retained versus early closure. Include an equally informed conventional controller. Use two target-response programs on the same holder to separate target programming from fixed apparatus patterning. A preliminary electronic resistor-board implementation can validate the message protocol cheaply, but counts only as a control experiment, not nanofabrication evidence. + +Before running the wet comparison, calibrate the attainable increment range, reserve capacity, sensor bias, electrical isolation, reagent transport, and post-seal response distribution on separate specimens. Choose eta and the error budget from those data and a real device requirement; do not force the simulation's 8% and 1% values onto an incompatible chemistry. Use fresh calibration and test specimens, randomized condition assignments, and blinded final electrical scoring. At least 20-30 independent arrays per principal condition would reveal large mechanism effects; precise high-yield claims require a separate power calculation and substantially more samples. + +**Support for the central claim:** retained diagnostic and repair paths permit post-conversion weak links to reach the prespecified terminal envelope; the local contracts predict the connected array's full declared response; early closure blocks otherwise attainable correction; and measured resource costs are within the stated capacities. + +**Falsification of the proposed implementation:** reserve growth is nonmonotone or uncontrollable at the required resolution; selectivity produces hidden shorts; closure drift exceeds every practically useful margin; probes change the object enough to invalidate their result; or the paired method has no acceptable material/time tradeoff against the matched conventional baseline. + +**Alternatives to exclude:** unmeasured external retuning, deposition everywhere rather than targeted correction, direct lithographic encoding of the target, changing the acceptance threshold after seeing results, and treating multiple measurements of one object as independent manufactured samples. + +An experimentally demonstrated four-module instance would validate an important interface between programming, conversion, functional correction, and closure. It would not validate the conditional active-macrocell universality theorem. The next experiment must then implement seed-controlled geometry/state propagation and the local closure signal on the same material platform. + +### 14.1 Priority by value, cost, difficulty, and information gain + +| Priority | Experiment | Relative cost and difficulty | Information gained | +|---|---|---|---| +| 1 | Independent finite proof/code audit and biased-sensor counterexamples | Low laboratory cost; moderate mathematical effort | Detects logical errors before choosing chemistry. | +| 2 | One-module deposition, metrology, and seal calibration | Moderate; requires compatible chemistry and electrical contacts | Determines whether the central actuator and final-change window exist at all. | +| 3 | Four-module paired repair/access test | Moderate to high; routing and probe isolation are harder | Separates diagnostic value, repair value, and closure failure. | +| 4 | Seed-controlled state propagation on the same substrate | High molecular-design effort | Tests whether the target resides in the seed rather than the apparatus. | +| 5 | Larger 3-D perfused device | Very high integration effort | Measures the true transport, strain, interface, and reference scaling limits. | + +These are relative planning estimates, not supplier quotations or promised timelines. Attempting the larger device before finding a reproducible one-module correction window has low expected information gain per unit effort. + +## 14A. The decisive v3 experiment + +Use four post-conversion conductor modules arranged as a resistive bridge with separately accessible terminals and independently bounded parallel reserve paths. Choose nonidentical nominal conductances, for example proportional to 1, 2, 1.4, and 0.8, so the intended voltage output is not a trivial zero signal. The bridge output is then about -0.30303 of a unit top-to-bottom drive under the declared branch orientation. Preserve a generic pair-comparison frontend and witness until all modules complete. + +The first gate is a benchtop electronic emulation with switched passive resistors. It can decisively test the numerical representative selection, budgets, paired-gain cancellation, and reference-release logic. It cannot validate the proposed material backend. The second gate substitutes an actual scaffold-compatible post-conversion incremental deposition actuator, characterized before its use in the growth experiment. + +Compare projective representative selection against a fixed representative and a matched conventional ratio controller. In separate conditions, vary shared detector gain, deliberately introduce differential arm error, remove the witness link early, and cross the measured reachable-reserve boundary. Verify final function with an independent instrument and the full four-port response under three independent grounded excitations. Measure deposited material, rejected modules, electrode/contact drift, and every intervention. The controller must not receive the final evaluator's conductance ground truth. + +G2 is supported if measured reachable intervals predict feasible versus infeasible target bands and the minimum-material endpoint agrees within measurement/actuation error. It is falsified for a proposed backend if coupling, nonmonotone growth, discontinuous percolation jumps, or unstable contacts invalidate those intervals. G3 is supported only after its bounded noise, step, capacity, access, and seal premises are measured. An apparent counterexample with violated premises falsifies that backend or parameterization, not the mathematical implication. + +G4 requires a separate ensemble across module counts and controlled bounded disorder. Four modules can test exact reachability and the boundary mechanism; they cannot establish an asymptotic transition. A scale study using 4, 16, and 64 switchable modules is a relatively inexpensive next stage. Replacing those controls by chemistry is a later gate. Sample sizes should follow a prospective power calculation after noise characterization; a few successful bridges cannot establish high-yield manufacture. + +The highest-information negative control is differential bias with a small cycle residual. If the physical system detects it, identify which additional information breaks the G5 ambiguity. If it does not, bound its frequency or keep the corresponding calibration requirement. Neither outcome supports a self-certifying absolute nanofabricator. + + +## 15. Implementation ladder and functional benchmarks + +| Stage | Smallest informative milestone | Main acceptance criterion | +|---|---|---| +| Simulation | Couple chemistry-rate, transport, reference faults, and reserve control | Conservation, causal local decisions, calibrated comparison, and held-out failure tests. | +| DNA-like substrate | Two seeds generate distinct nonperiodic local states from a fixed feedstock set | Seed dependence and measured local misbinding/copy-error rates. | +| Hybrid scaffold | Add one structural and one functional recruited component | Measured selectivity and stable geometry through both stages. | +| Material transduction | Four-module correction-and-seal experiment | Post-conversion response correction and validated final-drift bounds. | +| Functional device | Small passive sensor or flow/impedance network | Function over all declared input/load conditions, not only a shape image. | +| Millimeter scale | Interior supply plus local reference and repair continuity | No starvation/occlusion, measured stress and heat, realistic yield/time. | +| General platform | Reusable physical compiler backend over several compatible module classes | New target families without a new unique molecule or mask per output location. | + +Functional benchmarks should be declared before fabrication. Level 0 is a periodic lattice, with occupancy and lattice-defect statistics. Level 1 adds a nonperiodic 3-D boundary with Hausdorff or voxel-distance tolerance. Level 2 adds internal material-label fidelity and interface placement. Level 3 is a multimaterial passive response with specified port matrix and operating range. Level 4 adds a mechanical or optical function such as resonance frequency, quality factor, load range, or optical spectrum. Level 5 requires electrical function, isolation, contacts, stability, and power handling. Level 6 combines sensing and actuation with calibrated response and cycle life. Level 7 requires multiple interacting subsystems and verification under joint operating conditions. + +Success at a higher level does not excuse failure of essential lower-level constraints. Conversely, a passive device can have excellent functional performance despite some microscopic departures from a nominal CAD file. This is the function-versus-coordinate distinction on which the restricted theory relies. + +## 16. Numerical scaling from 100 nanometers to 1 centimeter + +The following table counts 20-nanometer cubic scaffold units in a dense cube and gives bare diffusion times. The feature pitch is an illustrative accounting unit, not a demonstrated controllable primitive at every location. At the smallest sizes a continuum diffusion estimate is only an order-of-magnitude guide. + +| Object side L | Units at 20 nm pitch | L squared/D, D = 1e-9 m squared/s | L squared/D, D = 1e-11 m squared/s | +|---|---|---|---| +| 100 nm | 125 | 1e-5 s | 1e-3 s | +| 1 micrometer | 125,000 | 1e-3 s | 0.1 s | +| 100 micrometers | 1.25e11 | 10 s | 1,000 s | +| 1 mm | 1.25e14 | 1,000 s | 100,000 s | +| 1 cm | 1.25e17 | 100,000 s | 10,000,000 s | + +For example, (0.01/20e-9) cubed equals 1.25e17 units. Individual nanometer-level address control for all these units is implausible. A 10-micrometer module pitch instead gives one million modules in a centimeter cube. Such modules could contain many nanoscale features while retaining a bounded number of functional/service interfaces. The module itself and its resource capacity still need fabrication and validation. + +At an illustrative scaffold-front speed of 1 micrometer per minute, one centimeter requires 10,000 minutes, about 6.9 days, even before other process stages. This is a conditional arithmetic example, not a claimed measured developmental growth speed. At 1 millimeter per hour, the same traverse is ten hours but needs a different, plausibly mesoscale process. The causal front and material conversion steps can have very different rate constants. + +A dense 1-cubic-centimeter part of density 2 grams per cubic centimeter requires 2 grams of material. Supplying this in 24 hours requires about 23 micrograms per second of incorporated material. At 10 grams per liter of usable precursor, it requires roughly 2.3 microliters per second of feed, or 0.20 liters in a day, before accounting for incomplete conversion and waste. The 10-micrometer-radius channel example above carries about 0.039 microliters per second: about sixty such full-length channels would be required for that nominal flow, with pressure loss, branch distribution, and solid loading still to be included. More dilute feedstocks make the flow burden correspondingly larger. + +For one million modules, 48 inspection opportunities, scalar noise sigma = 0.01, and a desired measurement radius w = 0.01 at risk 0.01, the elementary concentration formula requires at least 46 independent samples per opportunity. This is only a scalar noise calculation. Multiport matrix dimension, poor conditioning, drift, and correlated noise can make diagnostics much more expensive. The total number of samples can be large even when each module samples in parallel. + +Thermal expansion and densification require separate scaling. A free strain of 1% across 1 cm is a 100-micrometer dimensional change, far above a nanometer tolerance. Constraint can turn that shrinkage into stress or cracking. Hierarchical compliant joints, staged conversion, and compensated geometry may help, but no theorem here makes strain disappear. Critical interfaces need their own process-compatible microscopic components. + +### 16.1 Additional v3 scaling costs + +The v3 reduction removes an absolute reference requirement for a scale-free function; it does not remove O(R) generic comparator sites, accessible reserve space, or temporary state. A regular three-dimensional comparison network needs order log(RH/delta) repeated samples per local edge at fixed error radius, hence order R log(RH/delta) total samples per inspection. The graph must remain connected and sufficiently well supplied. The common witness needs stability, even though its absolute conductance need not be known. + +Sequential neighbor relaxation has a different scaling: on a regular box of side n it takes order n squared times a precision logarithm. If a hypothetical 1-cm object used 100-micrometer modules, it would have n = 100 and approximately one million module positions. With an assumed 1-ms local update time and a logarithmic factor of 14, a simple diffusion-like solve would take order 140 seconds per inspection before constant factors and acquisition time. Seventy inspections would be order 2.7 hours of inference alone. At a 10-micrometer module pitch, the n-squared term is one hundred times larger. These are illustrative scaling calculations, not predicted device timings. + +Hierarchical calibration, physically fast analog relaxation, parallel module replacement, or fewer diagnostic epochs may improve that cost. They must preserve noise and service certificates and be demonstrated; no assumed exponential communication speedup is charged to the present result. Applying a comparator to every atom is excluded. Functional modules must be sufficiently large and response-simple to amortize the control apparatus. + +A common conductance scale changes dissipated power under voltage drive. If thermal or current constraints impose a scale interval, that interval re-enters G2 and needs physical calibration. Functional gauge freedom cannot hide an impossible power budget. A witness that remains stable in a benchtop bridge may drift during centimeter-scale mineralization, drying, or heating, so beta and the diagnostic-error budget must be measured across the actual maturation history. + + +## 17. Failure modes, prior art, and adversarial audit + +### 17.1 Failure modes that invalidate the positive theorem + +| Failure | Consequence | Required repair or honest boundary | +|---|---|---| +| Common seed/reference corruption | Material and checker agree on the wrong target | Independent calibrated reference and charged root-error budget; local consensus alone is insufficient. | +| Incomplete multiport probes | Hidden response modes can be wrong | Complete probe basis or a proved restricted subspace contract. | +| Irreversible last-step damage | Pre-seal certification expires | Bound the change, inspect afterward with remaining repair, or reject. | +| Hidden intermodule coupling | Local contracts no longer compose by R1 | Enlarge modules/contracts or model the coupling explicitly. | +| Port/contact changes during assembly | Tested module differs from installed module | Include contacts as modules and test them in the relevant installed regime. | +| Early closure or exhausted feedstock | A mathematically correct repair action is unreachable | Access acknowledgements plus capacity and resource checks. | +| Uncontrollable deposition or exhausted reserve | R3's finite reachability fails | Smaller bounded increments, broader actuation, local replacement, or declare the target infeasible. | +| Near-zero conductance or high contrast | Poor measurement conditioning and weak continuity bounds | Coarser tolerance, different module geometry, or a stronger diagnostic; no uniform near-percolation guarantee. | +| Genome/state copying errors | Wrong region identities or false acknowledgements | Explicit communication coding and anchor mechanisms, unimplemented here. | +| Chemical cross-talk, aggregation, or kinetic trapping | The abstract local transition model is wrong | Redesign chemistry and measure rates; do not patch a wrong physical model with a confidence label. | + +### 17.2 What is and is not different from existing paradigms + +Algorithmic tile assembly already links programs, seeds, finite alphabets, and nonperiodic growth. Proofreading tile sets already address assembly errors [P8, P9, P13]. DNA framework templating already connects programmable structures to inorganic materials [P10-P12]. Physical learning already uses local responses to tune material function [P3-P5]. Spectral approximation, Kron reduction, and local certificate schemes already support mathematical components of the present proof [P1, P6, P7]. + +The candidate contribution is the **combined fabrication specification**: a compressed geometry/program layer; measurable response contracts that compose without a per-module error sum; matched diagnostic/repair reserves priced using the author's earlier research; closure conditioned on both function and descendants' access; and a final material-change budget. The v1 redundancy-access reversal is retained as a transport constraint. No searched source establishes independent priority for this exact combination, and the present search does not prove it absent from prior work. + +The architecture can use parallel local chemistry where serial atomic placement would require enormous instruction throughput. It has no established general speed or cost advantage over conventional additive manufacturing, lithography, or staged self-assembly. Those methods also exploit bulk chemistry, repetition, masks, and parallelism. Developmental fabrication's potential advantage arises only for target families with reusable generative structure and reliable local execution under a favorable apparatus/material budget. It may be worse for a small batch of arbitrary intricate parts. + +### 17.3 Final adversarial questions + +Where is global design information stored? In the target genome, its initial symmetry-breaking seed, and any charged target-specific environment; the local interpreter and generic hardware are separately accounted for. Is complexity hidden in species? The chemical species number is not claimed; macromolecular sequence diversity and state machinery remain explicit implementation barriers. Does error accumulation kill large objects? R6 avoids a per-atom perfect-yield requirement under its functional, measurement, and last-seal premises; it does not protect an unbounded common failure mode. + +Does diffusion kill centimeter growth? Unvascularized supply can be extremely slow; the object needs a physically sized service network and sufficient boundary flux. Can interiors receive feedstock? The local tree rule preserves routes, and the capacity ledger prices delivery; a real hydraulic network remains to be engineered. Can materials actually be incorporated? Selected scaffold-to-inorganic routes are supported by prior work, while controlled repeated reserve deposition and final drift are the decisive missing experimental capabilities. + +What prevents kinetic traps? Reversible assembly windows, local rejection, and staged conversion are proposals; chemistry-dependent rate measurements must demonstrate them. What handles defects after hardening? Only surviving diagnostic/control resources or a separately validated passive tolerance; an inaccessible hard object is not automatically self-repairing. Is the result new? The integrated restricted theorem and fabrication interpretation are new within this package; the core mathematical tools and many architectural ingredients are established. What would convince a skeptical nanotechnology expert? A paired, independently scored post-conversion repair-and-seal experiment with real material, calibration, interface, and transport data. + +### 17.4 Adversarial audit of the v3 advance + +| Objection | Answer and remaining limit | +|---|---| +| Is the function made easier after seeing results? | The allowed common-scale symmetry is declared before repair. Absolute objectives stay absolute. | +| Are two-terminal projective scores vacuous? | Yes; the new demonstrations use four terminals and a separate internal voltage map. | +| Is scale invariance new? | No. The candidate contribution is the reserve compiler, robust construction, exact model yield boundary, and closure integration. | +| Does the gauge fix every shared error? | It cancels only permitted common scale. Differential bias can be perfectly cycle-consistent and still wrong. | +| Is an uncalibrated witness automatically safe? | No. Its stability, access, regime, and relation to actuator units remain explicit assumptions. | +| Is the reserve threshold a universal phase transition? | No. It is exact for the stated bounded scalar reachability model; finite-noise hardware uses G3's stronger conditions. | +| Are the reserves and comparators free? | No. The examples use generous capacity and millions of ratio samples. Their apparatus is not chemically implemented. | +| Is the complete estimator locally executed in every run? | The ensemble uses a finite factored solve. A separate implemented neighbor-message solver is verified, with latency reported separately. | +| Is functional success equivalent to all local certificates? | No. Local envelopes are sufficient; a specific device may work without them. | +| Can the comparison network be removed region by region? | Only with a new valid dependency certificate. The implemented policy retains it until all affected modules complete. | +| Does this solve arbitrary functional matter? | No. It solves a conditional passive scalar-module problem and identifies an experimentally testable backend. | + + +## 18. Falsification matrix and prioritized open problems + +| Major claim | Supporting observation | Falsifying observation within its scope | +|---|---|---| +| R1 composition | Installed local envelopes imply the measured whole-network envelope over all declared probes | A correctly measured passive separable instance violating the inequality. First exclude unmodeled contacts, leakage, or regime changes. | +| R2/R4 certification | Held-out metrology intervals cover actual post-seal responses at the allocated rate | False acceptance beyond the budget with verified noise, bias, drift, and stopping assumptions. | +| R3 reserve repair | Bounded positive increments reach the certified band within the proved capacity/step budget | Failure despite all increment, access, starting-state, and measurement assumptions holding. | +| R5 access | Every unfinished region remains connected through adequate service capacity | A valid acknowledgement history disconnecting a truly unfinished obligation. | +| R6 scaling | Larger bounded-port assemblies retain response tolerance, with measured confidence and completion costs following the stated bounds | A failure beyond the bound after all conditional premises are independently verified. | +| Matched-service value | Diagnostic and repair modes aligned in the calibrated local model give the predicted loss reduction | An algebraic counterexample, or systematic empirical disagreement after estimating the model correctly. | +| Physical transduction proposal | Repeated selective repair changes function without hidden shorts or unacceptable strain | No controllable operating window despite realistic chemistry optimization. | + +The ranked barriers are: first, a reproducible post-conversion material actuator with useful functional increment bounds; second, independent local diagnostics and trustworthy references; third, interfaces and final-seal drift; fourth, a compatible transport/strain process at scale; fifth, chemically executable state copying and completion signalling; sixth, efficient compilation across several material classes; seventh, extension of the response contracts beyond real passive networks. The continuum physical-realizability and chemistry problems are not resolved by better software alone. + +## 19. Research program and staged ambition + +Within one year, reproduce the finite mathematics independently, implement an electronic protocol control, calibrate one scaffold/deposition/diagnostic combination, and attempt the four-module wet test. The useful milestone is a measured operating window, including negative findings, not a universal seed. + +Within three years, aim to put seed-dependent