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-<script>window.__KB__={"version":"5.1.0","byline":"Lutar, Stephen P.","orcid":"0009-0001-0110-4173","email":"stephen@szlholdings.com","org":"SZL Holdings","generated_at":"2026-06-06T06:00:00Z","axioms":[{"id":"A1","name":"soundnessAxiom","statement":"For any receipt r, if gate_pass(r) then lambda(r) >= 0.90 conjunctively","source_file":"thesis.md","source_section":"§4.1","maturity":"proven","citation":"https://doi.org/10.5281/zenodo.20119582"},{"id":"A2","name":"moralGroundingFloor","statement":"moralGrounding axis floor = 0.95 (higher than default 0.90)","source_file":"thesis.md","source_section":"§4.1","maturity":"defined","citation":"https://doi.org/10.5281/zenodo.20119582"},{"id":"A3","name":"measurabilityHonestyFloor","statement":"measurabilityHonesty axis floor = 0.95","source_file":"thesis.md","source_section":"§4.1","maturity":"defined","citation":"https://doi.org/10.5281/zenodo.20119582"},{"id":"A4","name":"dualWitnessDisjointness","statement":"For rho-closure: witness_1_id != witness_2_id (enforced by registry at write time)","source_file":"thesis.md","source_section":"§4.3","maturity":"proven","citation":"https://doi.org/10.5281/zenodo.20119582"},{"id":"A5","name":"deterministicReplay","statement":"For canonical JSON + pinned PRNG + frozen registry, 5x replay yields byte-identical roots","source_file":"thesis.md","source_section":"§4.6","maturity":"measured","citation":"https://doi.org/10.5281/zenodo.20119582"},{"id":"A6","name":"hashChainIntegrity","statement":"Every spine entry hash-chain invariant: entry.chain = SHA256(prev_entry)","source_file":"thesis.md","source_section":"§3.4","maturity":"defined","citation":"https://doi.org/10.5281/zenodo.20119582"},{"id":"A7","name":"bekensteinBound","statement":"Receipt chain entropy H(R_n) bounded by information-theoretic limit from registry area","source_file":"thesis.md","source_section":"§4.5","maturity":"conjectured","citation":"https://doi.org/10.5281/zenodo.19944926"},{"id":"A8","name":"ingestDiscipline","statement":"Every ingest requires: source_url + content_hash + license (allow-list) + ORCID","source_file":"thesis.md","source_section":"§7","maturity":"defined","citation":"https://doi.org/10.5281/zenodo.20119582"},{"id":"A9","name":"doctrineCompleteness","statement":"doctrine.json v1.0.0 enumerates all 8 forbidden patterns; SHA-anchored","source_file":"szl-trust/doctrine.json","source_section":"§8","maturity":"defined","citation":"https://github.com/szl-holdings/szl-trust"}],"theorems":[{"id":"TH_L1","name":"Λ_uniqueness","statement":"Conjecture 1: the Lutar Invariant Λ_k (weighted geometric mean with Egyptian unit-fraction weights) is the unique aggregator satisfying axioms A1-A5. NOT a theorem: unconditional uniqueness is FALSE under A1-A5 (machine-checked counterexample maxAgg_ne_Lambda; max-aggregator satisfies A1-A5 yet differs from Λ at (4,1)). The conditional theorem lambda_unique_of_factors (uniqueness GIVEN factorization Φ x = ∏ x_i^α_i) IS fully proved; unconditional uniqueness closes only under a declared bisymmetry axiom A6 (Kolmogorov-Nagumo-Aczel).","source_file":"lutar-lean/Lutar/Round13/Lambda_Uniqueness.lean","maturity":"conjectured","citation":"https://doi.org/10.5281/zenodo.20053148"},{"id":"TH_L2","name":"Λ_min_max_bounds","statement":"Λ_k lies in [0,1] with min=0 iff any axis=0 and max=1 iff all axes=1","source_file":"lutar-lean/Lutar/Bound.lean","maturity":"proven","citation":"https://doi.org/10.5281/zenodo.20053148"},{"id":"TH_L3","name":"bekenstein_soundness","statement":"Bekenstein indicator fires at 49.5% under uniform seed (measured); formal proof pending in lutar-lean","source_file":"lutar-lean (pending PR #12)","maturity":"measured/conjectured","citation":"https://github.com/szl-holdings/lutar-lean"},{"id":"TH_L4","name":"rho_closure_production","statement":"100% rho-closure on 8,000/8,000 paired calls under v11 platform","source_file":"ouroboros v6.3.0 release","maturity":"measured","citation":"https://doi.org/10.5281/zenodo.20119582"}],"formulas":[{"id":"F0001","source_file":"thesis.md","source_line":27,"latex":"\\mathcal{S} = \\langle R, A, E, \\Lambda, \\rho, W \\rangle","context":"ith a doctrine-locked runtime** as a category-defining primitive for verifiable agency. We define the system as a tuple \\( \\mathcal{S} = \\langle R, A, E, \\Lambda, \\rho, W \\rangle \\) over an eight-regi","source_id":"thesis_session","maturity":"defined"},{"id":"F0002","source_file":"thesis.md","source_line":229,"latex":"\\mathtt{szl\\text{-}trust}","context":"d system.  - \\(A\\) — the set of **named actors**. Every actor in \\(A\\) carries a stable identity resolvable to a key in \\(\\mathtt{szl\\text{-}trust}\\). No edge in \\(E\\) may originate from or terminate ","source_id":"thesis_session","maturity":"defined"},{"id":"F0003","source_file":"thesis.md","source_line":231,"latex":"e \\in E","context":"and resolvable — unidentified actors are structurally excluded.  - \\(E\\) — the set of **receipt-bound edges**. An edge \\(e \\in E\\) is a tuple \\((a_{\\text{src}},\\; r_{\\text{src}},\\; r_{\\text{dst}},\\; \\","source_id":"thesis_session","maturity":"defined"},{"id":"F0004","source_file":"thesis.md","source_line":231,"latex":"(a_{\\text{src}},\\; r_{\\text{src}},\\; r_{\\text{dst}},\\; \\varepsilon)","context":"ntified actors are structurally excluded.  - \\(E\\) — the set of **receipt-bound edges**. An edge \\(e \\in E\\) is a tuple \\((a_{\\text{src}},\\; r_{\\text{src}},\\; r_{\\text{dst}},\\; \\varepsilon)\\) where \\(","source_id":"thesis_session","maturity":"defined"},{"id":"F0005","source_file":"thesis.md","source_line":231,"latex":"a_{\\text{src}} \\in A","context":"d edges**. An edge \\(e \\in E\\) is a tuple \\((a_{\\text{src}},\\; r_{\\text{src}},\\; r_{\\text{dst}},\\; \\varepsilon)\\) where \\(a_{\\text{src}} \\in A\\), \\(r_{\\text{src}}, r_{\\text{dst}} \\in R\\), and \\(\\varep","source_id":"thesis_session","maturity":"defined"},{"id":"F0006","source_file":"thesis.md","source_line":231,"latex":"r_{\\text{src}}, r_{\\text{dst}} \\in R","context":"E\\) is a tuple \\((a_{\\text{src}},\\; r_{\\text{src}},\\; r_{\\text{dst}},\\; \\varepsilon)\\) where \\(a_{\\text{src}} \\in A\\), \\(r_{\\text{src}}, r_{\\text{dst}} \\in R\\), and \\(\\varepsilon\\) is the receipt enve","source_id":"thesis_session","maturity":"defined"},{"id":"F0007","source_file":"thesis.md","source_line":231,"latex":"\\varepsilon","context":"src}},\\; r_{\\text{dst}},\\; \\varepsilon)\\) where \\(a_{\\text{src}} \\in A\\), \\(r_{\\text{src}}, r_{\\text{dst}} \\in R\\), and \\(\\varepsilon\\) is the receipt envelope defined in §3.3. No message may traverse","source_id":"thesis_session","maturity":"defined"},{"id":"F0008","source_file":"thesis.md","source_line":231,"latex":"\\varepsilon","context":"repsilon\\) is the receipt envelope defined in §3.3. No message may traverse a region boundary unless it carries a valid \\(\\varepsilon\\).  - \\(\\Lambda\\) — the **composable axis-gating function**. Forma","source_id":"thesis_session","maturity":"defined"},{"id":"F0009","source_file":"thesis.md","source_line":233,"latex":"\\Lambda","context":"ceipt envelope defined in §3.3. No message may traverse a region boundary unless it carries a valid \\(\\varepsilon\\).  - \\(\\Lambda\\) — the **composable axis-gating function**. Formally, \\(\\Lambda : [0,","source_id":"thesis_session","maturity":"defined"},{"id":"F0010","source_file":"thesis.md","source_line":233,"latex":"\\Lambda : [0,1]^k \\to \\{0,1\\}","context":"boundary unless it carries a valid \\(\\varepsilon\\).  - \\(\\Lambda\\) — the **composable axis-gating function**. Formally, \\(\\Lambda : [0,1]^k \\to \\{0,1\\}\\) for \\(k \\geq 9\\), defined as the conjunctive A","source_id":"thesis_session","maturity":"defined"},{"id":"F0011","source_file":"thesis.md","source_line":233,"latex":"k \\geq 9","context":"varepsilon\\).  - \\(\\Lambda\\) — the **composable axis-gating function**. Formally, \\(\\Lambda : [0,1]^k \\to \\{0,1\\}\\) for \\(k \\geq 9\\), defined as the conjunctive AND:  \\[ \\Lambda(\\mathbf{x}) = 1 \\iff \\","source_id":"thesis_session","maturity":"defined"},{"id":"F0012","source_file":"thesis.md","source_line":239,"latex":"\\mathbf{x}","context":"bilityHonesty}} \\geq 0.95 \\]    The composability property states that for any two independently evaluated axis vectors \\(\\mathbf{x}\\) and \\(\\mathbf{y}\\), their composed gate \\(\\Lambda(\\mathbf{x} \\wed","source_id":"thesis_session","maturity":"defined"},{"id":"F0013","source_file":"thesis.md","source_line":239,"latex":"\\mathbf{y}","context":"q 0.95 \\]    The composability property states that for any two independently evaluated axis vectors \\(\\mathbf{x}\\) and \\(\\mathbf{y}\\), their composed gate \\(\\Lambda(\\mathbf{x} \\wedge \\mathbf{y})\\) is","source_id":"thesis_session","maturity":"defined"},{"id":"F0014","source_file":"thesis.md","source_line":239,"latex":"\\Lambda(\\mathbf{x} \\wedge \\mathbf{y})","context":"rty states that for any two independently evaluated axis vectors \\(\\mathbf{x}\\) and \\(\\mathbf{y}\\), their composed gate \\(\\Lambda(\\mathbf{x} \\wedge \\mathbf{y})\\) is equivalent to \\(\\Lambda(\\mathbf{x})","source_id":"thesis_session","maturity":"defined"},{"id":"F0015","source_file":"thesis.md","source_line":239,"latex":"\\Lambda(\\mathbf{x}) \\wedge \\Lambda(\\mathbf{y})","context":"ctors \\(\\mathbf{x}\\) and \\(\\mathbf{y}\\), their composed gate \\(\\Lambda(\\mathbf{x} \\wedge \\mathbf{y})\\) is equivalent to \\(\\Lambda(\\mathbf{x}) \\wedge \\Lambda(\\mathbf{y})\\) — gate composition does not w","source_id":"thesis_session","maturity":"defined"},{"id":"F0016","source_file":"thesis.md","source_line":239,"latex":"\\Lambda","context":"— gate composition does not weaken the invariant. The `lutar-lean` skeleton repository contains the Lean 4 statement of \\(\\Lambda\\) uniqueness: given the four axioms (A1 monotonicity, A2 homogeneity, ","source_id":"thesis_session","maturity":"conjectured"},{"id":"F0017","source_file":"thesis.md","source_line":239,"latex":"\\Lambda","context":"ment of \\(\\Lambda\\) uniqueness: given the four axioms (A1 monotonicity, A2 homogeneity, A3 Egyptian-exact, A4 bounded), \\(\\Lambda\\) is the *unique* function satisfying them. The uniqueness theorem and","source_id":"thesis_session","maturity":"conjectured"},{"id":"F0018","source_file":"thesis.md","source_line":241,"latex":"\\rho(e)","context":"arget is zero.  - \\(\\rho\\) — the **dual-witness closure relation**. For any edge \\(e\\) carrying execution result \\(v\\), \\(\\rho(e)\\) holds iff two independent witnesses \\(w_1, w_2 \\in W\\) each produce ","source_id":"thesis_session","maturity":"defined"},{"id":"F0019","source_file":"thesis.md","source_line":241,"latex":"w_1, w_2 \\in W","context":"closure relation**. For any edge \\(e\\) carrying execution result \\(v\\), \\(\\rho(e)\\) holds iff two independent witnesses \\(w_1, w_2 \\in W\\) each produce byte-identical output on the same input, and the","source_id":"thesis_session","maturity":"defined"},{"id":"F0020","source_file":"thesis.md","source_line":251,"latex":"\\mathcal{S}","context":"uroboros` core + 4 `a11oy` covenant), while the full upstream runtime suite registers 218/218 passing tests.  