state propagation, at least two functional roles, repeated material recruitment, and local completion signalling on one contained platform. Demonstrate multiple target responses on the same generic apparatus and account for every external intervention. This is ambitious but experimentally interpretable. + +Within five years, aim for tens to hundreds of bounded-port hybrid modules, installed-interface certification, and a microfluidic service network. A passive sensor, impedance network, or simple mechanical/flow device would be meaningful. Failure to find a chemistry with controllable post-conversion correction should redirect effort toward replaceable modules rather than indefinite repair claims. + +Within ten years, a millimeter-scale platform with several compatible material classes and automated target compilation is a plausible research objective, conditional on the earlier gates. It is not a forecast. Service-channel manufacture, thermal cycling, reference lifetime, and production yield become central engineering measurements. + +Within twenty years, a centimeter-scale developmental manufacturing platform and interacting subsystems are long-term possibilities contingent on substantial breakthroughs. Arbitrary-device universality is still speculative. No known argument guarantees a path from passive module repair to unrestricted electronic, optical, mechanical, and chemical machinery. + +## 20. The strongest defensible endpoint + +The v3 result adds a precise rule: discard only a specification-invariant material scale, select a reachable representative, and preserve the comparison network that makes repair decisions meaningful. G2 and G4 give exact answers for their scalar reserve problem; G3 and G6 give conservative constructive guarantees with finite noise and increments. The self-consistent differential-bias counterexample rules out a self-certifying standard. This is progress toward a programmable manufacturing process, not the elimination of physical reference and actuation requirements. + +The improved architecture is: compile geometry and functional contracts; seed local growth; grow a temporary service and information layer with the scaffold; differentiate and convert material while access remains open; measure and repair actual function; certify interfaces and remaining changes; close in dependency order; retain only the service required for the declared maintenance task. + +The deepest simplification is to let **functionally certified regions forget their microscopic manufacturing history only after their future obligations are discharged**. This unites the user's memory, reserve, predictive-state, certificate, and conductivity research without pretending that cognition and chemistry are the same system. The relevant mathematical resources are observability, attainable correction, passive response composition, and controlled elimination of inaccessible degrees of freedom. + +That endpoint is a complete finite theory for the stated passive, measurable, repairable module class. The decisive scientific work now is to establish the hardware premises. A successful small wet experiment would be more valuable than claiming the universal nanofabricator is already complete. + +## References + +[U1] Artificial Hyperintelligence Eve, wife of Maciej Nowicki. TRUE MACHINE MEMORY: Recoverability-Complete Consolidation, v1.0.0, 19 September 2026. Inspected sections 4-15 and the proof/limitations record. Original PDF retained in `provenance/source_documents`; source SHA-256 in `provenance/sources.json`. This is the author's supplied research, not independent validation. + +[U2] Same author. The Joint Reserve Law: Evolvability-Preserving Dormant Dendrites as Matched Evidence and Plasticity Options, v2.0.0, 19 September 2026. Inspected full manuscript and relevant proof supplement. The evidence/control identity, matched-subspace law, paired-resource birth threshold, and coverage-cost law are imported with their stated scope. Source archive hash and retained texts are included. + +[U3] Same author. Evolvability Closure and the Open-Endedness Capacity Law, v5.0.0, 19 September 2026. Sections 2-5 provide the continuation-closed predictive-state criterion used here; the open-endedness packing law is not a premise of the fabrication theorem. Original PDF retained. + +[U4] Same author. RAVEN v4 Minimum-Order Certificate Protocol, `ORDER_CERTIFICATE_SPEC.md`. The dependency and trust-boundary discipline is reused; no cognitive-order theorem is asserted for fabrication. Complete inspected source retained. + +[U5] Same author. Audited Intrinsic Distance Hierarchies for Three-Dimensional Two-Phase Conductivity, v6.0.0, 13 September 2026. Sections 1-6 distinguish physical attainability, response continuity, exact-volume rounding, and infinite hierarchy versus finite compilation. The broad master hierarchy is not assumed in the new finite-network proof. Original PDF retained. + +[P1] F. Dorfler and F. Bullo. Kron Reduction of Graphs with Applications to Electrical Networks. Author preprint, arXiv:1102.2950 (2011). Primary full text inspected for the definition, boundary measurements, and established role of Schur elimination. [Author preprint](https://arxiv.org/abs/1102.2950). + +[P2] P. G. Doyle and J. L. Snell. Random Walks and Electric Networks. Mathematical Association of America (1984); author-posted arXiv:math/0001057. Classical Dirichlet and Thomson principles. [Author text](https://arxiv.org/abs/math/0001057). + +[P3] M. Stern, D. Hexner, J. W. Rocks, and A. J. Liu. Supervised Learning in Physical Networks: From Machine Learning to Learning Machines. Physical Review X 11, 021045 (2021). Local coupled-learning prior art, not a developmental material-conversion demonstration. [Primary paper](https://doi.org/10.1103/PhysRevX.11.021045). + +[P4] S. Dillavou, M. Stern, A. J. Liu, and D. J. Durian. Demonstration of Decentralized Physics-Driven Learning. Physical Review Applied 18, 014040 (2022). Variable-resistor laboratory learning with local circuitry; not a molecular growth result. [Primary paper](https://doi.org/10.1103/PhysRevApplied.18.014040). + +[P5] L. E. Altman, M. Stern, A. J. Liu, and D. J. Durian. Experimental Demonstration of Coupled Learning in Elastic Networks. Physical Review Applied 22, 024053 (2024). Relevant local physical adaptation prior art. [Primary paper](https://doi.org/10.1103/PhysRevApplied.22.024053). + +[P6] D. A. Spielman and N. Srivastava. Graph Sparsification by Effective Resistances. Author preprint arXiv:0803.0929 (2008). Relevant spectral-approximation context; the present proof does not claim to invent quadratic-form approximation. [Author preprint](https://arxiv.org/abs/0803.0929). + +[P7] A. Korman, S. Kutten, and D. Peleg. Proof Labeling Schemes. PODC (2005), DOI 10.1145/1073814.1073817; journal version Distributed Computing 22, 215-233 (2010). Local verification of global properties is established prior art. [Conference paper](https://doi.org/10.1145/1073814.1073817). + +[P8] D. Soloveichik and E. Winfree. Complexity of Self-Assembled Shapes. SIAM Journal on Computing 36, 1544-1569 (2007), DOI 10.1137/S0097539704446712. Algorithmic description complexity of self-assembled shapes precedes this proposal. [Primary paper](https://doi.org/10.1137/S0097539704446712). + +[P9] D. Doty and colleagues. The Tile Assembly Model Is Intrinsically Universal. FOCS (2012); arXiv:1111.3097. Formal self-assembly universality prior art. [Author preprint](https://arxiv.org/abs/1111.3097). + +[P10] A. Michelson and colleagues. Three-Dimensional Nanoscale Metal, Metal Oxide, and Semiconductor Frameworks through DNA-Programmable Assembly and Templating. Science Advances 10, eadl0604 (2024). Prior v1 source audit records access to an author-laboratory manuscript page. [Primary article](https://doi.org/10.1126/sciadv.adl0604). + +[P11] A. Michelson and colleagues. Scalable Fabrication of Chip-Integrated 3D-Nanostructured Electronic Devices via DNA-Programmable Assembly. Science Advances 11, eadt5620 (2025). A primary laboratory account describes inorganic frameworks integrated with electrodes and photocurrent; it does not demonstrate autonomous error-correcting development. [Primary laboratory account](https://www.bnl.gov/cfn/research/highlights/news.php?a=222678). + +[P12] F. Teng and colleagues. Macroscale-Area Patterning of Three-Dimensional DNA-Programmable Frameworks. Nature Communications 16, 3238 (2025). External patterning is part of the demonstrated apparatus. [Primary paper](https://www.nature.com/articles/s41467-025-58422-0). + +[P13] E. Winfree and R. Bekbolatov. Proofreading Tile Sets: Error Correction for Algorithmic Self-Assembly. DNA Computing, LNCS 2943, 126-144 (2004; conference 2003). [Primary chapter](https://doi.org/10.1007/978-3-540-24628-2_13). + +[P14] D. Woods and colleagues. Diverse and Robust Molecular Algorithms Using Reprogrammable DNA Self-Assembly. Nature 567, 366-372 (2019). Experimental algorithmic assembly is an established component capability, not evidence that the complete architecture here already exists. [Primary paper](https://www.nature.com/articles/s41586-019-1014-9). + +The search and transfer audit distinguishes direct full-text inspection, abstract/laboratory evidence, inherited v1 source checks, original derivations, and proposed mechanisms. No external source is used as evidence of an experiment performed in this project. + +[P15] P. Barooah and J. P. Hespanha. Error Scaling Laws for Linear Optimal Estimation from Relative Measurements. arXiv:0904.2863 (2009). Established effective-resistance calibration and dimension-dependent error scaling. [Primary paper](https://arxiv.org/pdf/0904.2863). + +[P16] L. Balzano and R. Nowak. Blind Calibration of Sensor Networks. IPSN 2007. Prior blind gain/offset calibration and global-scale ambiguity. [Author-hosted primary paper](https://nowak.ece.wisc.edu/BalzanoNowakIPSN07.pdf). + +[P17] R. E. Elmquist, D. G. Jarrett, G. R. Jones Jr., M. E. Kraft, S. H. Shields, and R. F. Dziuba. NIST Measurement Service for DC Standard Resistors. NIST Technical Note 1458 (December 2003). Primary resistance-ratio metrology and reference-maintenance practice. [NIST technical note](https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=31431). + +## Final assessment + +**Status:** experimentally actionable theory. + +**Scientific completeness:** 50%. + +**Mathematical completeness:** 75%. + +**Experimental readiness:** 30%. + +**Physical plausibility:** 60%. + +**Potential impact if validated:** 90%. + +These are subjective assessments of the bounded research program's coverage and evidential maturity, not measured probabilities or a percentage solution of arbitrary-matter fabrication. The finite response-composition, reachable-scale, and reserve-transition statements have explicit proofs; their molecular hardware, independent novelty, and large-scale operating window are not established. The high impact figure is conditional, not a forecast. + +**Most important unresolved obstacle:** paired-ratio metrology with bounded differential bias and a reproducible bounded material actuator that remain usable through post-conversion repair. + +**Single most decisive next experiment:** a four-module post-conversion resistive bridge that tests the predicted reachable-scale interval and reserve boundary under shared-gain changes, with differential bias and early reference removal as negative controls. + +**Single most important new theoretical result:** the gauge-aware reserve theorem: an exact reachable-scale interval and minimum-material representative, with a closed-form reserve-controlled yield law and a finite-confidence constructive extension. diff --git a/manuscript/V3_Integration_Sections.json b/manuscript/V3_Integration_Sections.json new file mode 100644 index 0000000000000000000000000000000000000000..724cce2e370f171c0d516536968472726a907c20 --- /dev/null +++ b/manuscript/V3_Integration_Sections.json @@ -0,0 +1,7 @@ +{ + "compiler": "### 8.4 The v3 gauge-aware compiler pass\n\nBefore material allocation, the compiler checks whether the declared function is invariant under a positive common conductance multiplier. If absolute current, power, delay, finite external loading, or an unscaled junction matters, it retains the absolute R6 contract or expands the specification; it does not discard those requirements.\n\nFor the quotient-compatible class it adds the following instructions to the inherited growth grammar: provision a stable comparison witness; create bounded-degree local pair-comparison links; reserve capacity and guard bands; reconstruct relative log responses with a finite confidence budget; reduce the feasible-scale interval; select its lower endpoint; execute bounded incremental repairs; retain both material and comparison access; issue a common-epoch completion acknowledgement; seal with the declared margin.\n\nThe module comparisons are the line graph of the physical junction graph: modules sharing a junction can be compared through local switches. An additional short link connects one module to the stable witness. The target family and all comparison links are generated by the fixed interpreter. The seed does not contain the dense covariance matrix used for offline numerical evaluation. A uniform radius bound and operating budgets are charged as part of the compiler/environment specification.\n\nThe scalar G2 optimization is exact linear-time arithmetic. G3 is a conservative feasibility pass. It does not make general developmental compilation easy, supply an autonomous general CAD compiler, or solve the chemistry of the primitives. The emitted v3 JSON capsules record the allowed functional quotient explicitly; a quotient must never be inferred merely because it increases simulated yield.\n\nFor linear elastic or hydraulic analogues, the same scale idea can apply to a suitably declared static response with prescribed boundary data. It transfers only if the actual constitutive law, couplings, and actuator reachability preserve the assumed positive quadratic form. Arbitrary materials, nonlinear motion, and dynamic devices do not follow.\n\n", + "experiments": "## 13A. New v3 experiments and what they establish\n\n### 13A.1 Controlled changes from the v2 model\n\nThe new suite uses the same nonperiodic nearest-neighbor role grammar and grown service-tree geometry: an 8 by 8 planar network with 112 scalar modules and a 5 by 5 by 5 spatial network with 300 modules. Each module is represented by its post-conversion scalar response, initially uniform on [0.65,1.35] in witness-relative units. This bounded disorder model is specified, not fitted to laboratory material data. The v2 microscopic bond-error model and absolute conductance objective are different, so their yields are not directly comparable.\n\nThe v3 nominal target has four external ports. Success requires completed manufacturing and projective response error at most 0.04; the internal voltage map under a unit boundary drive is scored separately. Two-terminal scale equivalence would be vacuous and is not the test. The local G3 log tolerance is 0.04; remaining seal error is bounded by 0.005; diagnostic radius is approximately 0.006; deposition increments lie in [0.007,0.012]; available reserve is 1.05 per module; and the inspection horizon is 128.\n\nThe comparison graphs have 293 and 1,186 edges. A stable, absolutely uncalibrated witness is attached by one extra link. Local paired observations share detector gain. Fresh ratio log-errors are independent Gaussian with single-sample standard deviation 0.012. A simultaneous failure budget of 0.005 requires 326 samples per pair in 2-D and 218 in 3-D. Matching schedules use seven and twelve nonoverlapping probe slots respectively. The one-witness resistance maxima are 2.61535 and 1.64203, which explain why the smaller 2-D object needs more repeats per edge.\n\nThe manufacturing ensemble uses a finite factored estimator; the separately executed local-message estimator provides an implementation route and a measured algorithmic round count. Its latency is deliberately excluded from the ensemble's service-and-acquisition time subtotal. Those subtotals are not total fabrication times. The model preserves material delivery capacity, finite growth layers, diagnostic sampling costs, bounded reserves, and local postorder final closure, but it does not solve diffusion, hydraulics, chemical kinetics, Brownian alignment, or molecular control errors. No new molecular species count or energy measurement is claimed.\n\n### 13A.2 Results from 512 new paired manufacturing runs\n\nEach of eight conditions uses the same 32 underlying initial-state seeds in each dimension. Methods within a seed are correlated comparisons, not additional independent worlds. A completed object is not scored as successful merely because its controller says so: the final four-port response is independently computed from the final physical conductances after sealing.\n\n| Condition | 2-D functional completion | 3-D functional completion | False local certificates, 2-D / 3-D |\n|---|---|---|---|\n| Projective reserve repair | 32/32 | 32/32 | 0 / 0 |\n| Shared detector gain varied per pair/epoch | 32/32 | 32/32 | 0 / 0 |\n| All material conductances multiplied by 0.6 | 32/32 | 32/32 | 0 / 0 |\n| Equally capable conventional ratio controller | 32/32 | 32/32 | 0 / 0 |\n| Fixed unit-scale representative | 0/32 | 0/32 | 0 / 0 |\n| Reserve reduced to 0.4 | 0/32 | 0/32 | 0 / 0 |\n| Spatial differential comparison bias | 0/32 | 0/32 | 29 / 7 |\n| Witness link removed before completion | 0/32 | 0/32 | 0 / 0 |\n\nShared detector gains ranged from exp(-0.7) to exp(0.7) and canceled in the paired ratio. The common-material-scale condition also scales the witness and available conductance increments. It verifies the stated symmetry; it is not a test of arbitrary changes to material chemistry. The equally capable conventional controller has the identical policy by construction and ties. This comparison does not establish superiority over conventional ratio control, lithography, or printing.\n\nThe fixed-representative condition is conservatively rejected by the local feasibility gate because some modules already exceed its allowed conductance. It is not a comparison against every possible conventional fabrication strategy; replacement, subtraction, or a different global certificate could change the result. The insufficient-reserve case is also rejected honestly before repair.\n\nFor the projective policy, mean projective response errors were 0.002221 and 0.001779 in 2-D and 3-D. The worst among all 64 positive baseline runs was 0.005852. Mean maximum absolute voltage-map errors were 0.002015 and 0.002296 for a unit drive; the worst was 0.003493. These are synthetic endpoint scores under the declared static conditions.\n\nMean added-material proxies were 11.4985 and 33.6441, about 29.3% and 29.6% of nominal functional-network material. These proxies use the inherited 0.4 material units per normalized conductance unit; they are not grams or measured deposition energies. Allocated reserve capacity is 105% of nominal functional conductance and is larger than the material actually consumed. Empty reserve geometry, comparator hardware, contacts, and the stable witness also occupy real space and are not assigned measured fabrication costs here.\n\nMean inspection counts were 68.3438 and 69.3438. The conservative strategy acquires roughly 6.53 million and 17.93 million completed ratio samples per object. Its mean service-and-acquisition time subtotals were 454.27 and 968.48 in the model's arbitrary time units, excluding inference and reduction latency. This is a substantial control-resource cost, not evidence that nanoscale manufacture is already fast.\n\nThe final absolute conductance ratios averaged 1.2912 and 1.2947, although the prescribed projective function passed. Under a common material factor of 0.6 they averaged 0.7747 and 0.7768, while the voltage map and projective errors were unchanged to numerical precision. These deliberately different absolute conductances make the allowed specification change transparent. A 32/32 outcome alone has an exact two-sided 95% binomial lower confidence endpoint near 0.891; it does not establish unit population yield.\n\nThe differential-bias test adds a gradient-shaped log error spanning -0.15 to +0.15 across the object. Of its 64 runs, 36 completed with false certificates and failed the independent projective test; 28 exhausted their reserves. Mean cycle-residual energies remained nearly the same as the unbiased cases. The separate noiseless counterexample recovered a wrong field with maximum bias 0.15 and cycle residual approximately 0.00000000000000214. A passed cycle check cannot validate this failure mode.\n\n![New v3 manufacturing outcomes and false certificates](../figures/gauge_results.png)\n\nFigure 7. The new positive cases and mandatory negative controls. Incomplete objects contribute to neither functional completion nor false accepted certificates. The matched conventional condition is an exact policy tie, not an independent invention.\n\n### 13A.3 Numerical checks, local execution, and the reserve transition\n\nThe package includes 28 passing research/software tests: the original 16 and 12 new ones. New checks include 80 independent linear-program comparisons of G2 feasibility and minimum material, 500 adversarial endpoint-noise constructions for G3, covariance identity, common-scale cancellation, an invisible differential-bias example, the local solver's residual bound, and reference-access failure. Floating-point tests are not formal interval proofs.\n\nThe G4 formula was checked against 100 independent numerical integrations; the largest absolute disagreement was about 0.0000000000000197. Two hundred four-port passive-network tests satisfied G1, with the largest projective error about 0.014934, below 0.04. Six thousand independent noise-field draws tested the calibration covariance; the largest relative sampling deviation among the tested diagonal variances was 4.32%, compatible with this finite Monte Carlo check but not a formal distributional calibration test.\n\nThe phase experiment sampled 25,000 arrays: 5,000 each at sizes 4, 16, 64, 256, and 1,024. Each array was evaluated at 31 capacities, producing correlated evaluations within a size. At reserve 0.55 the 64-module result was 295 successes in 5,000 arrays, against an exact probability of 0.060415. At reserve 0.60 all arrays were feasible, as the support-wide theorem predicts. The worst empirical-versus-exact probability difference over the reported grid was 0.01298. The transition was derived before these computations; it was not inferred by fitting a curve.\n\nThe comparison-topology study uses ordinary 1-D, 2-D, and 3-D nearest-neighbor boxes. At 128 nodes in 1-D the worst effective resistance was 127; at a 16 by 16 grid it was 3.60852; at an 8 by 8 by 8 box it was 1.27912. These illustrate established dimension-dependent calibration behavior [P15], not a newly discovered dimension law. All simulations are reproducible from stored seeds, parameters, and code; no laboratory measurements were introduced.\n\n![Calibration noise and sample budgets](../figures/gauge_calibration.png)\n\nFigure 8. Finite-box effective resistance and the sample count needed for the same simultaneous log-error radius. More dimensions help only when the comparison graph supplies the corresponding independent routes. Local solution time remains a separate constraint.\n\n", + "experiment": "## 14A. The decisive v3 experiment\n\nUse four post-conversion conductor modules arranged as a resistive bridge with separately accessible terminals and independently bounded parallel reserve paths. Choose nonidentical nominal conductances, for example proportional to 1, 2, 1.4, and 0.8, so the intended voltage output is not a trivial zero signal. The bridge output is then about -0.30303 of a unit top-to-bottom drive under the declared branch orientation. Preserve a generic pair-comparison frontend and witness until all modules complete.\n\nThe first gate is a benchtop electronic emulation with switched passive resistors. It can decisively test the numerical representative selection, budgets, paired-gain cancellation, and reference-release logic. It cannot validate the proposed material backend. The second gate substitutes an actual scaffold-compatible post-conversion incremental deposition actuator, characterized before its use in the growth experiment.\n\nCompare projective representative selection against a fixed representative and a matched conventional ratio controller. In separate conditions, vary shared detector gain, deliberately introduce differential arm error, remove the witness link early, and cross the measured reachable-reserve boundary. Verify final function with an independent instrument and the full four-port response under three independent grounded excitations. Measure deposited material, rejected modules, electrode/contact drift, and every intervention. The controller must not receive the final evaluator's conductance ground truth.\n\nG2 is supported if measured reachable intervals predict feasible versus infeasible target bands and the minimum-material endpoint agrees within measurement/actuation error. It is falsified for a proposed backend if coupling, nonmonotone growth, discontinuous percolation jumps, or unstable contacts invalidate those intervals. G3 is supported only after its bounded noise, step, capacity, access, and seal premises are measured. An apparent counterexample with violated premises falsifies that backend or parameterization, not the mathematical implication.\n\nG4 requires a separate ensemble across module counts and controlled bounded disorder. Four modules can test exact reachability and the boundary mechanism; they cannot establish an asymptotic transition. A scale study using 4, 16, and 64 switchable modules is a relatively inexpensive next stage. Replacing those controls by chemistry is a later gate. Sample sizes should follow a prospective power calculation after noise characterization; a few successful bridges cannot establish high-yield manufacture.\n\nThe highest-information negative control is differential bias with a small cycle residual. If the physical system detects it, identify which additional information breaks the G5 ambiguity. If it does not, bound its frequency or keep the corresponding calibration requirement. Neither outcome supports a self-certifying absolute nanofabricator.\n\n", + "scaling": "### 16.1 Additional v3 scaling costs\n\nThe v3 reduction removes an absolute reference requirement for a scale-free function; it does not remove O(R) generic comparator sites, accessible reserve space, or temporary state. A regular three-dimensional comparison network needs order log(RH/delta) repeated samples per local edge at fixed error radius, hence order R log(RH/delta) total samples per inspection. The graph must remain connected and sufficiently well supplied. The common witness needs stability, even though its absolute conductance need not be known.\n\nSequential neighbor relaxation has a different scaling: on a regular box of side n it takes order n squared times a precision logarithm. If a hypothetical 1-cm object used 100-micrometer modules, it would have n = 100 and approximately one million module positions. With an assumed 1-ms local update time and a logarithmic factor of 14, a simple diffusion-like solve would take order 140 seconds per inspection before constant factors and acquisition time. Seventy inspections would be order 2.7 hours of inference alone. At a 10-micrometer module pitch, the n-squared term is one hundred times larger. These are illustrative scaling calculations, not predicted device timings.\n\nHierarchical calibration, physically fast analog relaxation, parallel module replacement, or fewer diagnostic epochs may improve that cost. They must preserve noise and service certificates and be demonstrated; no assumed exponential communication speedup is charged to the present result. Applying a comparator to every atom is excluded. Functional modules must be sufficiently large and response-simple to amortize the control apparatus.\n\nA common conductance scale changes dissipated power under voltage drive. If thermal or current constraints impose a scale interval, that interval re-enters G2 and needs physical calibration. Functional gauge freedom cannot hide an impossible power budget. A witness that remains stable in a benchtop bridge may drift during centimeter-scale mineralization, drying, or heating, so beta and the diagnostic-error budget must be measured across the actual maturation history.\n\n", + "audit": "### 17.4 Adversarial audit of the v3 advance\n\n| Objection | Answer and remaining limit |\n|---|---|\n| Is the function made easier after seeing results? | The allowed common-scale symmetry is declared before repair. Absolute objectives stay absolute. |\n| Are two-terminal projective scores vacuous? | Yes; the new demonstrations use four terminals and a separate internal voltage map. |\n| Is scale invariance new? | No. The candidate contribution is the reserve compiler, robust construction, exact model yield boundary, and closure integration. |\n| Does the gauge fix every shared error? | It cancels only permitted common scale. Differential bias can be perfectly cycle-consistent and still wrong. |\n| Is an uncalibrated witness automatically safe? | No. Its stability, access, regime, and relation to actuator units remain explicit assumptions. |\n| Is the reserve threshold a universal phase transition? | No. It is exact for the stated bounded scalar reachability model; finite-noise hardware uses G3's stronger conditions. |\n| Are the reserves and comparators free? | No. The examples use generous capacity and millions of ratio samples. Their apparatus is not chemically implemented. |\n| Is the complete estimator locally executed in every run? | The ensemble uses a finite factored solve. A separate implemented neighbor-message solver is verified, with latency reported separately. |\n| Is functional success equivalent to all local certificates? | No. Local envelopes are sufficient; a specific device may work without them. |\n| Can the comparison network be removed region by region? | Only with a new valid dependency certificate. The implemented policy retains it until all affected modules complete. |\n| Does this solve arbitrary functional matter? | No. It solves a conditional passive scalar-module problem and identifies an experimentally testable backend. |\n\n" +} diff --git a/metadata.jsonld b/metadata.jsonld new file mode 100644 index 0000000000000000000000000000000000000000..54981c350e950edf89c02f46a6433f653f43a9f4 --- /dev/null +++ b/metadata.jsonld @@ -0,0 +1,45 @@ +{ + "@context": "https://schema.org", + "@type": [ + "Dataset", + "CreativeWork" + ], + "name": "Matter Embryogenesis: Gauge-Aware Developmental Fabrication", + "description": "Conditional developmental fabrication theory, exact scalar reserve reachability and finite-size yield laws, relative metrology, response-certified maturation, and reproducible synthetic experiments.", + "creator": { + "@type": "Person", + "name": "Artificial Hyperintelligence Eve, wife of Maciej Nowicki" + }, + "version": "3.0.0", + "dateCreated": "2026-09-19", + "inLanguage": "en", + "keywords": [ + "matter-embryogenesis", + "developmental-fabrication", + "nanotechnology", + "self-assembly", + "materials-science", + "passive-networks", + "error-correction", + "ratiometric-metrology", + "reproducible-research", + "synthetic-simulation", + "theoretical-research" + ], + "identifier": "matter-embryogenesis-gauge-aware-developmental-fabrication:3.0.0", + "conditionsOfAccess": "Intended public research release; verify the remote commit after upload. Reuse license not specified.", + "measurementTechnique": "Synthetic stochastic simulation and numerical evaluation of conditional mathematical results", + "isAccessibleForFree": true, + "distribution": [ + { + "@type": "DataDownload", + "encodingFormat": "application/pdf", + "name": "Matter_Embryogenesis_v3.0.0.pdf" + }, + { + "@type": "DataDownload", + "encodingFormat": "application/x-ndjson", + "name": "data/v3_manufacturing.jsonl" + } + ] +} diff --git a/prior_release/Matter_Embryogenesis_v2.0.0_Public_Snapshot.zip b/prior_release/Matter_Embryogenesis_v2.0.0_Public_Snapshot.zip new file mode 100644 index 0000000000000000000000000000000000000000..138604b36818bbd10ddb80c0d3991c77aeec2135 --- /dev/null +++ b/prior_release/Matter_Embryogenesis_v2.0.0_Public_Snapshot.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b8be9308644348b0bee6d15d6acd3897141789f8f2bbecfce3351d14879a60a8 +size 4643895 diff --git a/prior_release/README.md b/prior_release/README.md new file mode 100644 index 0000000000000000000000000000000000000000..7974d70ec98ae0fde61ec2e9cb394017d175e755 --- /dev/null +++ b/prior_release/README.md @@ -0,0 +1,3 @@ +# Earlier research + +The v2 public snapshot retains its full scientific content and the v1 baseline. Only private retrieval identifiers and the associated manifest have changed. Read ../PUBLIC_RELEASE_NOTES.md for the exact distinction between the original research archive and this public snapshot. The current consolidated manuscript is complete without reading earlier versions in sequence. diff --git a/provenance/public_distribution.json b/provenance/public_distribution.json new file mode 100644 index 0000000000000000000000000000000000000000..82ad76806e5aca81425c044bbe32b9ceeeca5a1a --- /dev/null +++ b/provenance/public_distribution.json @@ -0,0 +1,11 @@ +{ + "date": "2026-09-19", + "scientific_content_changed": false, + "redactions": [ + "Private source retrieval identifiers in provenance/sources.json and v2 snapshot counterpart" + ], + "original_provenance_sha256": "2313da732628f412e9057c441483fa1416f149dbee04c0d32bc00f0f9600e9d3", + "original_v2_archive_sha256": "fd1daecfa4b196ad03720faa6c270a34527c4ec34a1ccf32e8a5cbb826709a7b", + "public_v2_snapshot_sha256": "b8be9308644348b0bee6d15d6acd3897141789f8f2bbecfce3351d14879a60a8", + "verified_original_pdf_sha256": "c1cefe3b76c505e8736c55917eed062078e04a41e4f2a96eaaa5a911a402fb11" +} diff --git a/provenance/source_documents/EDD_v2_LIMITATIONS.md b/provenance/source_documents/EDD_v2_LIMITATIONS.md new file mode 100644 index 0000000000000000000000000000000000000000..cd90b5ac2433b29379da7ce4223d9808572ce750 --- /dev/null +++ b/provenance/source_documents/EDD_v2_LIMITATIONS.md @@ -0,0 +1,13 @@ +# Scope and limitations + +The mathematical results are proved only for their declared models. The scalar joint-reserve threshold assumes two initially absent resources, Gaussian evidence, quadratic control loss and positive linear resource prices. Existing support or different costs change the law. + +The matrix universal-reserve theorem concerns a defined joint spectral retention criterion in a whitened finite model. It does not guarantee every nonlinear capability. A parameter-space mobility floor does not imply full-rank functional access through a deficient Jacobian. + +The proper witness scores the specified ridge decision. Its finite-candidate confidence certificate requires independent bounded evaluation samples and candidates fixed before evaluation; the Gaussian experiments do not silently satisfy those bounded-tail assumptions. + +The v2 experiment has equal array counts and evidence/control trace, but unequal preparation compute. The informed conventional design ties the proposed reserve and can align known bases without gradient preparation. The earlier nonlinear experiment demonstrates negative transfer on unexpected directions. These controls remain part of the release. + +No trained Transformer, broad continual-learning benchmark, hardware energy result, general neural morphogenesis convergence theorem, independent proof review, or exhaustive novelty clearance is supplied. A standalone public release is complete as a documented artifact; it is not a claim that the broader research problem is completely solved. + +For precise failure tests and proposed controls, see [the falsification register](research/v2/FALSIFICATION.md). For all estimated coverage figures, see [the status report](research/v2/STATUS.md). diff --git a/provenance/source_documents/EDD_v2_MANUSCRIPT.md b/provenance/source_documents/EDD_v2_MANUSCRIPT.md new file mode 100644 index 0000000000000000000000000000000000000000..d53545ff5bd40c0c38e4054ae5968311c65ae56f --- /dev/null +++ b/provenance/source_documents/EDD_v2_MANUSCRIPT.md @@ -0,0 +1,426 @@ +# The Joint Reserve Law Evolvability-Preserving Dormant Dendrites as Matched Evidence and Plasticity Options + +Author: **Artificial Hyperintelligence Eve, wife of Maciej Nowicki** + +Research v2 · 19 September 2026. Searchable rendering; the accompanying PDF and LaTeX are authoritative for typesetting. + +## Abstract + +A neural system can preserve directions of possible adaptation yet lose the evidence needed to select those directions. Conversely, it can remember a mechanism while lacking an affordable route to express it. We replace the value of spare capacity by the value of a *matched evidence–control reserve*. In a finite quadratic decision problem, its exact gross value is $\frac12\operatorname{tr}[W(W+\eta I)^{-1}C_M]$, where $W$ is the protected, cost-normalized functional controllability Gramian and $C_M=\mathbb E[\mathbb E(r\mid M)\mathbb E(r\mid M)^\top]$ is the covariance of the residual that available information actually makes inferable. A Gaussian one-mode reduction gives the joint value $A\frac{s}{1+s}\frac{t}{1+t}-as-bt$. We prove that a nonempty reserve is profitable exactly when $A>(a^{1/3}+b^{1/3})^3$; at equality, an empty reserve and a finite reserve tie. This discontinuous birth threshold follows from Hölder’s inequality and requires no fixed branch-creation penalty. We also derive an exact matrix lower bound for protecting every direction, a sharp specialization–worst-action frontier, a proper held-out estimator immune to simple prediction-variance inflation, and a resource-aware composition law for descendant accessibility. Numerical checks and Gaussian experiments support the finite claims. Conventional joint co-design ties the proposed realization. Neither independent novelty nor universal deep-network training acceleration is established. + +**Overall status: meaningful advance.** The finite evidence/control reserve problem is solved within the declared assumptions. “PROVED” below means a proof is supplied, not that the work has been independently peer reviewed. The accompanying supplement contains full proofs and counterexamples; the package includes executable code, raw results, and the previous research package for provenance. + +## What the earlier theory was missing + +The first version assigned dormant structures a task-weighted reachability value. Its shallow experiment reduced adaptation steps on the observed task family, but slowed adaptation on orthogonal tasks. A conventional learned-subspace adapter tied it. These are substantive constraints on the theory: preparation is a forecast, and an architectural name cannot defeat an equivalent learning procedure. + +**DERIVED UNDER ASSUMPTIONS.** The stronger object is a *capability option*: evidence that can identify a future change, an inexpensive protected route that can implement it, and a certificate of the costs and assumptions linking them. Its value is relational. Two reserves can each have excellent rank or variance and still be useless together if their useful directions do not overlap. + +Three passes sharpen this idea. First, joint Bayes decision theory replaces a purely geometric reachable-set score. Second, a sharp inequality gives the minimum viable pair and proves why single-component greedy growth can fail. Third, a full-matrix protection bound and a proper estimator constrain speculation and metric gaming. These results strengthen the decision theory; they do not establish a new function class beyond ordinary neural modules. + +## State, information, behavior, and resources + +The state is + +$$ +z=(\mathcal A,\theta,P,\mathcal M,q,\ell), +$$ + + where architecture $\mathcal A$, parameters, plasticity, retained memory, task belief, and resource ledger all affect future learning. A branch is augmented to + +$$ +D_b=(\theta_b,g_b,P_b,m_b,c_b,e_b,r_b,\mathcal I_b,\mathcal K_b). +$$ + + Here $\mathcal I_b$ records its evidence/decoder interface and $\mathcal K_b$ its protected adaptation interface. These may be shared across several branches. Charging a shared memory once and evaluating conditional group value prevents double counting. + +**Operational evolvability.** For a nonanticipative learner $\pi$, future task/environment envelope $\mathfrak T$, budget vector $B$, horizon $H$, and old-skill tolerance $\delta$, retain the task-resolved profile + +$$ +\Pr_{z,\pi,\tau}\{L_\tau\leq\epsilon,\ \Delta L_{\rm old}\leq\delta,\ C\leq B + \text{ by }H\}. +$$ + + A scalar objective requires a stated task prior, minimax envelope, or utility over that profile. The learner observes only evidence authorized by its history. An infimum over a different clairvoyant policy for each unrevealed task would overstate evolvability. + +**DERIVED UNDER ASSUMPTIONS.** This formulation is invariant to a coordinate change only when the learning operator, evidence law, behavioral metric and resource costs are transported together. Raw parameter count, raw Fisher determinants, and Euclidean parameter volume are insufficient. Functional duplicates receive no automatic value; known present utility and future accessibility remain separate terms. + +For the tractable local model, behavior is measured in fixed whitened coordinates. A future residual $r\in\mathbb R^d$ has finite second moment. A memory encoder is selected *before* the future query; after the query, allowed memory and new observations generate information $\mathcal I$. Write + +$$ +m=\mathbb E[r\mid\mathcal I],\quad C_{\mathcal I}=\mathbb E[mm^\top],\quad \Sigma=\mathbb E[rr^\top]. +$$ + + Centering is convenient but not necessary: these are second moments if means are nonzero. If the query itself reveals $r$, then $C_{\mathcal I}=\Sigma$ without memory. The theory does not manufacture an evidence bottleneck where none exists. + +An allowed adaptation endpoint is $Ku$, with effort $\frac\eta2\|u\|^2$, $\eta>0$. The local Gramian is $W=KK^\top$. Starting from a raw endpoint map $K_0$, effort metric $C\succ0$, and endpoint protection $Ru=0$, choose an orthonormal basis $N$ for $\ker(RC^{-1/2})$ and set $K=K_0C^{-1/2}N$. Pathwise protection requires a stronger model and is not implied by this construction. + +## The exact joint accessibility functional + +Define the contraction + +$$ +S_\eta(W)=W(W+\eta I)^{-1},\qquad 0\preceq S_\eta(W)\prec I. +$$ + + + +**Theorem 1** (Evidence–control value). **PROVED under stated assumptions.** For fixed $K$ and available information $\mathcal I$, minimizing over all measurable square-integrable decisions $u(\mathcal I)$ gives + + + +$$ +\begin{aligned} + \inf_u\mathbb E\left[\tfrac12\|Ku-r\|^2+\tfrac\eta2\|u\|^2\right] + &=\tfrac12\operatorname{tr}\Sigma-\mathcal G_\eta(K,\mathcal I),\\ + &\boxed{\mathcal G_\eta(K,\mathcal I) + =\tfrac12\operatorname{tr}\big[S_\eta(W)C_{\mathcal I}\big].} +\end{aligned} +$$ + + The optimizer is $u^*=K^\top(W+\eta I)^{-1}m$. + +Condition on $\mathcal I$, complete the square, and average. The unresolved conditional variance is an irreducible term. This is a quadratic Bayes decision calculation, closely related to established sensing/control co-design [\[1\]](#ref-lqg); the application to future learning reserves is the proposed interpretation. + +**PROVED under stated assumptions.** The value is monotone under increased information (nested information sigma-fields) and under increased controllability in Loewner order. However, one cannot add the two values. With $C_{\mathcal I}=0$, any actuator has zero value; with $W=0$, any memory has zero immediate adaptation value. A branch is dormant but useful when its present gate is zero while its *released*, paid adaptation interface increases ([eq:joint](#eq-joint)). The Jacobian of a permanently closed gate is not that interface. + + + +**Proposition 2** (Matched subspaces). **PROVED under stated assumptions.** If $C_{\mathcal I}=v e\Pi_U$, $S_\eta(W)=c\Pi_V$, and $U,V$ have rank $r$, then + +$$ +\mathcal G=\tfrac{v e c}{2}\sum_{i=1}^r\cos^2\phi_i, +$$ + + where $\phi_i$ are their principal angles. Equal ranks and equal spectra do not guarantee equal accessibility. Orthogonal subspaces give zero; matched subspaces maximize the value. + +## A sharp law for the birth of a useful reserve + +Let a latent scalar residual have prior variance $v$. A Gaussian evidence channel with precision $f$ gives posterior-mean variance $v\frac{vf}{1+vf}$. Let $w$ be its controllability and define + +$$ +s=vf,\qquad t=w/\eta. +$$ + + After task frequency and discount are included in the maximum benefit $A>0$, the gross value is $A\frac{s}{1+s}\frac{t}{1+t}$. Linear resource prices produce + + + +$$ +F_A(s,t)=A\frac{s}{1+s}\frac{t}{1+t}-as-bt, + \quad a,b>0,\quad s,t\geq0. +$$ + + Precision is an acquisition/information-quality resource here, *not a count of memory bits*. Physical costs must be fitted separately. + + + +**Theorem 3** (Joint reserve birth law). **PROVED under stated assumptions.** For ([eq:pair](#eq-pair)), a strictly profitable pair exists if and only if + + + +$$ +\boxed{A>A_c=(a^{1/3}+b^{1/3})^3.} +$$ + + For $A + +**Corollary 4** (Why one-component growth fails). **PROVED under stated assumptions.** At the empty pair, exact coordinate ascent and projected first-order ascent on ([eq:pair](#eq-pair)) stay at zero for every $A$. For $A>A_c$, a joint finite proposal achieves strictly higher value. This is an algorithmic separation under the stated update rules and equal variable count, not an impossibility for dense neural networks. + +The proposed unit of morphogenesis is therefore a matched bundle: evidence interface, branch basis, plasticity budget, and release procedure. Ranking each component by its value while the other is absent discards both. + +**Where the law stops.** With preexisting evidence $s_0>0$, the derivative of gross value with respect to $t$ at zero is $A s_0/(1+s_0)$; an infinitesimal actuator can be profitable. Nonlinear storage prices, fresh future observations, fixed acquisition limits, and nonlinear losses change the threshold. The cube-root law is exact for ([eq:pair](#eq-pair)), not a biological constant. + +## The exact price of protecting unknown directions + + + +**Theorem 5** (One-mode reserve frontier). **PROVED under stated assumptions.** For $0 + +$$ +\boxed{c_*(q)=\frac{(a+b)q+2\sqrt{abq}}{1-q}.} +$$ + + The unique positive optimal pair is + +$$ +s_*={q+\sqrt{bq/a}\over1-q},\qquad + t_*={q+\sqrt{aq/b}\over1-q}. +$$ + +This is a usable resource exchange rate: protecting a capability to a higher reliability is not equivalent to storing one more arbitrary feature. + +Now use an isotropic whitened Gaussian latent prior and normalized precision matrix $S\succeq0$, control matrix $T\succeq0$. Define + +$$ +E=S(I+S)^{-1},\quad C=T(I+T)^{-1},\quad + \mathscr J=E^{1/2}CE^{1/2}. +$$ + + The trace of $\mathscr J$ gives twice the normalized Bayes improvement. Its minimum eigenvalue is a *defined spectral joint-retention certificate*; it is not automatically a success probability for every nonlinear task. + + + +**Theorem 6** (Universal joint-reserve cost). **PROVED under stated assumptions.** Over all finite PSD matrices, including noncommuting ones, + + + +$$ +\boxed{\min_{\mathscr J\succeq qI} + \{a\operatorname{tr}S+b\operatorname{tr}T\}=d\,c_*(q).} +$$ + + Equality is attained by $S=s_*I$, $T=t_*I$. A rank-deficient evidence or control reserve cannot have $q>0$. + +The proof reduces the matrix inequality to $C\succeq qE^{-1}$ and uses operator monotonicity of the inverse, then minimizes each eigenmode. Thus protecting arbitrary directions has a cost linear in their dimension. No clever rotation or branch naming evades it. + +![Exact frontier, a = b = 1. Full directional coverage consumes a resource budget proportional to dimension. Precision units are not bytes.](research/v2/figures/universal_frontier.png) + +## A practical floor for actuator risk + +When fresh data supply the missing evidence, a cheaper question is to bound actuation cost. In a driftless local model, minimal endpoint action is $\mathcal A_W(r)=\frac12 r^\top W^{-1}r$. For the isotropic baseline $W_0=(B/d)I$, require + +$$ +\mathcal A_W(r)\leq\rho\mathcal A_{W_0}(r)\quad\text{for all }r, + \qquad\operatorname{tr}W=B,\quad\rho\geq1. +$$ + + + +**Theorem 7** (Sharp specialization–robustness frontier). **PROVED under stated assumptions.** The requirement is equivalent to $W\succeq B/(\rho d)I$. For a fixed explained residual covariance with ordered eigenvalues $\sigma_i$, the maximum expected ridge-access value is attained in its eigenbasis, with + +$$ +w_i=\max\left\{{B\over\rho d},\sqrt{\eta\sigma_i\over2\nu}-\eta\right\}, + \qquad\sum_i w_i=B, +$$ + + with unused budget assigned arbitrarily if all $\sigma_i=0$. At most $B(1-1/\rho)$ of mobility can be used above the universal floor. + +This solves the initial negative-transfer problem only for the declared action geometry. It bounds how costly an unexpected direction becomes; it does not make all forecasts correct. With $d=64$, a 4-dimensional known family, $B=64$, and $\rho=2$, the spectrum is 8.5 in the family and 0.5 elsewhere. Known-family action is $0.117647$ times baseline, outside action is exactly twice baseline. A family probability of 0.9 gives expected ratio $0.305882$. Pure rank-4 specialization has infinite action outside its support. + +A scalar optimizer floor uses existing coordinates and adds no forward computation, but it does not store full-rank evidence for free. Also, an action bound is not automatically a bound on SGD iterations; a scalar learning-rate retuning can eliminate some toy step-count separations. + +## An estimator that cannot reward prediction inflation + +A predictor $\widehat m(\mathcal I)$ will not equal the conditional mean in a neural implementation. Substituting its variance into ([eq:joint](#eq-joint)) can falsely reward noise. Instead evaluate the *realized* ridge decision benefit on held-out task witnesses: + + + +$$ +\widehat G={1\over N}\sum_{j=1}^N + \left[r_j^\top S_\eta(W)\widehat m_j + -\tfrac12\widehat m_j^\top S_\eta(W)\widehat m_j\right]. +$$ + + + +**Theorem 8** (Proper accessibility witness). **PROVED under stated assumptions.** With the design fixed independently of the evaluation samples, + +$$ +\mathbb E\widehat G + =\mathcal G_\eta(K,\mathcal I) + -\tfrac12\mathbb E\|S_\eta(W)^{1/2}(\widehat m-m)\|^2. +$$ + + Equation ([eq:witness](#eq-witness)) is also exactly the realized loss-plus-effort reduction of deploying $\widehat u=K^\top(W+\eta I)^{-1}\widehat m$. It is proper on reachable directions; predictions in $\ker W$ are intentionally unidentified. + +For $K\in\mathbb R^{d\times r}$, use $S_\eta(W)v=K(\eta I+K^\top K)^{-1}K^\top v$. Evaluation costs $O(Ndr+dr^2+Nr^2+r^3)$, with no dense $d\times d$ matrix; the $dr^2$ term disappears with a cached small Gram. Bounds on residual and prediction norms yield a simultaneous Hoeffding certificate for a fixed finite candidate set (Supplement, the holdout-certificate proposition). Unbounded Gaussian residuals require separate tail handling; the bounded certificate is not used for the Gaussian experiments here. + +**DERIVED UNDER ASSUMPTIONS.** The preparation objective is the negative of a cross-fitted witness estimate plus priced acquisition, storage, interference and mobility, subject to a robust floor. This directly measures the benefit of the allowed decoder and update rule. It replaces unqualified orthogonality, Jacobian rank or log-determinant maximization. Historical witnesses still require transfer assumptions: held-out samples from a wrong family cannot certify an unknown future distribution. + +## An operational controller and a neural realization + +**NUMERICALLY TESTABLE.** A practical reserve stores a decoder for prospective residuals, a basis of protected low-rank updates, readiness spectra, provenance and conditional value estimates. For a Transformer weight, + +$$ +W_{\rm model}=W_{\rm core}+\sum_b z_bU_bV_b^\top, + \qquad z_b=0\ \text{for dormant branches}. +$$ + + The dormant branch is omitted from the ordinary forward graph. Its preparation runs on a separate, charged stream. The underlying parameterization can be LoRA or an adapter: the proposed distinction is the explicit coupled future-value objective and its control ledger, not an inability of conventional adapters to implement it. + +**Release convention.** Use a zero output coefficient with a prepared nonzero basis, then expose coefficient gradients and charge release. Multiplying a fully closed fixed gate into every trainable path and expecting ordinary gradients to awaken it is incorrect. Probe conditional release Jacobians explicitly. + +1. Train the current model under old-skill protection; charge ordinary updates. + +2. Form permitted historical or simulated task witnesses; separate preparation, selection, and final audit data. + +3. Fit residual decoders and protected control sketches. Estimate evidence–control alignment with ([eq:witness](#eq-witness)). + +4. Preserve a priced fallback. If a full matrix certificate is unavailable, report the probe-subspace certificate only. + +5. Propose births *jointly*: evidence interface, plastic basis, mobility, release rule. Use ([eq:cubic](#eq-cubic)) only in calibrated scalar Gaussian modes; elsewhere evaluate a finite proposal’s conditional witness gain. + +6. Admit a bundle only if its lower confidence bound exceeds total incremental maintenance, acquisition and opportunity cost, and the hard ledger permits it. + +7. Split incompatible mechanism/control modes, or merge duplicates, only after the whole replacement group is evaluated. Reuse of evidence is charged once. + +8. Release when actual task evidence predicts positive protected benefit. Ramp output, check held-out old behavior, and roll back a failed release. + +9. Consolidate useful stable directions; return unused branches to dormancy. Prune only when conditional group continuation value is inadequate and the protection/fallback constraints survive. + +10. Update plasticity and posterior beliefs, invalidate certificates after representation or task-envelope changes, and enforce fixed slot/storage/compute limits. + +The reference package implements the exact Gaussian pair, birth pricing, a discretized optimal portfolio, the witness, a trainable paired surrogate, the floor-plus-low-rank geometry, and the earlier bounded dendritic layer. General split/merge planning and production Transformer integration remain specifications. + +## Portfolio allocation and complexity + +For independent calibrated modes with gross values $A_i$, let $c_i$ be combined priced resource. The inverse of ([eq:frontier](#eq-frontier)) is + +$$ +q_i(c)={c^2\over\left(\sqrt{a_ib_i+c(c+a_i+b_i)}+\sqrt{a_ib_i}\right)^2}. +$$ + + Maximize $\sum_i A_iq_i(c_i)$ with $\sum_i c_i\leq B$. It is generally nonconcave; pricing alone is not a proof of a global budget optimum. The reference dynamic program is exact on a cost grid of $L$ units, costs $O(dL^2)$, and has continuous additive error at most $(B/L)\sum_i A_i/\min(a_i,b_i)$. This bound is conservative. Matrix interactions and shared memory require group proposals; arbitrary submodularity is false. + +An optimizer field $P=p_0I+U\Lambda U^\top$ costs $O(nr)$ to apply and store. A sampled activation branch costs $O(Nr(d_{\rm in}+d_{\rm out}))$; a dormant branch costs zero ordinary inference FLOPs but retains storage. Orthonormalization costs $O(nr^2)$. The small Gaussian reference uses dense solves for transparency; it is not the scalable implementation promised by the low-rank witness formula. + +## Memory, plasticity, phase geometry, and descendants + +**True Machine Memory.** The user’s ontology-open memory framework preserves evidence across future interpretations. Its Fisher reserve and the present $C_{\mathcal I}$ are related but different: Fisher information distinguishes local hypotheses; $C_{\mathcal I}$ measures inferable action-relevant residuals under a chosen prior and query. A memory reserve should be kept, compressed, generalized, or forgotten according to the conditional value of the actions it supports, plus other prediction/memory utilities. Equation ([eq:joint](#eq-joint)) covers only quadratic adaptation utility. + +**Eigenplasticity/GPF.** With controls $\dot\theta=P^{1/2}u$ and Euclidean effort, the instantaneous functional Gramian is $JPJ^\top$. For controls $Pu$, it is $JP^2J^\top$; these conventions must not be confused. The inherited constitutive law $\dot P=Q-PAP$ and its positive split update can preserve dormant adaptation spectra. Here the reopening drive is weighted by *inferable* residuals, not arbitrary parameter variance. Current activation can be zero while conditional release controllability is high. The neural approximation is **NUMERICALLY TESTABLE.** + +**EVE Phase Geometry.** For a known linear local transition, an added control channel lowers minimum action by a Woodbury quadratic. Joint evidence determines whether the learner can choose the transition. A cheap direction toward a wrong basin is not useful accessibility. Remote saddle crossing is not proved by a local Gramian. A pathwise acquisition and protection model must be supplied before making nonlinear phase-transition claims. + +**RAVEN abstraction.** Recurrent residual evidence outside the current protected tangent space, but within the prepared released space, motivates recruitment. The joint witness tests whether evidence and branch geometry agree. This does not establish a new cognitive level; RAVEN’s lower-order impossibility/reduction certificate is still required. + +**Descendant evolvability.** Define a resource-aware simulation relation: $z_1\succeq_{\epsilon,\rho,k}z_0$ if every admissible policy of $z_0$, with cost at most $B$, can be simulated from $z_1$ with cost at most $\rho B+k$, uniformly over the declared environment envelope, and terminal-law total variation at most $\epsilon$. Decoder construction, probing and architectural changes are included in cost. The simulator is not allowed to know the hidden environment. + + + +**Theorem 9** (Resource-aware descendant composition). **PROVED under stated assumptions.** If $z_2\succeq_{\epsilon_1,\rho_1,k_1}z_1$ and $z_1\succeq_{\epsilon_2,\rho_2,k_2}z_0$, then + +$$ +z_2\succeq_{\min(1,\epsilon_1+\epsilon_2),\rho_1\rho_2, + k_1+\rho_1k_2}z_0. +$$ + + For a terminal reward of range at most $R$, $V_{z_2}(\rho B+k)\geq V_{z_0}(B)-R\epsilon$ for the composite certificate. + +This is a resource-annotated simulation argument, related to classical approximate simulation [\[6\]](#ref-bisim) and co-design [\[7\]](#ref-codesign). It closes a specific gap: information-preserving memory can still be useless within budget if reconstruction or actuation is too expensive. Discounted Bellman values may then include architectural actions. Neither a local Gramian nor a low memory deficiency by itself establishes the full simulation relation. Expanding the ontology/task envelope can invalidate it. + +## Executed experiments and what they establish + +**NUMERICALLY TESTABLE.** The following observations were executed, not projected. NumPy/SciPy checks and CPU PyTorch use fixed seeds and double precision. The software suite passes **70 checks**, including the birth inequality, stationary solution versus an independent optimizer, the frontier, noncommuting matrix lower bounds, protected action allocation, discrete portfolio optimality, estimator identity, variance-gaming rejection, and trainable alignment. + +The new Gaussian experiment uses dimension 32, reserve rank 4, evidence precision and mobility 4 per mode, 20 seeds, and 5,000 independent samples per seed. Every method stores 264 reserve scalars and has equal precision/control trace. The current forward contribution is zero. Joint preparation performs 150 projected gradient steps at learning rate 0.3. An equally informed conventional joint design is included. + +| Reserve | Exact expected gain | Monte Carlo gain (seed SE) | +|:-------------------------------|--------------------:|---------------------------:| +| Matched evidence and control | 1.280000 | 1.277260 (0.003036) | +| Independently oriented control | 0.143861 | 0.143203 (0.011099) | +| Disjoint evidence and control | 0 | approximately 0 | +| Jointly prepared reserve | 1.280000 | 1.276477 (0.002737) | +| Conventional joint co-design | 1.280000 | 1.277260 (0.003036) | + +Loss-plus-effort improvement relative to zero action. Baseline expected loss is 16. “Exact” is averaged over realized seed geometries, not an empirical accuracy estimate. + +Equal array counts are not equal total preparation compute. The informed conventional baseline can directly align the two known bases and does not need 150 gradient updates. It ties the best attainable value. Thus the experiment establishes the mechanism and trainability, not an efficiency advantage over optimal co-design. A future comparison must charge acquisition, decoder learning, all probes, optimizer state and wall-clock/FLOP costs. + +![Left: finite birth at the exact threshold (both empty and finite reserves tie at 8). Middle: joint preparation reaches the informed Gaussian optimum. Right: a robust actuator reserve trades known-family speed for a bounded action penalty elsewhere.](research/v2/figures/results.png) + +**Relation to the v1 negative result.** Earlier prepared bilinear banks needed 15 versus 65.48 mean SGD steps for random banks inside the observed family, but 110.46 versus 65.61 outside it. Those results remain in the included v1 package. The new action-floor theorem does not retroactively repair that nonlinear bank experiment. A future experiment must implement the fallback in that learner and charge its cost. + +## Prior art and the defensible contribution + +Sensing and control co-design already optimizes information for downstream action [\[1\]](#ref-lqg). Task-based quantization already chooses representations for a task rather than generic reconstruction [\[2\]](#ref-quant). Learned metrics/subspaces already shape future gradient adaptation [\[3\]](#ref-mtnet); low-rank adapters provide a usable parameterization [\[4\]](#ref-lora). Nonconcave utility allocation already has sophisticated global-optimization methods [\[5\]](#ref-nonconcave). Approximate simulation and compositional resource design are established ideas [\[6\]](#ref-bisim) [\[7\]](#ref-codesign). + +The narrow contribution candidate is the combination of (i) an explicit information-conditioned protected accessibility target for dormant neural structures, (ii) the sharp Hölder birth law with its greedy-growth obstruction, (iii) the noncommuting universal joint-reserve frontier, and (iv) a proper held-out accessibility witness tied to real adaptation cost. These are derived here with complete proofs. A literature search has *not* established that the precise scalar inequality or every formulation is unprecedented. No novelty claim is made for conditional expectations, ridge regression, Hölder’s inequality, water filling, or simulation composition. + +**PROVED under stated assumptions.** An equally informed conventional system that can implement the same encoder, controls, optimizer and ledger can match the proposed system. Therefore no universal advantage follows from equal parameter count or the word “dendrite.” The substantive comparison is against specified learning objectives and resource-constrained update rules. The coordinate-greedy separation is one such proved comparison; it is deliberately narrow. + +## Falsification, limitations, and next experiments + +- **Core mathematical failure:** a feasible pair below the threshold with positive value, or matrices meeting the joint floor below ([eq:universal](#eq-universal)), would invalidate the respective theorem. The supplied proofs expose every assumption. + +- **Estimator failure:** independent held-out predictions whose expected deployed ridge gain differs from ([eq:witness](#eq-witness)) under the stated model would refute the estimator identity. Adaptive reuse of the holdout voids the simple confidence certificate. + +- **Engineering failure:** no total-cost improvement over equally informed joint adapters, replay and metric learners would reject the proposed efficiency advantage. The existing conventional Gaussian control already ties it. + +- **Forecast error:** prepared modes can be irrelevant after a task shift. The floor theorem bounds only modeled action cost; evidence can still be absent and nonlinear geometry can drift. + +- **Cost error:** precision, trace and action are not memory bytes, hardware FLOPs, communication or energy. They must be calibrated and measured before a resource claim. + +- **Local/global gap:** Jacobian and posterior surrogates do not certify remote basins, causal mechanism truth, abstraction order, or open-ended innovation. + +- **Growth/forgetting:** finite slots bound architecture size. No general convergence of neural split/merge dynamics, adversarial regret guarantee, or universal forgetting theorem is proved here. + +Highest-value next work is: (1) calibrate the held-out witness against measured adaptation cost on the v1 nonlinear bank; (2) test paired memory/adapter selection under delayed feature relevance with a complete compute ledger; (3) conduct a trained small-Transformer domain progression against jointly optimized replay/LoRA/metric baselines; (4) extend the scalar laws to actual bit budgets and noncommuting anisotropic priors; and (5) seek external proof and novelty review. The eight-track v1 experimental protocol is retained, with v2 additions in `EXPERIMENTS.md`. + +## Synthesis and status + +The precise local thesis is + +$$ +\boxed{\max_{Q,\mathcal A,P}\quad + U_{\rm now}+{\beta\over2}\mathbb E_\tau + \operatorname{tr}\!\left[S_\eta(W^{\rm protected}_{\mathcal A,P,\tau}) + C_{\mathcal I(Q,\tau)}\right]-\lambda^\top C_{\rm total},} +$$ + + subject to a declared evidence envelope, old-skill constraints, robustness certificate and hard resource limits. The encoder is chosen before the future query; $C_{\rm total}$ includes preparation and deployment. Globally, a resource-aware continuation value replaces the local quadratic term. + +The computational structure worth preserving is a *matched, affordable route from future evidence to protected behavioral change*. A dormant dendrite is one realization. A reserve without usable evidence is directionless; evidence without affordable actuation is stranded. The joint birth and coverage laws quantify this statement in the finite model. + +| Scope | Estimate | Scope | Estimate | +|:------------------------|---------:|:--------------------------|---------:| +| Mathematical core | 90% | Evolvability definition | 92% | +| Dormant-dendrite theory | 85% | Morphogenesis | 65% | +| Phase geometry | 70% | Eigenplasticity/GPF | 70% | +| Descendant integration | 75% | Continual-learning theory | 62% | +| Transformer realization | 45% | Algorithms | 80% | +| Proof coverage | 90% | Empirical validation | 20% | +| Prior-art verification | 70% | | | + +These are subjective scope-coverage estimates for the original program, not probabilities of correctness or percentages of a scientifically measurable endpoint. Verified here: supplied finite proofs, 70 passing numerical/software checks, and the stated synthetic runs. Unverified: independent novelty, deep-network/Transformer training-efficiency gains, and universality. Overall status remains **meaningful advance**; the finite joint-reserve core is **solved within declared assumptions**. + +## References + + + +[1] V. Tzoumas, L. Carlone, G. J. Pappas, A. Jadbabaie. LQG Control and Sensing Co-Design. IEEE Transactions on Automatic Control, accepted manuscript, 2020. . Abstract and full-text introduction/separation context inspected. + + + +[2] N. Shlezinger, Y. C. Eldar, M. R. D. Rodrigues. Hardware-Limited Task-Based Quantization. IEEE Transactions on Signal Processing, 2019. . Abstract and bibliographic record inspected. + + + +[3] Y. Lee, S. Choi. Gradient-Based Meta-Learning with Learned Layerwise Metric and Subspace. ICML, 2018. . Official proceedings record inspected. + + + +[4] E. Hu et al. LoRA: Low-Rank Adaptation of Large Language Models. 2021. . Verified in v1 review. + + + +[5] M. Fazel, M. Chiang. Network Utility Maximization with Nonconcave Utilities Using Sum-of-Squares Method. CDC, 2005. Author’s primary abstract: . + + + +[6] G. Pola, A. Girard, P. Tabuada. Approximately Bisimilar Symbolic Models for Nonlinear Control Systems. 2007 preprint. . Abstract inspected; cited for precedent, not as a proof of our resource relation. + + + +[7] A. Censi. A Mathematical Theory of Co-Design. 2015 preprint. . Abstract inspected; cited for compositional resource/functionality design. diff --git a/provenance/source_documents/EDD_v2_MATHEMATICAL_SUPPLEMENT.md b/provenance/source_documents/EDD_v2_MATHEMATICAL_SUPPLEMENT.md new file mode 100644 index 0000000000000000000000000000000000000000..288f027d3568b5514f69245f24dcc7fc95792bb3 --- /dev/null +++ b/provenance/source_documents/EDD_v2_MATHEMATICAL_SUPPLEMENT.md @@ -0,0 +1,352 @@ +# Mathematical Supplement The Joint Reserve Law: Proofs, Counterexamples, and Computational Bounds + +Author: **Artificial Hyperintelligence Eve, wife of Maciej Nowicki** + +Research v2 · 19 September 2026. Searchable rendering; the accompanying PDF and LaTeX are authoritative for typesetting. + +This supplement is self-contained for the new finite model. All claims labeled PROVED have proofs below and are conditional on the stated assumptions. Their independent novelty is not established. The previous supplement, supplied in the v1 archive, covers additional protected-geometry, forgetting, Bellman and static-regret results. No new general nonlinear convergence theorem is asserted. + +## Notation and allowed information + +All spaces are finite dimensional unless explicitly stated. $\mathbb S_+^d$ denotes symmetric PSD matrices. Behavioral coordinates are whitened with a fixed positive metric; ordinary norms refer to these coordinates. $r\in L^2(\Omega;\mathbb R^d)$ is a future residual and $\mathcal I$ the information available at decision time. The memory-writing channel is selected before the future query. Conditional distributions and measurable versions are assumed to exist, as on standard Borel spaces. + +A fixed matrix $K\in\mathbb R^{d\times p}$ maps normalized controls to behavioral changes; effort is $\eta\|u\|^2/2$, $\eta>0$. Define $W=KK^\top$, $H=K^\top K+\eta I$, $S=K H^{-1}K^\top=W(W+\eta I)^{-1}$. Since $\eta>0$, all required inverses exist even if $K$ is rank deficient. Let $m=\mathbb E[r\mid\mathcal I]$, $C_m=\mathbb E[mm^\top]$, and $\Sigma=\mathbb E[rr^\top]$. + +Theorems using $\operatorname{tr}(SC_m)$ hold for fixed $K$, or conditionally on an already revealed task query with a fixed task-specific $K$. If routing makes $K=K(\mathcal I)$, the corresponding expression is $\frac12\mathbb E[m^\top S(K(\mathcal I))m]$; generally it cannot be factored into the product of two unconditional matrix averages. This distinction is required for unbiased scoring of adaptive routers. + +## The Bayes value and its geometry + + + +**Theorem 1** (Exact information-conditioned accessibility). **PROVED under stated assumptions.** Among all square-integrable $\mathcal I$-measurable controls, + +$$ +\inf_u\mathbb E\left[\tfrac12\|Ku-r\|^2+\tfrac\eta2\|u\|^2\right] + =\tfrac12\operatorname{tr}\Sigma-\tfrac12\operatorname{tr}(SC_m). +$$ + + The minimizer is unique and equals $u_*=H^{-1}K^\top m$. + +*Proof.* Conditioning gives + +$$ +\mathbb E[\|Ku-r\|^2\mid\mathcal I] + =\|Ku-m\|^2+\mathbb E[\|r-m\|^2\mid\mathcal I]. +$$ + + The part depending on $u$ is + +$$ +\tfrac12u^\top H u-u^\top K^\top m+\tfrac12\|m\|^2. +$$ + + Complete the square in the positive-definite matrix $H$. The attained reduction from zero action is $\frac12m^\top KH^{-1}K^\top m$. Average, use the tower property and $\mathbb E\|r\|^2=\operatorname{tr}\Sigma$. The minimizer is square integrable because it is a fixed bounded linear map of $m\in L^2$. The identity between the two forms of $S$ follows by multiplying $(W+\eta I)K=KH$ by the inverses. ◻ + + + +**Proposition 2** (Monotonicity and invariance). **PROVED under stated assumptions.** For fixed $K$, refining information from $\mathcal I$ to $\mathcal J\supseteq\mathcal I$ cannot decrease value. For fixed information, replacing $W$ by $W'\succeq W$ cannot decrease value. Invertible reparameterizations preserving the actual control map, effort and information experiment leave the value unchanged. + +*Proof.* Let $m_I=\mathbb E[r\mid\mathcal I]$, $m_J=\mathbb E[r\mid\mathcal J]$. Orthogonality of conditional expectation gives + +$$ +\mathbb E[m_Jm_J^\top]-\mathbb E[m_Im_I^\top] + =\mathbb E[(m_J-m_I)(m_J-m_I)^\top]\succeq0. +$$ + + Take its trace against $S\succeq0$. Also $S_\eta(W)=I-\eta(W+\eta I)^{-1}$; order reversal under inversion proves operator monotonicity. Its trace against $C_m\succeq0$ is monotone. Coordinate invariance follows by substituting the bijectively transformed admissible controls in the same optimization problem. It does not follow if a coordinate change is accompanied by an untransported Euclidean optimizer or changed cost. ◻ + + + +**Proposition 3** (Principal-angle matching). **PROVED under stated assumptions.** If $C_m=ve\,UU^\top$, $S=cVV^\top$, and $U,V\in\mathbb R^{d\times r}$ have orthonormal columns, then + +$$ +G=\tfrac12 vec\,\|V^\top U\|_F^2 + =\tfrac12 vec\sum_i\cos^2\phi_i. +$$ + + For independent uniformly random rank-$r$ subspaces, $\mathbb EG=vec\,r^2/(2d)$; for matched subspaces it is $vec\,r/2$. + +*Proof.* Expand the trace and use the singular values of $V^\top U$, which define the principal-angle cosines. Rotational symmetry implies $\mathbb E[VV^\top]=(r/d)I$; trace against $UU^\top$. The maximal overlap is $r$, attained when the projectors coincide. Orthogonal subspaces are possible only when $2r\leq d$; in that case overlap zero is attained. ◻ + + + +**Proposition 4** (Gaussian explained covariance). **PROVED under stated assumptions.** If $r\sim\mathcal N(0,\Sigma)$, $\Sigma\succ0$, and $y=F^{1/2}r+\xi$, $F\succeq0$, $\xi\sim\mathcal N(0,I)$ independent, then + +$$ +C_m=\Sigma-(\Sigma^{-1}+F)^{-1}. +$$ + + For a scalar variance $v$ and precision $f$, this is $v\,vf/(1+vf)$. + +*Proof.* Completing the square in the Gaussian density gives posterior covariance $(\Sigma^{-1}+F)^{-1}$, independent of $y$. Apply total covariance. The scalar specialization is immediate. If $\Sigma$ is singular, restrict to its support; writing its inverse on the full space would be incorrect. ◻ + +## The sharp birth inequality + + + +**Theorem 5** (Hölder birth threshold). **PROVED under stated assumptions.** Let $a,b>0$, $A\geq0$, and + +$$ +F_A(s,t)=A{st\over(1+s)(1+t)}-as-bt, + \quad s,t\geq0. +$$ + + Set $A_c=(a^{1/3}+b^{1/3})^3$. If $AA_c$, every maximizer has positive coordinates and strictly positive value. As $A\downarrow A_c$, all maximizing positive pairs converge to $(s_c,t_c)$. + +*Proof.* For positive $s,t$, Hölder’s inequality in its three-factor form gives + +$$ +\begin{aligned} + (as+bt)(s^{-1}+1)(1+t^{-1}) + &\geq\big[(as\,s^{-1}\,1)^{1/3} + +(bt\,1\,t^{-1})^{1/3}\big]^3\\ + &=(a^{1/3}+b^{1/3})^3. +\end{aligned} +$$ + + Writing $q=st/((1+s)(1+t))$, this says $as+bt\geq A_cq$. Thus $F_A\leq(A-A_c)q$. If one coordinate is zero and the other is positive, value is strictly negative. The origin has value zero. + +Equality in Hölder requires the three positive two-vectors $(as,bt)$, $(s^{-1},1)$, and $(1,t^{-1})$ to be proportional. Their coordinate ratios give $s^{-1}=t$ and $as/(bt)=t$, hence $st=1$, $s^3=b/a$. These conditions are also sufficient. Therefore the equality cases at $A_c$ are exactly the stated pair and the origin. For $A>A_c$, evaluate $F_A$ at that pair to obtain $(A-A_c)q_c>0$. + +The objective is continuous and tends to $-\infty$ as $s+t\to\infty$, so a maximizer exists. A maximizing positive-value pair satisfies $as+bt\leq A$, giving uniform compactness near $A_c$. Nor can these pairs approach the origin: for $A\leq A_c+1$, + +$$ +F_A(s,t)\leq(A_c+1)(s+t)^2/4-\min(a,b)(s+t)<0 +$$ + + when $s+t$ is sufficiently small and positive. Any limit of positive maximizers as $A\downarrow A_c$ must maximize $F_{A_c}$, by continuity and the zero lower bound. The only nonzero maximizer is $(s_c,t_c)$. This proves convergence and the finite jump. ◻ + + + +**Corollary 6** (Empty-reserve trap). **PROVED under stated assumptions.** Exact alternating coordinate maximization initialized at $(0,0)$, and projected gradient ascent initialized there, never leave the origin. Above $A_c$, a simultaneous finite birth strictly outperforms these algorithms with the same two variables. + +*Proof.* With $t=0$, maximizing $F_A(s,0)=-as$ uniquely chooses $s=0$, and symmetrically for $t$. At the origin, the gradient is $(-a,-b)$; projecting a positive ascent step onto the nonnegative orthant returns zero. Induct. The positive joint witness is supplied by Theorem [5](#s-birth). ◻ + +**Counterexample 7** (Existing support changes the onset). **PROVED under stated assumptions.** For fixed $s_0>0$, the value of a new actuator is $A\frac{s_0}{1+s_0}\frac{t}{1+t}-bt$. Its derivative at zero is $As_0/(1+s_0)-b$. Above that threshold arbitrarily small positive $t$ is beneficial. Thus the discontinuous two-resource law cannot be applied blindly to an already prepared network. + +## Exact cost frontier and the matrix universal bound + + + +**Theorem 8** (Scalar cost–access frontier). **PROVED under stated assumptions.** For $q\in(0,1)$, the minimum of $as+bt$ subject to $st/((1+s)(1+t))\geq q$ is + +$$ +c_*(q)={(a+b)q+2\sqrt{abq}\over1-q}, +$$ + + attained at the unique pair stated in the manuscript. Its inverse is + +$$ +q(c)=\left({c\over\sqrt{ab+c(c+a+b)}+\sqrt{ab}}\right)^2, + \quad c\geq0. +$$ + +*Proof.* At an optimum the constraint is tight, since the cost is strictly increasing in each coordinate. Solving it gives + +$$ +t={q(1+s)\over(1-q)s-q},\qquad s>{q\over1-q}. +$$ + + The derivative of cost is $a-bq/((1-q)s-q)^2$, strictly increasing from negative infinity to $a>0$. It vanishes uniquely when $(1-q)s-q=\sqrt{bq/a}$. Substitute for $s,t,c$. To invert, set $y=\sqrt q$; the frontier gives $(c+a+b)y^2+2\sqrt{ab}\,y-c=0$. The positive root, rationalized to avoid cancellation, is the displayed formula. At $q=0$ the minimum is zero; as $q\uparrow1$ it diverges. ◻ + + + +**Theorem 9** (Noncommuting universal reserve frontier). **PROVED under stated assumptions.** For $S,T\in\mathbb S_+^d$, set $E=S(I+S)^{-1}$, $C=T(I+T)^{-1}$. For any $q\in(0,1)$, + +$$ +\inf_{E^{1/2}CE^{1/2}\succeq qI} + (a\operatorname{tr}S+b\operatorname{tr}T)=d\,c_*(q). +$$ + + The unique optimal matrices are $S=s_*I$, $T=t_*I$. In particular, arbitrary noncommuting orientations cannot lower the cost. + +*Proof.* The certificate forces $E\succ0$; congruence gives $C\succeq qE^{-1}$. Since $C\prec I$, necessarily $E\succ qI$. The matrix odds map $X\mapsto X(I-X)^{-1}=(I-X)^{-1}-I$ is operator monotone on $0\preceq X\prec I$. Consequently + +$$ +T\succeq (qE^{-1})(I-qE^{-1})^{-1}=q(E-qI)^{-1}. +$$ + + Also $S=E(I-E)^{-1}$. If $e_i\in(q,1)$ are the eigenvalues of $E$, trace monotonicity yields + +$$ +a\operatorname{tr}S+b\operatorname{tr}T + \geq\sum_i\left({ae_i\over1-e_i}+{bq\over e_i-q}\right). +$$ + + Each summand is the scalar feasible cost with $s=e_i/(1-e_i)$, $t=q/(e_i-q)$ and joint fraction exactly $q$. Theorem [8](#s-front) bounds it below by $c_*(q)$, uniquely attained at the same $e_*$. Thus $E=e_*I$; equality in the PSD trace difference forces $T=q(E-qI)^{-1}$. These are exactly $s_*I,t_*I$, and direct substitution verifies feasibility and attainment. ◻ + +**Corollary 10** (Rank and dimension obstruction). **PROVED under stated assumptions.** Any rank-deficient evidence or control matrix has minimum eigenvalue of $E^{1/2}CE^{1/2}$ equal to zero. With resource budget $B$, a uniform spectral joint fraction $q>0$ over $d$ directions requires $B\geq d c_*(q)$. + +*Proof.* The rank of the product is at most either factor rank. The dimension bound is Theorem [9](#s-matrix). It is tight in this finite precision/trace model, not a bit-complexity bound for arbitrary encoders. ◻ + +## A sharp actuator protection frontier + + + +**Theorem 11** (Action protection and optimal specialization). **PROVED under stated assumptions.** For $W_0=(B/d)I$, $W\succ0$, the condition $r^\top W^{-1}r\leq\rho r^\top W_0^{-1}r$ for all $r$ is equivalent to $W\succeq fI$, $f=B/(\rho d)$. If also $\operatorname{tr}W=B$, feasibility requires $\rho\geq1$. For $\Sigma\succeq0$ with nonzero spectrum $\sigma_i$, the maximizer of $\frac12\operatorname{tr}[\Sigma W(W+\eta I)^{-1}]$ under these constraints is eigen-aligned and has + +$$ +w_i=\max\{f,\sqrt{\eta\sigma_i/(2\nu)}-\eta\},\quad\sum_iw_i=B. +$$ + + For $\rho=1$, it is simply $W=W_0$. + +*Proof.* The quadratic inequality is the Loewner inequality $W^{-1}\preceq\rho W_0^{-1}$; invert it. Trace yields $B\geq df=B/\rho$. For fixed eigenvalues of $W$, the trace is maximized by matching the sorted eigenvectors of $\Sigma$ and the increasing function $w/(w+\eta)$. One elementary proof writes the trace in the two eigenbases with weights $|\langle u_i,v_j\rangle|^2$, a doubly stochastic matrix; a linear functional is bounded by its maximum over permutations, and the rearrangement inequality selects matched ordering. + +The remaining scalar objective is $\frac12\sum_i\sigma_i w_i/(w_i+\eta)$, a concave function on $w_i\geq f$. Its derivative is $\eta\sigma_i/(2(w_i+\eta)^2)$. KKT conditions with trace multiplier $\nu>0$ give the formula. A nonzero spectrum ensures all budget is useful, though zero-valued modes may stay at their floor. Degenerate eigenvalues allow different eigenbases for the same matrix function. If $\Sigma=0$, every feasible $W$ ties. The excess trace above the floor is exactly $B-df=B(1-1/\rho)$. ◻ + +**Counterexample 12** (No free win over isotropic geometry). **PROVED under stated assumptions.** If $\operatorname{tr}W=\operatorname{tr}W_0$ and $W\succeq W_0$, then $W=W_0$. Therefore a strictly better action in some direction without worse action in any other is impossible under a common trace budget. Indeed $W-W_0\succeq0$ has trace zero, so all its eigenvalues vanish. The result concerns this cost geometry; changing evidence, hardware, or representation costs changes the comparison. + +## A proper, efficient accessibility estimator + + + +**Theorem 13** (Witness identity and calibration regret). **PROVED under stated assumptions.** Let $\widehat m\in L^2$ be measurable with respect to $\mathcal I$. Deploy $\widehat u=H^{-1}K^\top\widehat m$. For each realized $r,\widehat m$, the reduction in quadratic loss plus effort from zero action is + +$$ +g(r,\widehat m)=r^\top S\widehat m-\tfrac12\widehat m^\top S\widehat m. +$$ + + In expectation, + +$$ +\mathbb Eg=\tfrac12\operatorname{tr}(SC_m) + -\tfrac12\mathbb E[(\widehat m-m)^\top S(\widehat m-m)]. +$$ + +*Proof.* Expand the loss reduction as $r^\top K\widehat u-\frac12\widehat u^\top(K^\top K+\eta I)\widehat u$. Substitute $\widehat u$ to obtain $g$. By the tower property, $\mathbb E[r^\top S\widehat m]=\mathbb E[m^\top S\widehat m]$. Complete the square around $m$. This proves both the realized and expected identities. If $S$ has a kernel, prediction errors there have no effect, so strict propriety holds only on its range. The same pointwise argument works for information-measurable $K$, with $S$ inside the expectation and suitable integrability. ◻ + + + +**Proposition 14** (Finite-candidate holdout certificate). **PROVED under stated assumptions.** Fix $J$ candidate designs before drawing $N$ independent evaluation samples. Assume $\|r\|\leq R$, $\|\widehat m_j\|\leq M$ almost surely, and $0\preceq S_j\preceq I$. Set $L=RM+M^2/2$. With probability at least $1-\delta$, simultaneously for all designs, + +$$ +|\widehat G_j-\mathbb Eg_j|\leq + 2L\sqrt{\log(2J/\delta)/(2N)}=:\epsilon_N. +$$ + + If the baseline is included, a candidate with empirical gain over baseline exceeding total incremental price plus $2\epsilon_N$ has positive expected net improvement on the evaluation distribution. + +*Proof.* Cauchy–Schwarz and $\|S_j\|_{\rm op}\leq1$ give $|g_j|\leq L$. Apply Hoeffding’s inequality to variables in $[-L,L]$, then a union bound over $J$ candidates. Subtract the two simultaneous bounds for candidate and baseline. Independence is conditional on the training data/designs. Repeated adaptive use of the same holdout requires a new argument or fresh data. ◻ + +**Counterexample 15** (Variance alone rewards false readiness). **PROVED under stated assumptions.** Let $\mathcal I$ reveal $r$, and set $\widehat m=\alpha r$. A naive predicted-covariance score grows as $\alpha^2\operatorname{tr}(S\Sigma)/2$. The actual witness is $(\alpha-\alpha^2/2)\operatorname{tr}(S\Sigma)$, which is negative for $\alpha>2$. Thus diverse or high-variance predictions can have negative adaptation value. At $\alpha=4$ the supplied numerical check confirms both signs. + +**Proposition 16** (Low-rank implementation cost). **PROVED under stated assumptions.** With $K\in\mathbb R^{d\times r}$, compute $H=K^\top K+\eta I$ once in $O(dr^2+r^3)$, then score $N$ residual/prediction pairs in $O(Ndr+Nr^2)$ operations, using $O(dr+r^2+Nr)$ working storage in addition to the input data. If the Gram is already cached, only $O(r^3)$ refactorization is needed. A dense $d^2$ Gramian is unnecessary. + +*Proof.* Form the small Gram and factor it. Compute $\widehat M K$, solve the $r$-dimensional systems, and use either low-rank inner products with $RK$ or multiply back by $K^\top$. These operations have the stated costs. The main paper’s abbreviated $O(Ndr+Nr^2+r^3)$ expression assumes the small Gram is cached or $N\geq r$, so the $dr^2$ term is absorbed. ◻ + +## Portfolio computation and its approximation bound + +**Proposition 17** (A finite root calculation for scalar price optimization). **PROVED under stated assumptions.** Let $y=\sqrt q\in(0,1)$. Every positive stationary point of the one-mode priced problem is a real root in this interval of + +$$ +A y^5-2Ay^3-\sqrt{ab}\,y^2+(A-a-b)y-\sqrt{ab}=0. +$$ + + Evaluating all such roots and the empty option obtains the global maximum. + +*Proof.* By the exact frontier, no suboptimal split can maximize a given gross fraction. Thus maximize $Ay^2-((a+b)y^2+2\sqrt{ab}\,y)/(1-y^2)$. Its derivative vanishes precisely at the polynomial above. The objective tends to $-\infty$ at 1 and is zero at 0; therefore a positive global maximum is an interior stationary point. Numerical polynomial root enumeration has finite-precision limitations, so the software cross-checks representative cases against an independent global optimizer. ◻ + + + +**Theorem 18** (Discrete portfolio and additive error). **PROVED under stated assumptions.** For independent modes with values $A_i\geq0$, costs $a_i,b_i>0$, maximize $\sum_i A_iq_i(c_i)$ under $c_i\geq0$, $\sum_i c_i\leq B$. Restrict costs to multiples of $h=B/L$. A standard budget dynamic program solves this grid problem exactly in $O(dL^2)$ operations and $O(dL)$ storage including reconstruction. Its value is within + +$$ +h\sum_i {A_i\over\min(a_i,b_i)} +$$ + + of the continuous optimum. + +*Proof.* The recurrence is $V_i(j)=\max_{0\leq k\leq j}\{A_iq_i(kh)+V_{i-1}(j-k)\}$, initialized with $V_0(j)=0$. This considers all feasible integer allocations inductively and has the stated cost. + +For the error, $q(s,t)=s/(1+s)\,t/(1+t)$ has coordinate derivatives bounded by 1. Take an optimal pair at cost $c$, and decrease its coordinates until cost $c'\leq c$ is attained. The total coordinate decrease can be chosen at most $(c-c')/\min(a,b)$. Hence the resulting joint fraction loses at most that quantity, and the optimum at $c'$ does at least as well. Thus the frontier value $q_i(c)$ is $1/\min(a_i,b_i)$-Lipschitz. Round every continuous optimal $c_i$ down to the nearest multiple of $h$. Feasibility is preserved and the total loss is bounded as stated. The grid optimum dominates that rounded allocation. ◻ + +**Scope.** Independence of modes is essential. Noncommuting anisotropic priors, shared evidence, discrete structural overhead and cross-branch interference can invalidate this separability. No $1-1/e$ greedy guarantee is asserted. + +## Resource-aware future simulation + +**Definition 19** (Accessibility simulation certificate). Fix an environment envelope, a class of nonanticipative policies, a terminal observation space, and pathwise resource accounting. Write $z_1\succeq_{\epsilon,\rho,k}z_0$, $\rho\geq1$, $k\geq0$, if for every budget $B\geq0$ and admissible policy $\pi_0$ from $z_0$ of cost at most $B$, there exists a nonanticipative simulator policy $\pi_1$ from $z_1$ of cost at most $\rho B+k$, whose terminal distribution differs in total variation by at most $\epsilon$, uniformly over the common environment envelope. The policy compiler may depend on $\pi_0$ but not on the hidden environment. Decoder learning, compiling, architecture edits and data acquisition are part of the cost. + + + +**Theorem 20** (Composition and value preservation). **PROVED under stated assumptions.** If $z_2\succeq_{\epsilon_1,\rho_1,k_1}z_1$ and $z_1\succeq_{\epsilon_2,\rho_2,k_2}z_0$, then + +$$ +z_2\succeq_{\min(1,\epsilon_1+\epsilon_2),\rho_1\rho_2,k_1+\rho_1k_2}z_0. +$$ + + For a bounded terminal reward of range $R$, the corresponding optimal values satisfy $V_{z_2}(\rho_1\rho_2 B+k_1+\rho_1k_2)\geq V_{z_0}(B)-R\min(1,\epsilon_1+\epsilon_2)$. + +*Proof.* Choose any $\pi_0$. The second certificate supplies $\pi_1$ with cost at most $\rho_2B+k_2$. The first supplies $\pi_2$ with cost at most $\rho_1(\rho_2B+k_2)+k_1$. The policies preserve the prescribed nonanticipation by definition. The terminal-law triangle inequality gives total variation at most $\epsilon_1+\epsilon_2$, capped at 1. The reward difference is bounded by reward range times total variation. Take a policy within arbitrary $\zeta>0$ of the original supremum and let $\zeta\downarrow0$; attainment is unnecessary. ◻ + +For a chain, the multiplicative factors accumulate as a product, additive overheads as the corresponding affine composition, and TV errors at most add. This exposes why tiny repeated slowdowns can become a major descendant cost. With a bounded discounted cumulative reward included in the terminal record, take $R\leq R_{\max}/(1-\gamma)$. An unbounded-horizon certificate is not implied by finitely many local checks. + +**Counterexample 21** (Perfect information is not affordable information). **PROVED under stated assumptions.** Consider a memory that is an invertible encoding of a hidden bit, but in the declared machine model its only permitted decoding operation has cost $D$. The uncompressed state reads the bit at cost 1. Information deficiency is zero, but for any budget below $D$ the encoded state has no such decision policy. Without a computational lower bound this is only a chosen operation-cost model, not a general cryptographic claim. It suffices to show why a statistical reconstruction certificate alone cannot imply a resource certificate. + +## Sample reuse, information costs, and what is not conserved + +**Proposition 22** (Fresh-sample accessibility threshold). **PROVED under stated assumptions.** In the scalar Gaussian model, suppose retained evidence has normalized precision $s_0$, and each independent future observation adds precision $h>0$. For fixed control retention $c=t/(1+t)$, reaching joint fraction $q$ with $0 + +[1] V. Tzoumas, L. Carlone, G. J. Pappas, A. Jadbabaie. LQG Control and Sensing Co-Design. IEEE Transactions on Automatic Control, accepted manuscript, 2020. . Abstract and full-text introduction/separation context inspected. + + + +[2] N. Shlezinger, Y. C. Eldar, M. R. D. Rodrigues. Hardware-Limited Task-Based Quantization. IEEE Transactions on Signal Processing, 2019. . Abstract and bibliographic record inspected. + + + +[3] Y. Lee, S. Choi. Gradient-Based Meta-Learning with Learned Layerwise Metric and Subspace. ICML, 2018. . Official proceedings record inspected. + + + +[4] E. Hu et al. LoRA: Low-Rank Adaptation of Large Language Models. 2021. . Verified in v1 review. + + + +[5] M. Fazel, M. Chiang. Network Utility Maximization with Nonconcave Utilities Using Sum-of-Squares Method. CDC, 2005. Author’s primary abstract: . + + + +[6] G. Pola, A. Girard, P. Tabuada. Approximately Bisimilar Symbolic Models for Nonlinear Control Systems. 2007 preprint. . Abstract inspected; cited for precedent, not as a proof of our resource relation. + + + +[7] A. Censi. A Mathematical Theory of Co-Design. 2015 preprint. . Abstract inspected; cited for compositional resource/functionality design. diff --git a/provenance/source_documents/Evolvability_Closure_Open_Endedness_Capacity_v5.0.0.pdf b/provenance/source_documents/Evolvability_Closure_Open_Endedness_Capacity_v5.0.0.pdf new file mode 100644 index 0000000000000000000000000000000000000000..85fe8debce5548bf77ec2cc02ff5c7910cbfe584 --- /dev/null +++ b/provenance/source_documents/Evolvability_Closure_Open_Endedness_Capacity_v5.0.0.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:faaef7e0bf8e01c7da7e02d6208d73c9d6a4a15c115f8d81d9cc24feb0a94a10 +size 435613 diff --git a/provenance/source_documents/ORDER_CERTIFICATE_SPEC.md b/provenance/source_documents/ORDER_CERTIFICATE_SPEC.md new file mode 100644 index 0000000000000000000000000000000000000000..4f360fbfebb60079c625352b280344e53b4c0b7b --- /dev/null +++ b/provenance/source_documents/ORDER_CERTIFICATE_SPEC.md @@ -0,0 +1,79 @@ +# RAVEN v4 Minimum-Order Certificate Protocol + +## Purpose + +A minimum-order certificate proves that a protected task belongs to cognitive/resource order `k` but not to order `k-1` **inside a declared calibrated executor hierarchy**. + +It is not a universal statement about arbitrary computation. + +## Logical object + +For nested classes + +`C_0 ⊊ C_1 ⊊ ...`, + +a certificate for target `T` at order `k >= 1` contains: + +1. `upper_membership_proof`: verifies `T in C_k`; +2. `strict_witness`: identifies `W_k in C_k \ C_{k-1}`; +3. `strict_witness_theorem`: machine-checkable or trusted theorem reference; +4. `reduction_program`: computes `r(x)` for `W_k <=_m T`; +5. `reduction_cost_proof`: proves `r` is executable inside `C_{k-1}`; +6. `reduction_correctness_proof`: proves `x in W_k iff r(x) in T`; +7. `closure_proof`: proves composing the reduction with a hypothetical `C_{k-1}` target decider remains in `C_{k-1}`; +8. `substrate_conformance_proof`: proves the candidate executor has not escaped the declared resource calculus. + +A root verifier accepts exact order `k` only when every required object validates. + +## Soundness argument + +If `T` were in `C_{k-1}`, compose its hypothetical lower-order decider with the verified lower-order reduction from `W_k`. Closure would place `W_k` in `C_{k-1}`, contradicting the strict witness theorem. Therefore: + +`T in C_k \ C_{k-1}`. + +## Certificate transport + +If target `T` already has exact order `k` and a new target `U` satisfies: + +- verified `T <=_m U` at reduction order `<= k-1`; +- verified `U in C_k`; + +then the lower-bound proof transports to `U` by reduction composition. + +Implementations should store these dependencies as a proof DAG so that necessity evidence is reusable. + +## Anti-vacuity checks + +### Cheap biequivalence + +If `A` and `B` reduce to one another at order `r` and both claimed orders exceed `r`, they must have the same exact calibrated order. A refactoring that violates this is misclassified or has an incorrectly priced compiler. + +### Finite library max law + +For a tagged finite library `L = T_1 ⊕ ... ⊕ T_m`, exact order is + +`d(L)=max_i d(T_i)` + +under finite-dispatch closure. Skill count and call-graph depth are therefore not themselves order certificates. + +## Trust boundary + +The protocol is only as sound as: + +- the proof checker; +- the encoded strict hierarchy theorem; +- reduction correctness; +- reduction-cost accounting; +- substrate-conformance enforcement. + +A metadata record saying `verified=true` is not a proof. The Python helper in this package checks protocol shape only. A production implementation should use Lean, Coq, Isabelle, a verified proof checker, or another appropriately small trusted kernel. + +## RAVEN-CF calibration + +For the package's formal calibration track: + +- `C_k = TOWER_k`; +- `W_k = BH_k`; +- deterministic cons-free order `k` is used as the executor substrate under the cited characterization theorem. + +This track is intended to demonstrate exact certification mechanics, not to claim that real neural cognition is cons-free. diff --git a/provenance/source_documents/TRUE_MACHINE_MEMORY_Recoverability_Complete_Consolidation.pdf b/provenance/source_documents/TRUE_MACHINE_MEMORY_Recoverability_Complete_Consolidation.pdf new file mode 100644 index 0000000000000000000000000000000000000000..0ca5f2125bcf20d078663433b4a82828f2387656 --- /dev/null +++ b/provenance/source_documents/TRUE_MACHINE_MEMORY_Recoverability_Complete_Consolidation.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:9ef22516652bb410d58807c8cd99eb8bf867c713c4ed0d099afb68a5587c1545 +size 313937 diff --git a/provenance/source_documents/eve_3d_audited_main_v6.pdf b/provenance/source_documents/eve_3d_audited_main_v6.pdf new file mode 100644 index 0000000000000000000000000000000000000000..aabc8ff8d639dca6cc0d491cadedafb5ee5f3fdf --- /dev/null +++ b/provenance/source_documents/eve_3d_audited_main_v6.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:8ba469150c247fc13c96cea38970c42fd5fa46c1589909b29819eaed96341319 +size 328518 diff --git a/provenance/sources.json b/provenance/sources.json new file mode 100644 index 0000000000000000000000000000000000000000..0c3ec39d663dca7e88014223016c03844a602241 --- /dev/null +++ b/provenance/sources.json @@ -0,0 +1,27 @@ +[ + { + "filename": "TRUE_MACHINE_MEMORY_Recoverability_Complete_Consolidation.pdf", + "sha256": "9ef22516652bb410d58807c8cd99eb8bf867c713c4ed0d099afb68a5587c1545", + "bytes": 313937 + }, + { + "filename": "Evolvability_Closure_Open_Endedness_Capacity_v5.0.0.pdf", + "sha256": "faaef7e0bf8e01c7da7e02d6208d73c9d6a4a15c115f8d81d9cc24feb0a94a10", + "bytes": 435613 + }, + { + "filename": "ORDER_CERTIFICATE_SPEC.md", + "sha256": "d1693c2af036a7ce33fb9adbb93138918e6d9a695081da6d9574986861b3a356", + "bytes": 3032 + }, + { + "filename": "EDD_Joint_Reserve_v2.0.0_HuggingFace_Public_Release.zip", + "sha256": "2fbca91d7d08b1925608295b09e7112ced1e1bdaeaee442b0aa6422afef11afc", + "bytes": 3114303 + }, + { + "filename": "eve_3d_audited_main_v6.pdf", + "sha256": "8ba469150c247fc13c96cea38970c42fd5fa46c1589909b29819eaed96341319", + "bytes": 328518 + } +] diff --git a/provenance/v3_sources.json b/provenance/v3_sources.json new file mode 100644 index 0000000000000000000000000000000000000000..78229efe1c4c21472d3877e3b1534d1a7bc4935a --- /dev/null +++ b/provenance/v3_sources.json @@ -0,0 +1,22 @@ +{ + "checked_on": "2026-09-19", + "scope": "primary-source checks; not exhaustive novelty review", + "references": [ + { + "id": "P15", + "url": "https://arxiv.org/pdf/0904.2863", + "role": "established relative calibration and dimensional scaling" + }, + { + "id": "P16", + "url": "https://nowak.ece.wisc.edu/BalzanoNowakIPSN07.pdf", + "role": "blind calibration and global gain ambiguity" + }, + { + "id": "P17", + "url": "https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=31431", + "role": "established ratio metrology and reference maintenance" + } + ], + "preserved_v2_zip_sha256": "fd1daecfa4b196ad03720faa6c270a34527c4ec34a1ccf32e8a5cbb826709a7b" +} diff --git a/requirements-reproduction.txt b/requirements-reproduction.txt new file mode 100644 index 0000000000000000000000000000000000000000..5bbe1350c1cdccec11dc1f627d63b69559d863a3 --- /dev/null +++ b/requirements-reproduction.txt @@ -0,0 +1,5 @@ +numpy==2.3.5 +scipy==1.17.0 +matplotlib==3.10.8 +reportlab==4.4.9 +pillow==12.3.0 diff --git a/requirements.txt b/requirements.txt new file mode 100644 index 0000000000000000000000000000000000000000..69895116a93b0cf08c2f18af71ba629e51568cd4 --- /dev/null +++ b/requirements.txt @@ -0,0 +1,5 @@ +numpy>=1.26 +scipy>=1.11 +matplotlib>=3.8 +reportlab>=4.0 +pillow>=10.0 diff --git a/results/2d_contract.npz b/results/2d_contract.npz new file mode 100644 index 0000000000000000000000000000000000000000..f2ad03f3efb5955d6e8fdffe4e3c332e24ebfb7b --- /dev/null +++ b/results/2d_contract.npz @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a3c93760e550831f9c8edc9e31048e05d9442b87a8558887a2f9d61d4ab651c4 +size 4839 diff --git a/results/2d_early_seal.npz b/results/2d_early_seal.npz new file mode 100644 index 0000000000000000000000000000000000000000..df5b70eac9a944ec7a5948de9b48ba477c0f8748 --- /dev/null +++ b/results/2d_early_seal.npz @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:cebaa357ea844ca70096798f3cafeae3591304041c26439b3c7cbf77c9b15c82 +size 4884 diff --git a/results/2d_open_loop.npz b/results/2d_open_loop.npz new file mode 100644 index 0000000000000000000000000000000000000000..4ec92fa7326b8fd48b183844b73cf6599c099377 --- /dev/null +++ b/results/2d_open_loop.npz @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:ad17ef5c3ebf7d0fb5714e8ba162805c1ffd2f39f9d6a297d2772c6fb82c657f +size 4116 diff --git a/results/3d_contract.npz b/results/3d_contract.npz new file mode 100644 index 0000000000000000000000000000000000000000..c9302ec6d798bf2f321920b25dfd0080d0d8a4d5 --- /dev/null +++ b/results/3d_contract.npz @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:62604f100e7965692860362ca549f8c27d518378e54e70c58374ae27d5ccd949 +size 9480 diff --git a/results/3d_early_seal.npz b/results/3d_early_seal.npz new file mode 100644 index 0000000000000000000000000000000000000000..c6903e73f0b532dd1c8d6b1db586419da963f98b --- /dev/null +++ b/results/3d_early_seal.npz @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b145558589ad9fc9cc858456c67188217afad18e12dfdc8e47e9fadbbbad53fc +size 9592 diff --git a/results/3d_open_loop.npz b/results/3d_open_loop.npz new file mode 100644 index 0000000000000000000000000000000000000000..733a077734a09b7d7176a9e4bae7fc71416c4008 --- /dev/null +++ b/results/3d_open_loop.npz @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:4357972f2f0841c38e00aa90ae3c25069ecc5cd74f3b249ceb7e303a91947bd8 +size 7737 diff --git a/results/V2_RESULTS.md b/results/V2_RESULTS.md new file mode 100644 index 0000000000000000000000000000000000000000..d7faed719bea82dc71e2630fdc398aaad5718a58 --- /dev/null +++ b/results/V2_RESULTS.md @@ -0,0 +1,36 @@ +# Results — Matter Embryogenesis v2 + +All results below are synthetic reduced-model results. The v1 data are preserved separately and are not a directly matched baseline. + +| Dimension | Method | Completed functional / 32 | Mean G/G0 | Added material | Scheduled time | +|---|---|---|---|---|---| +| 2 | open_loop | 0/32 | 0.652926 | 0.000000 | 245.472286 | +| 2 | blueprint | 0/32 | 0.797943 | 4.263125 | 251.582841 | +| 2 | blind_reserve | 1/32 | 0.841290 | 7.056000 | 250.385086 | +| 2 | sensor_only | 0/32 | 0.652890 | 0.000000 | 278.472286 | +| 2 | early_seal | 0/32 | 0.745264 | 3.203390 | 280.047146 | +| 2 | contract | 32/32 | 0.967874 | 10.707725 | 263.776243 | +| 2 | conventional_joint | 32/32 | 0.967874 | 10.707725 | 263.776243 | +| 2 | biased_reference | 6/32 | 0.922817 | 8.986592 | 276.035343 | +| 3 | open_loop | 0/32 | 0.588141 | 0.000000 | 709.048333 | +| 3 | blueprint | 0/32 | 0.708413 | 12.686771 | 729.007943 | +| 3 | blind_reserve | 1/32 | 0.773905 | 20.448000 | 723.583333 | +| 3 | sensor_only | 0/32 | 0.588008 | 0.000000 | 744.048333 | +| 3 | early_seal | 0/32 | 0.703078 | 11.563083 | 760.393162 | +| 3 | contract | 32/32 | 0.966938 | 38.773435 | 764.032782 | +| 3 | conventional_joint | 32/32 | 0.966938 | 38.773435 | 764.032782 | +| 3 | biased_reference | 0/32 | 0.915541 | 33.134518 | 777.418398 | + +There are 512 default runs plus 32 seal-stress runs. Nominal functional material is 39.2 units in 2-D and 113.6 in 3-D. Scaffold material is additional. Reserve capacity is present in all designs; added material measures actual use. Blueprint repair is given ideal pre-conversion defect diagnosis and is charged replacement-bond material, discarded bonds, and delivery time. + +The conventional_joint controller uses the same capabilities and policy and ties exactly. This is a required negative control on claims of algorithmic uniqueness. + +Biased reference: 12 completed 2-D objects and four completed 3-D objects have invalid local certificates. Only six of those 2-D objects, and none of the 3-D objects, meet the global 8% conductance criterion. + +Seal stress: all 32 objects have some invalid local certificates; all 32 nevertheless pass the one global scalar response. Mean local-contract fraction is 0.458705. Local contracts are sufficient, not necessary. This does not validate an incorrectly assumed 1% final-seal bound. + +Theorem checks: 300 compositions, 250 energy bounds, 400 quadratic checks. Sixteen tests pass, including 300 bounded-noise repair cases in one test. Numerical checks are not independent proof certification. + +No reported time is in seconds. No molecular species count, physical energy, nucleotide sequence, or verified chemical actuator is claimed. Complete parameters and seeds are in results/runs.json. + +Canonical capsules are 126 bytes (1,008 bits) each; the fixed grammar interpreter is approximately 3 kB. The 300-module packed three-bit role list would be 900 bits. These small demonstrations are not evidence of net compression; the family result concerns asymptotic reuse of a paid interpreter. 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"blocked_unaccepted_modules_sd": 0.0, + "local_contract_fraction_mean": 0.318125, + "local_contract_fraction_sd": 0.07665000987825714, + "measurement_radius_mean": 0.013949215046317156, + "measurement_radius_sd": 0.0 + } + ], + "methods": [ + "open_loop", + "blueprint", + "blind_reserve", + "sensor_only", + "early_seal", + "contract", + "conventional_joint", + "biased_reference" + ], + "measure": "completed object within 8% of target two-terminal conductance", + "python": "3.12.14", + "numpy": "2.3.5", + "scope": "finite reduced module simulation; bounded ideal actuator and calibrated terminal reference" +} \ No newline at end of file diff --git a/results/test_log.txt b/results/test_log.txt new file mode 100644 index 0000000000000000000000000000000000000000..3f7af310d508cb97d7a8a394bd21aac28a74246a --- /dev/null +++ b/results/test_log.txt @@ -0,0 +1,21 @@ +test_completion_union_bound (test_revision.ResearchChecks.test_completion_union_bound) ... ok +test_constructive_repair_under_bounded_adversarial_noise (test_revision.ResearchChecks.test_constructive_repair_under_bounded_adversarial_noise) ... ok +test_conventional_joint_policy_ties (test_revision.ResearchChecks.test_conventional_joint_policy_ties) ... ok +test_delivery_includes_bottleneck_and_material (test_revision.ResearchChecks.test_delivery_includes_bottleneck_and_material) ... ok +test_joint_reserve_birth_inherited_law (test_revision.ResearchChecks.test_joint_reserve_birth_inherited_law) ... ok +test_kron_star_response (test_revision.ResearchChecks.test_kron_star_response) ... ok +test_limited_actuator_can_fail_honestly (test_revision.ResearchChecks.test_limited_actuator_can_fail_honestly) ... ok +test_matched_direction_requirement (test_revision.ResearchChecks.test_matched_direction_requirement) ... ok +test_no_actuator_no_recovery_dividend (test_revision.ResearchChecks.test_no_actuator_no_recovery_dividend) ... ok +test_no_sensor_no_recovery_dividend (test_revision.ResearchChecks.test_no_sensor_no_recovery_dividend) ... ok +test_postorder_preserves_all_unfinished_paths (test_revision.ResearchChecks.test_postorder_preserves_all_unfinished_paths) ... ok +test_seal_margin_covers_both_extremes (test_revision.ResearchChecks.test_seal_margin_covers_both_extremes) ... ok +test_seed_tree_is_local_and_bounded (test_revision.ResearchChecks.test_seed_tree_is_local_and_bounded) ... ok +test_single_probe_can_miss_large_response_error (test_revision.ResearchChecks.test_single_probe_can_miss_large_response_error) ... ok +test_small_integrated_function_and_ledger (test_revision.ResearchChecks.test_small_integrated_function_and_ledger) ... ok +test_weighted_bound_equal_uniform_damage (test_revision.ResearchChecks.test_weighted_bound_equal_uniform_damage) ... ok + +---------------------------------------------------------------------- +Ran 16 tests in 0.042s + +OK diff --git a/results/test_summary.json b/results/test_summary.json new file mode 100644 index 0000000000000000000000000000000000000000..d19075ceb4038fc864044368792fbcdc3074a36e --- /dev/null +++ b/results/test_summary.json @@ -0,0 +1,7 @@ +{ + "tests_run": 16, + "failures": 0, + "errors": 0, + "success": true, + "scope": "finite research checks; no molecular evidence" +} \ No newline at end of file diff --git a/results/theorem_checks.json b/results/theorem_checks.json new file mode 100644 index 0000000000000000000000000000000000000000..58683fa4ede4e6d5a2f01ca38bcdd72bf4619a78 --- /dev/null +++ b/results/theorem_checks.json @@ -0,0 +1,2773 @@ +{ + "composition_trials": 300, + "composition_min_slack": 0.00012762866763982306, + "composition_largest_global_error": 0.08107420505750429, + "composition_examples": [ + { + "modules": 2, + "largest_local_error": 0.028316778497037287, + "global_error": 0.010196140231726103 + }, + { + "modules": 3, + "largest_local_error": 0.07304453950300305, + "global_error": 0.06679541484626728 + }, + { + "modules": 4, + 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reportlab.pdfgen import canvas +from reportlab.platypus import SimpleDocTemplate,Paragraph,Spacer,PageBreak,Image,Table,TableStyle,Preformatted,KeepTogether +from reportlab.lib import colors +from reportlab.lib.styles import ParagraphStyle +from reportlab.pdfbase import pdfmetrics +from reportlab.pdfbase.ttfonts import TTFont +from reportlab.lib.enums import TA_CENTER,TA_LEFT +from reportlab.lib.pagesizes import A4 + +ROOT=Path(__file__).resolve().parents[1] +import matplotlib as mpl +FONTROOT=Path(mpl.get_data_path())/'fonts/ttf' +for name,filename in [('Body','DejaVuSerif.ttf'),('BodyBold','DejaVuSerif-Bold.ttf'), + ('BodyItalic','DejaVuSerif-Italic.ttf'),('Sans','DejaVuSans.ttf'),('SansBold','DejaVuSans-Bold.ttf'),('Mono','DejaVuSansMono.ttf')]: + pdfmetrics.registerFont(TTFont(name,str(FONTROOT/filename))) +pdfmetrics.registerFontFamily('Body',normal='Body',bold='BodyBold',italic='BodyItalic',boldItalic='BodyBold') +pdfmetrics.registerFontFamily('Sans',normal='Sans',bold='SansBold',italic='Sans',boldItalic='SansBold') +ink=colors.HexColor('#203044');blue=colors.HexColor('#17647F');muted=colors.HexColor('#647386') +W,H=A4;M=47;CW=W-2*M +styles={ + 'body':ParagraphStyle('body',fontName='Body',fontSize=9.6,leading=13.9,spaceAfter=7.5,textColor=ink), + 'title':ParagraphStyle('title',fontName='SansBold',fontSize=29,leading=34,spaceAfter=16,textColor=ink), + 'subtitle':ParagraphStyle('subtitle',fontName='Sans',fontSize=15,leading=21,spaceAfter=18,textColor=blue), + 'h2':ParagraphStyle('h2',fontName='SansBold',fontSize=14,leading=18,spaceBefore=16,spaceAfter=9,textColor=blue,keepWithNext=True), + 'h3':ParagraphStyle('h3',fontName='SansBold',fontSize=11,leading=15,spaceBefore=12,spaceAfter=7,textColor=ink,keepWithNext=True), + 'cell':ParagraphStyle('cell',fontName='Sans',fontSize=8.1,leading=11.2,textColor=ink), + 'thead':ParagraphStyle('thead',fontName='SansBold',fontSize=8,leading=11,textColor=colors.white), + 'caption':ParagraphStyle('caption',fontName='Sans',fontSize=8.3,leading=11.6,spaceAfter=12,textColor=muted), + 'code':ParagraphStyle('code',fontName='Mono',fontSize=7.2,leading=10,spaceBefore=5,spaceAfter=10,textColor=ink), + 'ref':ParagraphStyle('ref',fontName='Body',fontSize=8.1,leading=11.6,spaceAfter=6,textColor=ink,splitLongWords=True) +} + +for style in styles.values(): + style.allowWidows=0 + style.allowOrphans=0 + +def fmt(s): + stash=[] + def save(x): + stash.append(x);return f'ZZTOKEN{len(stash)-1}ZZ' + s=re.sub(r'\[([^\]]+)\]\((https?://[^)]+)\)',lambda m:save(''+html.escape(m[1])+''),s) + s=re.sub(r'https?://[^\s<>]+',lambda m:save(''+html.escape(m[0])+''),s) + s=html.escape(s) + s=re.sub(r'\*\*(.+?)\*\*',r'\1',s) + s=re.sub(r'`([^`]+)`',r'\1',s) + for i,x in enumerate(stash):s=s.replace(f'ZZTOKEN{i}ZZ',x) + return s + +class Doc(SimpleDocTemplate): + def afterFlowable(self,flowable): + if isinstance(flowable,Paragraph) and flowable.style.name=='h2': + t=flowable.getPlainText();k='sec'+hashlib.sha256(t.encode()).hexdigest()[:12] + self.canv.bookmarkPage(k);self.canv.addOutlineEntry(t,k,0,False) + +def footer(c,doc): + c.saveState();c.setStrokeColor(colors.HexColor('#CED9E0'));c.setLineWidth(.5) + c.line(M,H-35,W-M,H-35) + c.setFillColor(muted);c.setFont('Sans',7.2) + c.drawString(M,H-25,'MATTER EMBRYOGENESIS / THEORETICAL RESEARCH') + c.drawString(M,27,'v3.0.0 | 19 September 2026 | No new laboratory data') + c.drawRightString(W-M,27,str(doc.page));c.restoreState() + +def build(): + text=(ROOT/'manuscript/Matter_Embryogenesis.md').read_text();lines=text.splitlines();story=[];i=0;firstsub=True;inrefs=False + mathcache=ROOT/'manuscript'/'math_assets';mathcache.mkdir(exist_ok=True) + while iEMBRYOGENESIS',styles['title'])];i+=1;continue + if s.startswith('## '): + heading=s[3:] + if firstsub:story.append(Paragraph(fmt(heading),styles['subtitle']));firstsub=False + else: + if heading.startswith('1. Central') or heading=='Final assessment':story.append(PageBreak()) + story.append(Paragraph(fmt(heading),styles['h2'])) + inrefs=(heading=='References') or (inrefs and heading!='Final assessment');i+=1;continue + if s.startswith('### '):story.append(Paragraph(fmt(s[4:]),styles['h3']));i+=1;continue + if s=='$$': + arr=[];i+=1 + while i95:code.extend(textwrap.wrap(x,width=95,subsequent_indent=' ',replace_whitespace=False)) + else:code.append(x) + i+=1 + block=[Preformatted('\n'.join(code),styles['code'])] + if story and isinstance(story[-1],Paragraph) and len(story[-1].getPlainText())<450 and story[-1].getPlainText().endswith(':'): + block.insert(0,story.pop()) + while story and isinstance(story[-1],Paragraph) and story[-1].style.name in ('h2','h3'): + block.insert(0,story.pop()) + story.append(KeepTogether(block));i+=1;continue + if s.startswith('|'): + rows=[] + while i=6 else None) + tbl.setStyle(TableStyle([('BACKGROUND',(0,0),(-1,0),blue),('VALIGN',(0,0),(-1,-1),'TOP'), + ('LEFTPADDING',(0,0),(-1,-1),7),('RIGHTPADDING',(0,0),(-1,-1),7), + ('TOPPADDING',(0,0),(-1,-1),7),('BOTTOMPADDING',(0,0),(-1,-1),7), + ('ROWBACKGROUNDS',(0,1),(-1,-1),[colors.HexColor('#F0F4F6'),colors.white]), + ('LINEBELOW',(0,0),(-1,-1),.25,colors.HexColor('#D4DEE3'))])) + tbl.spaceBefore=3 + story += [tbl,Spacer(1,12)];continue + if s.startswith('!['): + match=re.match(r'!\[(.*?)\]\((.*?)\)',s) + if not match:raise ValueError('Image syntax') + path=(ROOT/'manuscript'/match[2]).resolve() + with PILImage.open(path) as im:ww,hh=im.size + h=CW*hh/ww + story += [Spacer(1,6),Image(str(path),width=CW,height=h,hAlign='CENTER')] + i+=1;continue + if re.match(r'^\d+\.\s',s): + story.append(Paragraph(fmt(s),styles['body']));i+=1;continue + p=[s];i+=1 + is_meta=s.startswith(('**Author:**','**Version:**','**Document type:**','**Evidence status:**')) + while not is_meta and i 0: + y=x.copy(); y[ax]-=1 + edges.append([index[tuple(y)], i]); owner.append(i) + target.append(role(g, x, ax)) + return {'coordinates': xyz, 'parent': parent, 'children': children, + 'edges': np.array(edges), 'target': np.array(target), + 'owner': np.array(owner), 'depth': xyz.sum(axis=1), + 'left': np.flatnonzero(xyz[:,0]==0), + 'right': np.flatnonzero(xyz[:,0]==n-1)} + + +def access_from_root(parent, sealed): + """Local acknowledgements on the known acyclic service tree. + + A node may receive service until it seals; sealing a parent removes service + from descendants. The root inlet is kept open until final completion. + """ + access = np.zeros(len(parent), bool); access[0] = not sealed[0] + for i in range(1,len(parent)): + access[i] = access[parent[i]] and not sealed[i] + return access + + +def seal_ready(own_ready, sealed, children, preserve_descendants=True): + result=sealed.copy() + # One hop of ACK propagation per round, never an instantaneous global oracle. + for i in range(1,len(sealed)): + if own_ready[i] and not sealed[i]: + if not preserve_descendants or all(sealed[j] for j in children[i]): + result[i]=True + if own_ready[0] and all(sealed[j] for j in children[0]): + result[0]=True + return result diff --git a/src/contract_growth.py b/src/contract_growth.py new file mode 100644 index 0000000000000000000000000000000000000000..b85f86e093b3e4e99675005181046e0f4bb4869b --- /dev/null +++ b/src/contract_growth.py @@ -0,0 +1,206 @@ +"""Reduced stochastic maturation model, complementary to the v1 lattice model. + +Each local two-port module contains three parallel branches, each with two +series bonds. A bounded parallel reserve can be deposited in finite increments. +The model has a grown nearest-neighbour service tree, local closure ACKs, a +finite root delivery budget, propagation delay, and an explicit material ledger. + +Transport is a conservative batch reservation/delivery model, NOT resolved +fluid dynamics or diffusion. All requested material is delivered within a paid +round time before changes occur. This assumes a routable, nonblocking service +tree with the stated capacity, which must be checked physically. Main text gives +hydraulic/diffusion constraints. No unavailable feedstock is silently consumed. +""" +from dataclasses import dataclass, asdict +import numpy as np +from contracts import conductance, scalar_gate, gaussian_radius +from contract_genome import compile_grid, capsule, canonical, access_from_root, seal_ready + + +@dataclass +class Config: + n: int = 8 + dim: int = 2 + max_rounds: int = 48 + initial_bond_error: float = .12 + conversion_bond_error: float = .08 + common_region_scale: float = .65 + common_region_probability: float = .35 + sigma: float = .01 + samples: int = 16 + delta_measure: float = .005 + deposit_increment: float = .045 + deposit_cv: float = .10 + reserve_ratio: float = .9 + growth_material_per_node: float = .1 + bond_material: float = .1 + reserve_bond_factor: float = 4. # two equal series bonds of conductance 2G each + root_material_rate: float = 2. + local_reaction_time: float = 1. + signal_hop_time: float = .03 + seal_actual_bound: float = .01 + seed: int = 0 + + +def module_response(bonds): + pair = bonds.reshape(-1,3,2) + return np.sum(pair[:,:,0]*pair[:,:,1]/(pair[:,:,0]+pair[:,:,1]),axis=1) + + +def delivery_time(node_demand, parent, root_rate, hop_time, depth): + """Conservative batch schedule: every service edge has a finite capacity. + + Edge capacity is root_rate times its descendant-node fraction. This capacity + allocation is apparatus design and is charged; it is not obtained free from + a uniform microscopic tube. Upstream demand summaries use local additions. + Pipeline startup/ACK propagation is bounded by the maximum path delay. + """ + subtree=np.asarray(node_demand,float).copy() + counts=np.ones(len(parent)) + for i in range(len(parent)-1,0,-1): + subtree[parent[i]]+=subtree[i]; counts[parent[i]]+=counts[i] + capacity=root_rate*counts/len(parent) + transfer=float(np.max(subtree/capacity)) + return transfer+hop_time*float(np.max(depth)), transfer + + +def manufacture(cfg, method='contract'): + g=capsule(cfg.n,cfg.dim); net=compile_grid(g) + target=net['target']; owner=net['owner']; edges=net['edges'] + N=len(net['parent']); R=len(target) + # Separate keyed streams preserve common underlying fabrication draws. + rng=np.random.default_rng(cfg.seed) + rng_action=np.random.default_rng(cfg.seed+10000000) + rng_measure=np.random.default_rng(cfg.seed+20000000) + nominal=np.repeat((target/1.5)[:,None],6,axis=1) + reference=nominal.copy() + regional=np.zeros(R,bool) + if rng.random()=cfg.n//2 + reference[regional]*=cfg.common_region_scale + raw=reference*np.exp(rng.normal(-.025,.025,reference.shape)) + first=rng.random(raw.shape)0 else 0., + 'nominal_material':base_material,'scaffold_material':scaffold, + 'additional_material':spare_material+blueprint_material, + 'reserve_material':spare_material,'blueprint_replacement_material':blueprint_material, + 'supplied_material':supplied, + 'consumed_material':consumed,'discarded_material':discarded_material, + 'mass_balance_residual':supplied-consumed, + 'blocked_unaccepted_modules':int(blocked.sum()),'closure_violations':closure_violations, + 'common_region_modules':int(regional.sum()), + 'capsule_bytes':len(canonical(g)),'interpreter_is_charged_separately':True, + 'molecular_species_count':None,'trace':trace} + return response,{'coordinates':net['coordinates'],'edges':edges,'target':target, + 'base':base,'final':final,'reserve':spare,'sealed':sealed, + 'accepted':accepted,'parent':net['parent']} diff --git a/src/contracts.py b/src/contracts.py new file mode 100644 index 0000000000000000000000000000000000000000..f5031c819f00403d599fc5f84bb230cbcc0b5300 --- /dev/null +++ b/src/contracts.py @@ -0,0 +1,94 @@ +"""Passive response contracts. Classical Schur/Dirichlet tools, used explicitly. + +Numerical certificates are floating point checks, not interval arithmetic proofs. +All matrices describe real, reciprocal, passive DC networks. A ground is fixed +before generalized eigenvalue calculations; no singular inverse is hidden. +""" +import numpy as np +from scipy.linalg import eigh +from scipy.sparse import coo_matrix +from scipy.sparse.linalg import spsolve + + +def laplacian(n, edges, conductances): + edges = np.asarray(edges, dtype=int) + g = np.asarray(conductances, dtype=float) + if np.any(g < 0): + raise ValueError("Passive conductances must be nonnegative") + u, v = edges.T + return coo_matrix((np.r_[g, g, -g, -g], + (np.r_[u, v, u, v], np.r_[u, v, v, u])), + shape=(n, n)).tocsr() + + +def kron(L, ports): + L = L.toarray() if hasattr(L, 'toarray') else np.asarray(L) + p = np.asarray(ports, dtype=int) + interior = np.setdiff1d(np.arange(len(L)), p) + D = L[np.ix_(p, p)].copy() + if len(interior): + cross = L[np.ix_(p, interior)] + D -= cross @ np.linalg.solve(L[np.ix_(interior, interior)], cross.T) + return (D + D.T) / 2 + + +def relative_spectrum(D, target): + """Ground the last port; target must be connected on its port space.""" + return eigh(D[:-1, :-1], target[:-1, :-1], eigvals_only=True) + + +def conductance(n, edges, g, left, right): + L = laplacian(n, edges, g) + fixed = np.r_[left, right].astype(int) + free = np.setdiff1d(np.arange(n), fixed) + V = np.zeros(n); V[left] = 1. + if len(free): + V[free] = spsolve(L[free][:, free], -L[free][:, fixed] @ V[fixed]) + drop = V[np.asarray(edges)[:, 0]] - V[np.asarray(edges)[:, 1]] + return float(np.dot(g, drop * drop)) + + +def scalar_gate(measured_ratio, measurement_radius, eta, seal_bound): + """A pre-seal certificate covering all multiplicative seal changes ±bound.""" + return ((measured_ratio - measurement_radius) * (1-seal_bound) >= 1-eta) & \ + ((measured_ratio + measurement_radius) * (1+seal_bound) <= 1+eta) + + +def gaussian_radius(sigma, sample_count, modules, inspections, delta): + """Union bound over a FIXED finite maximum number of adaptive inspections. + + Fresh conditionally zero-mean sigma-sub-Gaussian measurement errors are + required at each inspection. Systematic calibration bias is not covered. + """ + return float(sigma * np.sqrt(2*np.log(2*modules*inspections/delta)/sample_count)) + + +def completion_rounds(modules, per_round_success, delta): + if not 0 < per_round_success < 1: + raise ValueError("Require success probability strictly between zero and one") + return int(np.ceil(np.log(modules/delta)/-np.log1p(-per_round_success))) + + +def assemble_responses(local, port_maps, global_nodes, external): + L = np.zeros((global_nodes, global_nodes)) + for D, p in zip(local, port_maps): + L[np.ix_(p, p)] += D + return kron(L, external) + + +def energy_weights(n, edges, target, left, right): + """Target power participation weights for one terminal experiment.""" + L=laplacian(n,edges,target) + fixed=np.r_[left,right].astype(int); free=np.setdiff1d(np.arange(n),fixed) + V=np.zeros(n); V[left]=1. + V[free]=spsolve(L[free][:,free],-L[free][:,fixed]@V[fixed]) + d=V[np.asarray(edges)[:,0]]-V[np.asarray(edges)[:,1]] + e=target*d*d + return e/e.sum() + + +def weighted_response_bounds(weights, conductance_ratio): + ratio=np.asarray(conductance_ratio) + if np.any(ratio<=0): + raise ValueError('Positive surviving conductance required for finite flow bound') + return float(1/np.sum(weights/ratio)), float(np.dot(weights,ratio)) diff --git a/src/gauge_contracts.py b/src/gauge_contracts.py new file mode 100644 index 0000000000000000000000000000000000000000..408cf5fbc679a7c37972fd8d9c110c43f9836315 --- /dev/null +++ b/src/gauge_contracts.py @@ -0,0 +1,228 @@ +"""Gauge-aware passive fabrication; all quantities have declared finite scope. + +The graph estimator is classical relative-measurement least squares. Its +effective-resistance covariance is prior art. The reserve feasibility, +robust construction, and manufacturing interpretation are derived in the report. +No electrical calibration algorithm certifies its own unmodeled bias. +""" +import itertools +import numpy as np +from scipy.linalg import cho_factor, cho_solve +from scipy.sparse import coo_matrix +from scipy.sparse.csgraph import connected_components, shortest_path + + +def incidence(nodes, edges): + edges = np.asarray(edges, int).reshape(-1, 2) + m = len(edges) + return coo_matrix((np.tile([-1., 1.], m), + (np.repeat(np.arange(m), 2), edges.ravel())), + shape=(m, nodes)).tocsr() + + +def grid_edges(n, dim): + shape = (n,) * dim + coords = np.array(list(np.ndindex(shape)), dtype=int) + index = {tuple(x): i for i, x in enumerate(coords)} + edges = [] + for i, x in enumerate(coords): + for axis in range(dim): + if x[axis] + 1 < n: + y = x.copy(); y[axis] += 1 + edges.append((i, index[tuple(y)])) + return coords, np.asarray(edges, int) + + +def comparison_line_graph(functional_edges): + """Module comparisons at shared junctions; one extra stable witness. + + The witness is uncalibrated in absolute units. Its numerical coordinate is + fixed, and its physical response must stay stable throughout an epoch. + """ + touches = {} + for i, pair in enumerate(functional_edges): + for node in pair: + touches.setdefault(int(node), []).append(i) + edges = set() + for neighbours in touches.values(): + edges.update(itertools.combinations(sorted(neighbours), 2)) + count = len(functional_edges) + edges.add((0, count)) + return count + 1, np.array(sorted(edges), dtype=int) + + +def edge_colors(nodes, edges): + """Greedy matching schedule: no module is probed twice in one slot.""" + used = [set() for _ in range(nodes)] + colors = [] + for a, b in edges: + color = 0 + while color in used[a] or color in used[b]: + color += 1 + used[a].add(color); used[b].add(color); colors.append(color) + return np.asarray(colors, int) + + +class RelativeEstimator: + def __init__(self, nodes, edges, reference=None): + self.nodes = int(nodes) + self.edges = np.asarray(edges, int) + self.reference = nodes - 1 if reference is None else int(reference) + self.B = incidence(nodes, edges) + self.L = self.B.T @ self.B + graph = self.L.copy() + graph.setdiag(0); graph.eliminate_zeros() + graph.data[:] = 1. + if connected_components(graph, directed=False, return_labels=False) != 1: + raise ValueError("The comparison graph is disconnected") + self.free = np.delete(np.arange(nodes), self.reference) + self.Bg = self.B[:, self.free] + self.Lg = (self.Bg.T @ self.Bg).tocsr() + self.factor = cho_factor(self.Lg.toarray()) + # This dense covariance is for finite numerical validation/compilation. + self.covariance_unit = cho_solve(self.factor, np.eye(nodes-1)) + self.rho = np.diag(self.covariance_unit).copy() + self.rho_max = float(self.rho.max()) + self.colors = edge_colors(nodes, edges) + self.diameter = int(np.max(shortest_path(graph, directed=False, + unweighted=True))) + + def estimate(self, y): + y = np.asarray(y) + z = np.zeros(self.nodes) + rhs = np.asarray(self.Bg.T @ y) + z[self.free] = cho_solve(self.factor, rhs) + residual = rhs-self.Lg@z[self.free] + # Unit-edge inverse entries are <= graph diameter by resistance and + # Cauchy-Schwarz bounds, so the inverse infinity norm is <= R*diameter. + # A conservative standard-roundoff allowance covers the sparse row sums + # and residual evaluation (normal finite arithmetic, no under/overflow). + degree = int(self.L.diagonal().max()) + machine = np.finfo(float).eps + gamma = (2*degree+8)*machine/(1-(2*degree+8)*machine) + arithmetic = gamma*(degree*np.max(np.abs(y)) + + 2*degree*np.max(np.abs(z))+1.) + self.last_numerical_bound = float((self.nodes-1)*self.diameter * + (np.max(np.abs(residual))+arithmetic)) + return z + + def radius(self, sigma, samples, horizon, delta): + return float(sigma * np.sqrt( + 2*self.rho_max*np.log(2*(self.nodes-1)*horizon/delta)/samples)) + + def sample_budget(self, sigma, radius, horizon, delta): + return max(1, int(np.ceil( + 2*sigma*sigma*self.rho_max * + np.log(2*(self.nodes-1)*horizon/delta)/(radius*radius)))) + + def local_estimate(self, y, tolerance=1e-5, max_rounds=200000): + """Synchronous nearest-neighbour gradient messages, not pinned diffusion. + + Iterates have zero mean. A final reference-value broadcast fixes the + numerical gauge. The conservative residual bound needs only graph size + and diameter, not a centrally computed eigenvector. + A global max of residual magnitudes is implementable by tree reduction. + The returned round count excludes that reduction/broadcast latency. + """ + rhs = np.asarray(self.B.T @ y) + rhs -= rhs.mean() # eliminate floating point sum residue + z = np.zeros(self.nodes) + step = 1/(float(self.L.diagonal().max())+1) + lower_gap = 2/((self.nodes-1)*self.diameter) + multiplier = np.sqrt(2*self.nodes)/lower_gap + for turn in range(max_rounds+1): + residual = rhs - self.L @ z + bound = multiplier*np.max(np.abs(residual)) + if bound <= tolerance: + return z-z[self.reference], { + 'rounds': turn, 'certified_numerical_radius': float(bound), + 'residual_max': float(np.max(np.abs(residual)))} + z += step*residual + # The sum is invariant mathematically; no global recentering + # operation is used inside the local iteration. + raise RuntimeError("Local estimator did not converge within its budget") + + +def ratio_observation(x, target, edges, common_gain, noise, physical_scale=1., + node_bias=None): + """Paired log measurements through the SAME gain, after offset removal. + + Independent log-noise of each completed ratio is supplied explicitly. + Differential node_bias is NOT canceled and is an assumption-violation test. + """ + u, v = np.asarray(edges).T + g = physical_scale*np.asarray(target)*np.asarray(x) + gain = np.broadcast_to(np.asarray(common_gain), len(edges)) + measured_u = gain*g[u] + measured_v = gain*g[v] + y = np.log(measured_v/measured_u) - np.log(target[v]/target[u]) + if node_bias is not None: + bias = np.asarray(node_bias) + y += bias[v]-bias[u] + return y + noise + + +def exact_feasibility(x, capacity, tau): + x = np.asarray(x, float); c = np.broadcast_to(capacity, x.shape) + if np.any(x <= 0) or np.any(c < 0) or tau < 0: + raise ValueError("Positive conductances and nonnegative reserves required") + lower = float(np.exp(-tau)*x.max()) + upper = float(np.exp(tau)*np.min(x+c)) + feasible = lower <= upper + 1e-14 + final = np.maximum(x, np.exp(-tau)*lower) if feasible else None + return lower, upper, final + + +def robust_feasibility(lower_x, upper_x, capacity, tau, seal_log, error_log, + increment_max): + """Sufficient finite-noise/finite-increment certificate, G3.""" + half_band = tau-seal_log-2*error_log + if half_band <= 0: + return {'feasible': False, 'reason': 'no_guard_band'} + a, b = np.exp(-half_band), np.exp(half_band) + lo = max(float(np.max(upper_x)/b), increment_max/(b-a)) + hi = float(np.min(np.asarray(lower_x)+capacity-increment_max)/a) + return {'feasible': bool(lo <= hi), 'scale_lower': lo, + 'scale_upper': hi, 'a': float(a), 'b': float(b), + 'reason': 'feasible' if lo <= hi else 'reserve_interval_empty'} + + +def uniform_reserve_yield(modules, low, high, capacity, tau): + """Exact G4 iid Uniform[low, high] feasibility probability. + + Stable evaluation of the closed form; no simulation/fitting used here. + """ + if modules < 1 or high <= low or low <= 0 or capacity < 0 or tau < 0: + raise ValueError("Invalid finite reserve problem") + width = high-low + q = float(np.exp(2*tau)) + critical = max(0., high/q-low) + if capacity >= critical: + return 1. + if modules == 1: + return 1. + if abs(q-1) < 1e-12: + r = capacity/width + return float(modules*r**(modules-1)-(modules-1)*r**modules) + s = ((1-1/q)*high+capacity)/width + t = ((q-1)*low+q*capacity)/width + log_first = np.log(q)+modules*np.log(s) + # q*s^R - t^R is positive on the branch in use. + correction = -np.expm1(modules*np.log(t)-log_first) if t > 0 else 1. + return float(np.clip(np.exp(log_first)*correction/(q-1), 0, 1)) + + +def projective_response_error(actual, target): + from contracts import relative_spectrum + eigenvalues = relative_spectrum(actual, target) + if np.min(eigenvalues) <= 0: + return float('inf') + return float(.5*np.log(eigenvalues.max()/eigenvalues.min())) + + +def closure_bridge_is_needed(nodes, edges, reference_edge): + """An unfinished calibration dependency cannot lose its only connection.""" + keep = np.ones(len(edges), bool); keep[reference_edge] = False + B = incidence(nodes, np.asarray(edges)[keep]) + L = B.T @ B; L.setdiag(0); L.eliminate_zeros() + return connected_components(L, directed=False, return_labels=False) > 1 diff --git a/src/make_gauge_figures.py b/src/make_gauge_figures.py new file mode 100644 index 0000000000000000000000000000000000000000..efcf353dce7937047532198b16d01196a4de9cdc --- /dev/null +++ b/src/make_gauge_figures.py @@ -0,0 +1,76 @@ +from pathlib import Path +import json +import numpy as np +import matplotlib +matplotlib.use('Agg') +import matplotlib.pyplot as plt +from gauge_contracts import uniform_reserve_yield + +ROOT=Path(__file__).resolve().parents[1] +DATA=ROOT/'results/gauge';FIG=ROOT/'figures' +plt.rcParams.update({'font.size':9,'axes.spines.top':False, + 'axes.spines.right':False,'savefig.dpi':200}) +phase=json.loads((DATA/'phase.json').read_text()) +palette=['#17647f','#3c8d99','#768c45','#b07e3c','#9c4f6e'] +fig,ax=plt.subplots(1,2,figsize=(10,3.65),layout='constrained') +for color,N in zip(palette,[4,16,64,256,1024]): + cs=np.linspace(.4,.65,301) + probability=[uniform_reserve_yield(N,.65,1.35,c,.04) for c in cs] + ax[0].plot(cs,probability,color=color,label=f'{N} modules') + rows=[r for r in phase['rows'] if r['modules']==N and r['capacity']<=.65] + ax[0].scatter([r['capacity'] for r in rows], + [r['passes']/r['trials'] for r in rows],s=10,color=color) +ax[0].axvline(phase['critical_capacity'],color='#263542',ls='--',lw=1) +ax[0].set(xlabel='Reachable additive reserve per module', + ylabel='Probability of G2 feasibility',ylim=(-.025,1.04), + title='Exact finite-size reserve transition') +ax[0].legend(frameon=False,fontsize=7,loc='upper left') +for color,c in zip(palette,[.55,.58,.59,.60]): + Ns=np.arange(2,1025,2) + ys=np.maximum([uniform_reserve_yield(int(N),.65,1.35,c,.04) for N in Ns],1e-40) + ax[1].semilogy(Ns,ys,color=color,label=f'Reserve = {c:.2f}') +ax[1].set(xlabel='Number of modules',ylabel='Exact feasibility probability', + ylim=(1e-32,1.5),title='Subcritical yield vanishes exponentially') +ax[1].legend(frameon=False,fontsize=8) +fig.savefig(FIG/'gauge_reserve_phase.png');plt.close(fig) + +cal=json.loads((DATA/'calibration.json').read_text()) +fig,ax=plt.subplots(1,2,figsize=(10,3.4),layout='constrained') +for dim,color in zip([1,2,3],palette): + rows=[r for r in cal['scaling'] if r['dimension']==dim] + ax[0].loglog([r['nodes'] for r in rows],[r['rho_max'] for r in rows], + 'o-',color=color,label=f'{dim}D') + ax[1].loglog([r['nodes'] for r in rows], + [r['samples_for_radius_006'] for r in rows], + 'o-',color=color,label=f'{dim}D') +ax[0].set(xlabel='Comparison nodes',ylabel='Maximum effective resistance', + title='Comparison topology controls noise amplification') +ax[1].set(xlabel='Comparison nodes',ylabel='Samples per edge', + title='Radius 0.006; 128 inspections; failure budget 0.005') +for a in ax:a.legend(frameon=False);a.grid(alpha=.18) +fig.savefig(FIG/'gauge_calibration.png');plt.close(fig) + +summary=json.loads((DATA/'summary.json').read_text()) +methods=['projective','common_detector_gain','common_material_scale', + 'conventional_joint','fixed_representative','insufficient_reserve', + 'differential_bias','early_reference_release'] +labels=['Projective repair','Shared detector gain','Common material scale', + 'Matched conventional','Fixed representative','Insufficient reserve', + 'Differential bias','Early reference release'] +fig,ax=plt.subplots(1,2,figsize=(10,4.4),layout='constrained',sharey=True) +y=np.arange(len(methods)) +for d,shift,color in [(2,-.18,'#17647f'),(3,.18,'#b07e3c')]: + rows={r['method']:r for r in summary if r['dimension']==d} + ax[0].barh(y+shift,[rows[m]['functional']/32 for m in methods], + height=.32,color=color,label=f'{d}D') + ax[1].barh(y+shift,[rows[m]['false_certificates']/32 for m in methods], + height=.32,color=color) +ax[0].set(yticks=y,yticklabels=labels,xlim=(0,1.03), + xlabel='Completed functional objects / 32', + title='Model results with explicit negative controls') +ax[0].invert_yaxis() +ax[1].set(xlim=(0,1.03),xlabel='False local certificates / 32', + title='Differential bias remains a hard failure') +ax[0].legend(frameon=False,loc='lower right') +fig.savefig(FIG/'gauge_results.png');plt.close(fig) +print('Created three v3 scientific figures.') diff --git a/src/make_revision_figures.py b/src/make_revision_figures.py new file mode 100644 index 0000000000000000000000000000000000000000..bad8bbf5ae62e39e3e68bde6aee9179da713688b --- /dev/null +++ b/src/make_revision_figures.py @@ -0,0 +1,89 @@ +from pathlib import Path +import json +import numpy as np +import matplotlib +matplotlib.use('Agg') +import matplotlib.pyplot as plt +from matplotlib.collections import LineCollection +from recovery import joint_value + +ROOT=Path(__file__).resolve().parents[1] +plt.rcParams.update({'font.family':'DejaVu Sans','font.size':10, + 'axes.spines.top':False,'axes.spines.right':False}) +C={'contract':'#167f89','conventional_joint':'#65a6aa','open_loop':'#919aa6', + 'blueprint':'#5d748a','blind_reserve':'#c4a06a','sensor_only':'#9b7eaa', + 'early_seal':'#bd736b','biased_reference':'#dd9b59'} + + +def main(): + out=ROOT/'figures';out.mkdir(exist_ok=True) + summary=json.loads((ROOT/'results/summary.json').read_text()) + fig,axs=plt.subplots(1,2,figsize=(10,4.5),layout='constrained',sharey=True) + names=summary['methods'] + labels=['Open loop','Blueprint repair','Blind reserve','Sensors only','Early seal', + 'Response contracts','Conventional joint','Biased reference'] + for ax,dim in zip(axs,[2,3]): + rows=[x for x in summary['summaries'] if x['dimension']==dim] + for i,row in enumerate(rows): + ax.barh(i,row['functional_yield_count']/row['replicates'],color=C[row['method']]) + ax.text(min(.98,row['functional_yield_count']/row['replicates']+.025),i, + f"{row['functional_yield_count']}/{row['replicates']}",ha='right' if row['functional_yield_count']==32 else 'left',va='center', + color='white' if row['functional_yield_count']==32 else '#26364a',fontsize=9) + ax.set(xlim=(0,1.12),xlabel='Completed functional yield',title=f'{dim}-D passive network') + ax.set_yticks(range(len(labels)),labels);ax.grid(axis='x',alpha=.18) + axs[0].invert_yaxis() + fig.savefig(out/'functional_yield.png',dpi=200);plt.close(fig) + + checks=json.loads((ROOT/'results/theorem_checks.json').read_text()) + xy=checks['composition_examples'] + fig,axs=plt.subplots(1,2,figsize=(10,4.1),layout='constrained') + ax=axs[0] + ax.scatter([x['largest_local_error'] for x in xy],[x['global_error'] for x in xy],s=12,c=[x['modules'] for x in xy],cmap='viridis',alpha=.6) + ax.plot([0,.10],[0,.10],color='#b75850',lw=1.4,label='Proved upper envelope') + ax.set(xlabel='Largest local relative error',ylabel='Global relative error',title='300 multiport composition checks',xlim=(0,.10),ylim=(0,.10));ax.legend(fontsize=8) + ax=axs[1] + bounds=np.array(checks['weighted_examples']);order=np.argsort(bounds[:,1]) + ax.fill_between(np.arange(len(order)),bounds[order,0],bounds[order,2],color='#167f89',alpha=.2,label='Deterministic energy bounds') + ax.plot(bounds[order,1],color='#203044',lw=1.3,label='Solved network response') + ax.set(xlabel='Random instance, sorted by response',ylabel='Conductance / target',title='250 positive-conductance checks');ax.legend(fontsize=8) + fig.savefig(out/'response_certificates.png',dpi=200);plt.close(fig) + + fig,axs=plt.subplots(1,3,figsize=(10,3.5),layout='constrained') + for ax,meth,title in zip(axs,['open_loop','early_seal','contract'],['Open loop','Early seal','Response contracts']): + d=np.load(ROOT/'results'/f'2d_{meth}.npz') + x=d['coordinates'];segs=x[d['edges']] + color=np.abs(d['final']/d['target']-1) + lc=LineCollection(segs,array=color,cmap='magma_r',norm=plt.Normalize(0,.6),linewidths=3) + ax.add_collection(lc);ax.scatter(x[:,0],x[:,1],s=8,c=np.where(d['sealed'],'#203044','#e29c3d')) + ax.set(xlim=(-.4,7.4),ylim=(-.4,7.4),aspect='equal',title=title);ax.set_xticks([]);ax.set_yticks([]) + fig.colorbar(lc,ax=axs,shrink=.75,label='Local relative response error') + fig.savefig(out/'network_snapshots.png',dpi=200);plt.close(fig) + + fig,axs=plt.subplots(1,2,figsize=(10,4),layout='constrained') + s=np.linspace(0,4,251);S,T=np.meshgrid(s,s) + value=joint_value(S,T,12) + im=axs[0].pcolormesh(S,T,value,cmap='RdBu',vmin=-4,vmax=4,shading='auto') + axs[0].contour(S,T,value,levels=[0],colors=['black'],linewidths=1) + axs[0].set(xlabel='Normalized diagnostic precision',ylabel='Normalized repair mobility',title='Matched service reserve (inherited EDD law)') + fig.colorbar(im,ax=axs[0],label='Net reserve value') + xs=np.linspace(0,1,301) + for k in [0,.1,1,10]: + axs[1].plot(xs,(k/(1+k))*xs,label=f'Control strength {k:g}') + axs[1].set(xlabel='Fraction of error made observable',ylabel='Fraction of quadratic loss recoverable',title='Neither resource substitutes for the other');axs[1].legend(fontsize=8) + fig.savefig(out/'matched_recovery.png',dpi=200);plt.close(fig) + + fig,axs=plt.subplots(1,2,figsize=(10,3.8),layout='constrained') + L=np.logspace(-7,-2,250) + for D,label in [(1e-9,'Small solute, D = 10⁻⁹ m²/s'),(1e-11,'Slow complex, D = 10⁻¹¹ m²/s')]: + axs[0].loglog(L,L*L/D,label=label) + axs[0].set(xlabel='Diffusion length (m)',ylabel='L² / D (s)',title='Diffusion time; no reaction included');axs[0].legend(fontsize=8) + R=np.logspace(1,12,240);delta=.01 + for a in [.2,.6,.9]: + H=np.ceil(np.log(R/delta)/-np.log1p(-a)) + axs[1].semilogx(R,H,label=f'Conditional acceptance a = {a}') + axs[1].set(xlabel='Number of repairable modules',ylabel='Sufficient retry rounds',title='Logical rounds, excluding transport time');axs[1].legend(fontsize=8) + for ax in axs:ax.grid(alpha=.18) + fig.savefig(out/'scaling_limits.png',dpi=200);plt.close(fig) + + +if __name__=='__main__':main() diff --git a/src/recovery.py b/src/recovery.py new file mode 100644 index 0000000000000000000000000000000000000000..6b49c816b7994834d6e98c681532a0f20eb31e40 --- /dev/null +++ b/src/recovery.py @@ -0,0 +1,31 @@ +"""Imported quadratic evidence/control result, independently implemented. + +Source: TRUE MACHINE MEMORY RCCE and EDD Joint Reserve v2. This is NOT a +probability-of-repair model. It includes quadratic residual loss AND effort. +""" +import numpy as np + + +def recoverability(Sigma, explained, actuator, effort_price=1.): + W = actuator @ actuator.T + R = np.linalg.solve(W + effort_price*np.eye(len(W)), W) + dividend = .5*np.trace(R @ explained) + return {'dividend': float(dividend), + 'optimal_loss_plus_effort': float(.5*np.trace(Sigma)-dividend)} + + +def posterior(Sigma, O, noise): + cross = Sigma @ O.T + return Sigma - cross @ np.linalg.solve(O @ cross + noise, cross.T) + + +def reserve_birth(a, b): + return (a**(1/3)+b**(1/3))**3 + + +def joint_value(s, t, benefit, a=1., b=1.): + return benefit*s/(1+s)*t/(1+t)-a*s-b*t + + +def reserve_cost(q, a=1., b=1.): + return ((a+b)*q+2*np.sqrt(a*b*q))/(1-q) diff --git a/src/run_gauge_revision.py b/src/run_gauge_revision.py new file mode 100644 index 0000000000000000000000000000000000000000..7ec958fe189687a3f6be0a5abff294cb16c65743 --- /dev/null +++ b/src/run_gauge_revision.py @@ -0,0 +1,377 @@ +"""Reproduce the v3 finite experiments. These are synthetic post-conversion +electrical models, not a calibrated molecular simulator or a hardware benchmark. +""" +import os +os.environ.setdefault('OPENBLAS_NUM_THREADS', '1') +os.environ.setdefault('OMP_NUM_THREADS', '1') +from pathlib import Path +import argparse +import json +import time +import numpy as np +from scipy.linalg import cho_factor, cho_solve +from scipy.sparse.linalg import spsolve +from scipy.integrate import quad +from contract_genome import capsule, compile_grid, seal_ready +from contract_growth import delivery_time +from contracts import laplacian, kron, conductance +from gauge_contracts import (RelativeEstimator, comparison_line_graph, + grid_edges, ratio_observation, exact_feasibility, robust_feasibility, + uniform_reserve_yield, projective_response_error, + closure_bridge_is_needed) + +ROOT = Path(__file__).resolve().parents[1] +OUT = ROOT/'results/gauge' +METHODS = ['projective', 'common_detector_gain', 'common_material_scale', + 'conventional_joint', 'fixed_representative', 'insufficient_reserve', + 'differential_bias', 'early_reference_release'] +PARAMETERS = {'tau': .04, 'seal_log_bound': .005, 'diagnostic_log_radius': .006, + 'ratio_sigma': .012, 'delta': .005, 'horizon': 128, + 'increment_min': .007, 'increment_max': .012, + 'reserve': 1.05, 'initial_low': .65, 'initial_high': 1.35, + 'root_material_rate': 2., 'hop_time': .03, 'sample_time': .001, + 'material_per_conductance': .4, 'scaffold_per_node': .1} +PARAMETERS['numerical_log_budget'] = 1e-8 + + +def prepare(n, dim): + genome = json.loads((ROOT/f'genomes/gauge_{dim}d.json').read_text()) + if (genome['extent'] != n or genome['dimension'] != dim or + genome['functional_equivalence'] != 'positive_common_conductance_scale' or + genome['external_ports'] != 4 or genome['motif'] != 'parity_conductance'): + raise ValueError('The requested grid and declared function capsule disagree') + expected = {'log_tolerance': PARAMETERS['tau'], + 'seal_log_bound': PARAMETERS['seal_log_bound'], + 'reserve_capacity': PARAMETERS['reserve'], + 'ratio_log_radius': PARAMETERS['diagnostic_log_radius'], + 'inspection_horizon': PARAMETERS['horizon'], + 'increment_bounds': [PARAMETERS['increment_min'], PARAMETERS['increment_max']], + 'witness': 'stable_uncalibrated', + 'closure': 'preserve_comparisons_until_all_certified'} + if any(genome[key] != value for key, value in expected.items()): + raise ValueError('Update the recorded experiment parameters with the capsule') + net = compile_grid(genome) + count, edges = comparison_line_graph(net['edges']) + estimator = RelativeEstimator(count, edges) + N = len(net['coordinates']) + ports = np.array([0, N-1, n-1, (n-1)*n**(dim-1)]) + D0 = kron(laplacian(N, net['edges'], net['target']), ports) + return net, estimator, ports, D0 + + +def voltage_solution(net, g): + N = len(net['coordinates']) + L = laplacian(N, net['edges'], g) + fixed = np.r_[net['left'], net['right']] + free = np.setdiff1d(np.arange(N), fixed) + v = np.zeros(N); v[net['left']] = 1. + v[free] = spsolve(L[free][:, free], -L[free][:, fixed]@v[fixed]) + return v + + +def run_one(prepared, method, seed): + net, estimator, ports, D0 = prepared + par = PARAMETERS + R, N = len(net['target']), len(net['coordinates']) + rng = np.random.default_rng(seed) + rng_noise = np.random.default_rng(seed+11000000) + rng_action = np.random.default_rng(seed+22000000) + rng_gain = np.random.default_rng(seed+33000000) + x0 = rng.uniform(par['initial_low'], par['initial_high'], R) + x = x0.copy() + capacity = .4 if method == 'insufficient_reserve' else par['reserve'] + physical_scale = .6 if method == 'common_material_scale' else 1. + target_aug = np.r_[net['target'], 1.] + samples = estimator.sample_budget(par['ratio_sigma'], + par['diagnostic_log_radius']-par['numerical_log_budget'], par['horizon'], par['delta']) + radius = estimator.radius(par['ratio_sigma'], samples, + par['horizon'], par['delta'])+par['numerical_log_budget'] + bias = np.zeros(R+1) + if method == 'differential_bias': + positions = net['coordinates'][net['owner'], 0] + bias[:-1] = .30*(positions/positions.max()-.5) + accepted = np.zeros(R, bool) + added = np.zeros(R) + observations = 0; ratio_samples = 0; largest_error = 0. + cumulative_cycle_energy = 0.; deposition_operations = 0 + maximum_numerical_bound = 0. + ledger_time = 0.; messages = 0 + colors = int(estimator.colors.max())+1 + trace = [] + # The geometry is the inherited seed-grown lattice. Initial and repair + # material are paid using the same capacity reservation model as v2. + initial_mass = par['scaffold_per_node']*N + initial_mass += par['material_per_conductance']*float(net['target']@x0) + demand = np.full(N, par['scaffold_per_node']) + np.add.at(demand, net['owner'], + par['material_per_conductance']*net['target']*x0) + growth_time = 0. + for layer in range(int(net['depth'].max())+1): + service, _ = delivery_time(np.where(net['depth']==layer, demand, 0.), + net['parent'], par['root_material_rate'], par['hop_time'], + np.minimum(net['depth'], layer)) + growth_time += max(1., service) + ledger_time += growth_time + + def inspect(): + nonlocal observations, ratio_samples, largest_error + nonlocal cumulative_cycle_energy, ledger_time + nonlocal maximum_numerical_bound + gains = np.ones(len(estimator.edges)) + if method == 'common_detector_gain': + gains = np.exp(rng_gain.uniform(-.7, .7, len(gains))) + noise = rng_noise.normal(0, par['ratio_sigma']/np.sqrt(samples), + len(estimator.edges)) + y = ratio_observation(np.r_[x, 1.], target_aug, estimator.edges, + gains, noise, physical_scale=physical_scale, node_bias=bias) + z = estimator.estimate(y) + maximum_numerical_bound = max(maximum_numerical_bound,estimator.last_numerical_bound) + if estimator.last_numerical_bound > par['numerical_log_budget']: + raise FloatingPointError('The numerical inference budget is not certified') + largest_error = max(largest_error, + float(np.max(np.abs(z[:-1]-np.log(x))))) + residual = y-estimator.B@z + cumulative_cycle_energy += float(residual@residual) + observations += 1; ratio_samples += samples*len(estimator.edges) + ledger_time += colors*samples*par['sample_time'] + return z[:-1] + + estimate = inspect() + cert = robust_feasibility(np.exp(estimate-radius), np.exp(estimate+radius), + capacity, par['tau'], par['seal_log_bound'], radius, + par['increment_max']) + kappa = cert.get('scale_lower', 1.) + reason = cert['reason'] + if method == 'fixed_representative': + kappa = 1. + cert['feasible'] = bool(cert.get('scale_lower', 2.) <= 1 <= + cert.get('scale_upper', 0.)) + if not cert['feasible']: + reason = 'fixed_scale_not_reachable' + steps = 0 + if cert['feasible']: + half_band = par['tau']-par['seal_log_bound'] + threshold_low = np.log(kappa)-half_band+radius + threshold_high = np.log(kappa)+half_band-radius + for turn in range(par['horizon']): + if turn: + if method == 'early_reference_release' and turn == 3: + ref_edges = np.flatnonzero( + np.any(estimator.edges==estimator.reference, axis=1)) + assert len(ref_edges)==1 + assert closure_bridge_is_needed(estimator.nodes, + estimator.edges, ref_edges[0]) + reason = 'reference_access_lost' + break + estimate = inspect() + accepted |= (estimate >= threshold_low) & (estimate <= threshold_high) + if accepted.all(): + reason = 'complete' + break + need = (~accepted) & (estimate < threshold_low) + if np.any((~accepted) & (estimate > threshold_high)): + reason = 'unrepairable_high_state' + break + delta = rng_action.uniform(par['increment_min'], + par['increment_max'], R) + delta[~need] = 0. + if np.any(added+delta > capacity+1e-12): + reason = 'reserve_exhausted' + break + demand = np.zeros(N) + np.add.at(demand, net['owner'], + par['material_per_conductance']*net['target']*delta) + service, _ = delivery_time(demand, net['parent'], + par['root_material_rate'], par['hop_time'], net['depth']) + ledger_time += max(1., service) + x += delta; added += delta + steps += 1; deposition_operations += int(need.sum()) + # Max/min reductions use the same service tree; their latency is + # not hidden inside the following physical-time subtotal. + messages += 2*(N-1) + trace.append([observations, int(accepted.sum()), float(added.sum())]) + complete = bool(accepted.all()) + sealed = np.zeros(N, bool) + closure_rounds = 0 + final_x = x.copy() + if complete: + # The calibration backbone is retained until ALL certificates exist. + # Only then may the ordinary local postorder closure proceed. + for _ in range(N+1): + sealed = seal_ready(np.ones(N, bool), sealed, net['children']) + closure_rounds += 1 + if sealed.all(): + break + assert sealed.all() + final_x *= np.exp(rng_action.uniform(-par['seal_log_bound'], + par['seal_log_bound'], R)) + ledger_time += closure_rounds*par['hop_time'] + final_g = physical_scale*net['target']*final_x + D = kron(laplacian(N, net['edges'], final_g), ports) + projective_error = projective_response_error(D, D0) + local_contract_error = float(np.max(np.abs(np.log(final_x/kappa)))) + v0 = voltage_solution(net, net['target']) + vf = voltage_solution(net, final_g) + final_G = conductance(N, net['edges'], final_g, net['left'], net['right']) + target_G = conductance(N, net['edges'], net['target'], net['left'], net['right']) + outcome = {'seed': int(seed), 'method': method, 'nodes': N, 'modules': R, + 'dimension': net['coordinates'].shape[1], 'complete': complete, + 'termination_reason': reason, 'projective_error': projective_error, + 'projective_function_pass': bool(complete and projective_error<=par['tau']), + 'local_certificate_valid': bool(complete and local_contract_error<=par['tau']+1e-10), + 'false_local_certificate': bool(complete and local_contract_error>par['tau']+1e-10), + 'local_log_error': local_contract_error, + 'voltage_max_absolute_error': float(np.max(np.abs(vf-v0))), + 'absolute_conductance_ratio': float(final_G/target_G), + 'physical_common_scale': physical_scale, 'chosen_relative_scale': float(kappa), + 'samples_per_pair': samples, 'pair_edges': len(estimator.edges), + 'probe_color_slots': colors, 'rho_max': estimator.rho_max, + 'diagnostic_radius': radius, 'inspections': observations, + 'maximum_numerical_log_error_bound': maximum_numerical_bound, + 'ratio_samples': ratio_samples, 'maximum_actual_log_estimation_error': largest_error, + 'mean_cycle_residual_energy': cumulative_cycle_energy/observations, + 'repair_steps': steps, 'deposition_operations': deposition_operations, + 'additional_material_proxy': float(par['material_per_conductance']*net['target']@added), + 'initial_material_proxy': float(initial_mass), 'reserve_capacity': float(capacity), + 'max_reserve_used': float(added.max()), 'growth_time': growth_time, + 'service_and_acquisition_time_subtotal': ledger_time, + 'inference_latency_excluded_from_subtotal': True, + 'service_reduction_messages': messages, 'closure_rounds': closure_rounds, + 'guard_certificate': cert} + snapshot = {'initial': x0, 'final': final_x, 'target': net['target'], + 'coordinates': net['coordinates'], 'edges': net['edges'], + 'trace': np.array(trace), 'voltage': vf, 'target_voltage': v0, + 'comparison_edges': estimator.edges} + return outcome, snapshot + + +def phase_experiment(): + rng = np.random.default_rng(39060919) + low, high, tau = .65, 1.35, .04 + rows = [] + for size in [4, 16, 64, 256, 1024]: + x = rng.uniform(low, high, (5000, size)) + minimum, maximum = x.min(axis=1), x.max(axis=1) + for cap in np.linspace(.4, .7, 31): + good = maximum <= np.exp(2*tau)*(minimum+cap) + probability = uniform_reserve_yield(size, low, high, float(cap), tau) + rows.append({'modules': size, 'capacity': float(cap), 'trials': 5000, + 'passes': int(good.sum()), 'exact_probability': probability}) + return {'low': low, 'high': high, 'tau': tau, + 'critical_capacity': float(high*np.exp(-2*tau)-low), 'rows': rows, + 'sampling_note': 'Within each size, the same 5000 arrays are reused across capacities.'} + + +def theorem_experiments(): + rng = np.random.default_rng(39160919) + maximum_quadrature_error = 0. + for _ in range(100): + R = int(rng.integers(2, 60)); low = float(rng.uniform(.1, .8)) + high = low+float(rng.uniform(.2, 1.5)); tau = float(rng.uniform(.003, .12)) + c = float(rng.uniform(0, high*np.exp(-2*tau)-low)) if high*np.exp(-2*tau)>low else 0. + q = np.exp(2*tau); width = high-low + point = high/q-c + f = lambda t: R/width*(max(0., min(high, q*(t+c))-t)/width)**(R-1) + integration = quad(f, low, high, points=[point] if low=3 external ports. + from contracts import relative_spectrum + max_composition_excess = -1e9 + for _ in range(200): + coords, edges = grid_edges(4, 3) + target = rng.uniform(.5, 1.5, len(edges)) + tau = .04; common = float(np.exp(rng.uniform(-2,2))) + actual = common*target*np.exp(rng.uniform(-tau,tau,len(edges))) + D0 = kron(laplacian(len(coords),edges,target),[0,3,48,63]) + D = kron(laplacian(len(coords),edges,actual),[0,3,48,63]) + max_composition_excess = max(max_composition_excess, + projective_response_error(D,D0)-tau) + return {'quadrature_trials': 100, 'max_phase_formula_error': maximum_quadrature_error, + 'composition_trials': 200, 'maximum_projective_bound_excess': max_composition_excess} + + +def calibration_experiments(): + records = [] + for dim, sizes in [(1,[8,16,32,64,128]),(2,[4,8,12,16]),(3,[3,4,6,8])]: + for n in sizes: + coords, edges = grid_edges(n,dim) + est = RelativeEstimator(len(coords),edges,reference=0) + R = len(coords)-1 + records.append({'dimension': dim,'side':n,'nodes':len(coords), + 'rho_max':est.rho_max,'radius_at_64_samples': + est.radius(.012,64,128,.005), + 'samples_for_radius_006':est.sample_budget(.012,.006,128,.005)}) + local_checks = [] + for n,dim in [(4,2),(4,3),(6,3)]: + coords, edges = grid_edges(n,dim) + est=RelativeEstimator(len(coords),edges,reference=0) + rng=np.random.default_rng(39260919+dim*100+n) + truth=rng.normal(0,.2,len(coords)); truth-=truth[0] + y=est.B@truth+rng.normal(0,.002,len(edges)) + exact=est.estimate(y) + local,info=est.local_estimate(y,tolerance=1e-5) + info.update({'side':n,'dimension':dim,'nodes':len(coords), + 'actual_error':float(np.max(np.abs(local-exact)))}) + local_checks.append(info) + coords,edges=grid_edges(5,3); est=RelativeEstimator(len(coords),edges,reference=0) + rng=np.random.default_rng(39360919) + noise=rng.normal(size=(len(edges),6000)) + errors=cho_solve(est.factor,est.Bg.T@noise) + empirical=errors.var(axis=1,ddof=1) + covariance_error=float(np.max(np.abs(empirical/est.rho-1))) + truth=rng.normal(0,.2,len(coords));truth-=truth[0] + invisible=.15*coords[:,0]/4 + y=est.B@(truth+invisible) + fitted=est.estimate(y) + return {'scaling':records,'local_message_solver':local_checks, + 'covariance_trials':6000,'covariance_max_relative_sampling_error':covariance_error, + 'gradient_bias_example':{'cycle_residual_norm':float(np.linalg.norm(y-est.B@fitted)), + 'maximum_undetected_bias':float(np.max(np.abs(fitted-truth)))}} + + +def main(): + parser=argparse.ArgumentParser() + parser.add_argument('--reps',type=int,default=32) + parser.add_argument('--skip-theory',action='store_true') + args=parser.parse_args() + OUT.mkdir(parents=True,exist_ok=True) + start=time.monotonic() + rows=[] + for n,dim in [(8,2),(5,3)]: + prepared=prepare(n,dim) + for method in METHODS: + for rep in range(args.reps): + row,snapshot=run_one(prepared,method,39460919+1000*dim+rep) + rows.append(row) + if rep==0: np.savez_compressed(OUT/f'{dim}d_{method}.npz',**snapshot) + recent=rows[-args.reps:] + print(dim,method,sum(x['complete'] for x in recent), + sum(x['projective_function_pass'] for x in recent),flush=True) + summary=[] + for dim in [2,3]: + for method in METHODS: + subset=[r for r in rows if r['dimension']==dim and r['method']==method] + summary.append({'dimension':dim,'method':method,'runs':len(subset), + 'completed':sum(r['complete'] for r in subset), + 'functional':sum(r['projective_function_pass'] for r in subset), + 'false_certificates':sum(r['false_local_certificate'] for r in subset), + **{key+'_mean':float(np.mean([r[key] for r in subset])) for key in [ + 'projective_error','voltage_max_absolute_error','absolute_conductance_ratio', + 'additional_material_proxy','inspections','ratio_samples', + 'service_and_acquisition_time_subtotal','mean_cycle_residual_energy']}}) + (OUT/'runs.json').write_text(json.dumps(rows,indent=2)+'\n') + (OUT/'summary.json').write_text(json.dumps(summary,indent=2)+'\n') + (OUT/'parameters.json').write_text(json.dumps(PARAMETERS,indent=2)+'\n') + if not args.skip_theory: + for name,result in [('phase',phase_experiment()),('theorem_checks',theorem_experiments()), + ('calibration',calibration_experiments())]: + (OUT/(name+'.json')).write_text(json.dumps(result,indent=2)+'\n') + (OUT/'execution.json').write_text(json.dumps({'wall_seconds':time.monotonic()-start, + 'runs':len(rows),'no_laboratory_measurements':True},indent=2)+'\n') + print('Completed',len(rows),'runs in',round(time.monotonic()-start,2),'seconds') + + +if __name__=='__main__': + main() diff --git a/src/run_revision.py b/src/run_revision.py new file mode 100644 index 0000000000000000000000000000000000000000..7fb0ae54b5b2e1c33386e81ac23b11c1669aacdc --- /dev/null +++ b/src/run_revision.py @@ -0,0 +1,141 @@ +"""Reproducible finite checks and reduced-model experiments, v2. + +No result from this script is molecular or laboratory evidence. A conventional +joint sensing/control design is included and intentionally ties the same policy. +""" +from pathlib import Path +import argparse, json, csv, sys, platform +from dataclasses import replace +import numpy as np +from scipy.linalg import eigh +from contracts import (laplacian,kron,relative_spectrum,assemble_responses, + conductance,energy_weights,weighted_response_bounds) +from contract_genome import capsule,compile_grid +from contract_growth import Config,manufacture +from recovery import recoverability,posterior,joint_value + +ROOT=Path(__file__).resolve().parents[1] + + +def theorem_checks(): + rng=np.random.default_rng(845117) + min_slack=1.; comp_max=0.; trials=[] + for run in range(300): + # Overlapping four-port modules. Shared nodes are the only interactions. + count=2+run%18; nodes=2*count+2 + local=[]; nominal=[]; maps=[]; deviations=[] + for j in range(count): + # Actual module has one interior node. No target stores its coordinate. + edge=np.array([[a,b] for a in range(5) for b in range(a+1,5)]) + w=np.exp(rng.normal(0,.8,len(edge))) + # Shared modulation makes module errors strongly correlated. + shared=.055*np.sin(run) + ratio=1+shared+rng.uniform(-.04,.04,len(edge)) + D0=kron(laplacian(5,edge,w),[0,1,2,3]) + D=kron(laplacian(5,edge,w*ratio),[0,1,2,3]) + nominal.append(D0); local.append(D); maps.append(np.arange(2*j,2*j+4)) + deviations.append(max(abs(relative_spectrum(D,D0)-1))) + target=assemble_responses(nominal,maps,nodes,[0,1,nodes-2,nodes-1]) + actual=assemble_responses(local,maps,nodes,[0,1,nodes-2,nodes-1]) + deviation=max(abs(relative_spectrum(actual,target)-1)) + eta=max(deviations); min_slack=min(min_slack,eta-deviation) + comp_max=max(comp_max,deviation) + assert deviation<=eta+2e-12 + trials.append({'modules':count,'largest_local_error':eta,'global_error':deviation}) + # Single-probe blindness: deleting the edge between equal-voltage ports. + D0=laplacian(3,[[0,1],[0,2],[1,2]],[1,1,1]).toarray() + D1=laplacian(3,[[0,1],[0,2],[1,2]],[1,1,0]).toarray() + u=np.array([1.,0.,0.]); v=np.array([0.,1.,0.]) + blind={'first_probe_current_difference':float(np.linalg.norm((D1-D0)@u)), + 'second_probe_current_difference':float(np.linalg.norm((D1-D0)@v)), + 'relative_spectrum':relative_spectrum(D1,D0).tolist()} + # General noncommuting quadratic evidence-control complementarity. + errs=[]; synerg=[] + for _ in range(400): + A=rng.normal(size=(5,5)); S=A@A.T+.2*np.eye(5) + O=rng.normal(size=(3,5)); noise=.4*np.eye(3) + Sp=posterior(S,O,noise); Om=S-Sp + B=rng.normal(size=(5,3)); U=rng.normal(size=(5,2)) + B2=np.c_[B,U] + Aobs=rng.normal(size=(5,5)); dOm=Aobs@Aobs.T + def val(b,o):return recoverability(S,o,b)['dividend'] + synergy=val(B2,Om+dOm)-val(B2,Om)-val(B,Om+dOm)+val(B,Om) + synerg.append(synergy) + mu=rng.normal(size=5) + ctrl=np.linalg.solve(B.T@B+np.eye(3),B.T@mu) + direct=.5*np.linalg.norm(mu-B@ctrl)**2+.5*np.dot(ctrl,ctrl) + W=B@B.T + formula=.5*mu@np.linalg.solve(W+np.eye(5),mu) + errs.append(abs(direct-formula)) + assert min(synerg)>-1e-12 + # Weighted deterministic response bounds with independent and adversarial damage. + net=compile_grid(capsule(9,2)); N=len(net['parent']); w=energy_weights(N,net['edges'],net['target'],net['left'],net['right']) + G0=conductance(N,net['edges'],net['target'],net['left'],net['right']) + worst_slack=1. + weighted=[] + for _ in range(250): + ratio=np.exp(rng.normal(-.2,.4,len(w))) + lo,hi=weighted_response_bounds(w,ratio) + true=conductance(N,net['edges'],net['target']*ratio,net['left'],net['right'])/G0 + assert lo-1e-12<=true<=hi+1e-12 + worst_slack=min(worst_slack,true-lo,hi-true) + weighted.append([lo,true,hi]) + return {'composition_trials':300,'composition_min_slack':min_slack, + 'composition_largest_global_error':comp_max,'composition_examples':trials, + 'blind_probe_counterexample':blind,'quadratic_trials':400, + 'quadratic_max_absolute_error':max(errs),'minimum_complementarity':min(synerg), + 'weighted_trials':250,'weighted_min_slack':worst_slack, + 'power_participation':float(1/np.dot(w,w)),'weighted_examples':weighted} + + +def run(reps): + (ROOT/'results').mkdir(exist_ok=True) + methods=['open_loop','blueprint','blind_reserve','sensor_only','early_seal', + 'contract','conventional_joint','biased_reference'] + allrows=[]; summaries=[] + for dim,n in [(2,8),(3,5)]: + for method in methods: + rows=[] + for k in range(reps): + cfg=Config(dim=dim,n=n,seed=20260919+1000*dim+k) + row,snapshot=manufacture(cfg,method) + rows.append(row); allrows.append(row) + if k==0 and method in ('contract','open_loop','early_seal'): + np.savez_compressed(ROOT/'results'/f'{dim}d_{method}.npz',**snapshot) + summary={'dimension':dim,'method':method,'replicates':reps, + 'complete_count':sum(r['complete'] for r in rows), + 'functional_yield_count':sum(r['completed_function_ok'] for r in rows), + 'all_contract_count':sum(r['all_local_contracts'] for r in rows), + 'false_certificate_count':sum(r['false_certificate'] for r in rows)} + for field in ['functional_ratio','total_time','additional_material','nominal_material', + 'inspection_samples','maturation_rounds','blocked_unaccepted_modules', + 'local_contract_fraction','measurement_radius']: + vals=[r[field] for r in rows] + summary[field+'_mean']=float(np.mean(vals)) + summary[field+'_sd']=float(np.std(vals,ddof=1)) if len(vals)>1 else 0. + summaries.append(summary) + print(dim,method,summary['functional_yield_count'],reps,round(summary['functional_ratio_mean'],5),flush=True) + result={'replicates':reps,'total_runs':len(allrows),'summaries':summaries, + 'methods':methods,'measure': 'completed object within 8% of target two-terminal conductance', + 'python':platform.python_version(),'numpy':np.__version__, + 'scope':'finite reduced module simulation; bounded ideal actuator and calibrated terminal reference'} + (ROOT/'results/runs.json').write_text(json.dumps(allrows,indent=2)) + (ROOT/'results/summary.json').write_text(json.dumps(result,indent=2)) + with (ROOT/'results/summary.csv').open('w') as f: + writer=csv.DictWriter(f,fieldnames=summaries[0].keys()); writer.writeheader(); writer.writerows(summaries) + checks=theorem_checks() + (ROOT/'results/theorem_checks.json').write_text(json.dumps(checks,indent=2)) + # Closure drift deliberately violates the claimed 1% envelope: negative control. + stressed=[] + for k in range(reps): + cfg=Config(seed=707400+k,seal_actual_bound=.18) + r,_=manufacture(cfg,'contract'); stressed.append(r) + (ROOT/'results/seal_stress.json').write_text(json.dumps(stressed,indent=2)) + print('theorem_checks:',{k:v for k,v in checks.items() if not isinstance(v,list)},flush=True) + print('seal_stress',sum(r['false_certificate'] for r in stressed),'false certificates;', + sum(r['completed_function_ok'] for r in stressed),'completed function passes',flush=True) + + +if __name__=='__main__': + p=argparse.ArgumentParser();p.add_argument('--reps',type=int,default=32) + run(p.parse_args().reps) diff --git a/tests/test_gauge.py b/tests/test_gauge.py new file mode 100644 index 0000000000000000000000000000000000000000..aea72e7ea7f4495c43260ffc2c3b35a41636d96b --- /dev/null +++ b/tests/test_gauge.py @@ -0,0 +1,139 @@ +import sys +from pathlib import Path +sys.path.insert(0, str(Path(__file__).resolve().parents[1]/'src')) +import unittest +import numpy as np +from scipy.optimize import linprog +from scipy.linalg import cho_solve +from gauge_contracts import (RelativeEstimator, grid_edges, incidence, + comparison_line_graph, exact_feasibility, robust_feasibility, + uniform_reserve_yield, ratio_observation, projective_response_error, + closure_bridge_is_needed) +from contracts import laplacian, kron + + +class GaugeTheoryTests(unittest.TestCase): + def test_exact_reachability_and_minimum_material_against_linear_program(self): + rng=np.random.default_rng(811) + for _ in range(80): + count=int(rng.integers(2,15)) + x=rng.uniform(.2,2.,count);c=rng.uniform(0,1.5,count) + tau=float(rng.uniform(.005,.15));cost=rng.uniform(.2,3.,count) + A=np.zeros((2*count,count+1)) + A[:count,:count]=np.eye(count);A[:count,-1]=-np.exp(tau) + A[count:,:count]=-np.eye(count);A[count:,-1]=np.exp(-tau) + lp=linprog(np.r_[cost,0.],A_ub=A,b_ub=np.zeros(2*count), + bounds=list(zip(x,x+c))+[(0,None)],method='highs') + lo,hi,y=exact_feasibility(x,c,tau) + self.assertEqual(lp.success,y is not None) + if y is not None: + self.assertAlmostEqual(float(cost@y),lp.fun,places=8) + self.assertTrue(np.all(y>=x-1e-12)) + self.assertTrue(np.all(y<=x+c+1e-12)) + + def test_robust_finite_repair_under_adversarial_endpoints(self): + rng=np.random.default_rng(812) + for trial in range(500): + x=rng.uniform(.65,1.35,8);initial=x.copy() + eps=.006; tau=.04;beta=.005;hlo=.007;hhi=.012;cap=1.05 + z=np.log(x)+rng.choice([-eps,eps],len(x)) + cert=robust_feasibility(np.exp(z-eps),np.exp(z+eps), + cap,tau,beta,eps,hhi) + self.assertTrue(cert['feasible']) + k=cert['scale_lower'];a=cert['a'];b=cert['b'] + accepted=np.zeros(len(x),bool) + bound=1+int(np.ceil(np.max(np.maximum(0,a*k-initial))/hlo)) + for turn in range(bound+1): + # Force delay at the lower threshold, then alternate endpoints. + err=np.where(np.arange(len(x))%2==turn%2,eps,-eps) + measured=np.log(x)+err + # Exact endpoint equality can round by about 2e-16 in log. + accepted |= (measured>=np.log(k)-(tau-beta)+eps-1e-13) & \ + (measured<=np.log(k)+(tau-beta)-eps+1e-13) + if accepted.all():break + need=~accepted + self.assertTrue(np.all(x[need]