The tuple \\(\\mathcal{S}\\) is **doctrine-locked**: any runtime configuration in which (a) a","source_id":"thesis_session","maturity":"defined"},{"id":"F0021","source_file":"thesis.md","source_line":251,"latex":"\\Lambda","context":"which (a) a region is unnamed, (b) an actor is not in \\(A\\), (c) an edge is produced without a receipt envelope, or (d) \\(\\Lambda\\) is evaluated below threshold does not constitute a valid instantiati","source_id":"thesis_session","maturity":"defined"},{"id":"F0022","source_file":"thesis.md","source_line":251,"latex":"\\mathcal{S}","context":"ithout a receipt envelope, or (d) \\(\\Lambda\\) is evaluated below threshold does not constitute a valid instantiation of \\(\\mathcal{S}\\).  ---  ## The 8-Region Anatomy  The eight canonical regions of \\","source_id":"thesis_session","maturity":"defined"},{"id":"F0023","source_file":"thesis.md","source_line":257,"latex":"\\mathcal{S}","context":"of \\(R\\) are enumerated below. For each region the presentation gives: the repository identifier, its role in the tuple \\(\\mathcal{S}\\), its public interfaces, and its dependency relations within \\(E\\","source_id":"thesis_session","maturity":"defined"},{"id":"F0024","source_file":"thesis.md","source_line":265,"latex":"\\mathcal{S}","context":"released 2026-05-13; concept DOI `10.5281/zenodo.19944926`, v11 paper DOI `10.5281/zenodo.20119582`)  **Formal role in \\(\\mathcal{S}\\):** The Brain Stem is the runtime kernel that evaluates \\(\\Lambda\\","source_id":"thesis_session","maturity":"defined"},{"id":"F0025","source_file":"thesis.md","source_line":265,"latex":"\\Lambda","context":"DOI `10.5281/zenodo.20119582`)  **Formal role in \\(\\mathcal{S}\\):** The Brain Stem is the runtime kernel that evaluates \\(\\Lambda\\) and emits receipts. Every edge in \\(E\\) that crosses a region bounda","source_id":"thesis_session","maturity":"defined"},{"id":"F0026","source_file":"thesis.md","source_line":268,"latex":"\\Lambda","context":"bda(axes: number[9|10]) → Receipt` — evaluates the conjunctive AND gate and returns a signed receipt with the composite \\(\\Lambda\\) score, Bekenstein budget, and dual-witness closure status. - `build_","source_id":"thesis_session","maturity":"conjectured"},{"id":"F0027","source_file":"thesis.md","source_line":274,"latex":"\\Lambda","context":"chain root for third-party verification.  **Dependencies:** - Depends on: `lutar-lean` (Skeleton) — the axiom set that \\(\\Lambda\\) is required to satisfy is formally stated there; the Brain Stem is th","source_id":"thesis_session","maturity":"defined"},{"id":"F0028","source_file":"thesis.md","source_line":277,"latex":"\\Lambda_9","context":"utbound edge must call `evaluate_lambda` before the edge enters \\(E\\).  The gate composition benchmark for v6.3.0 shows \\(\\Lambda_9\\) base p50 = 3.12 µs and composed p50 = 3.29 µs; with the Platform v","source_id":"thesis_session","maturity":"defined"},{"id":"F0029","source_file":"thesis.md","source_line":285,"latex":"\\mathcal{S}","context":"a continuous supply-chain security posture.  ---  ### Heart — `a11oy`  **Repo:** `szl-holdings/a11oy`  **Formal role in \\(\\mathcal{S}\\):** The Heart is the covenant policy engine and the agent approva","source_id":"thesis_session","maturity":"defined"},{"id":"F0030","source_file":"thesis.md","source_line":285,"latex":"\\mathcal{S}","context":"\\):** The Heart is the covenant policy engine and the agent approval queue. It governs the *authorization* dimension of \\(\\mathcal{S}\\): while the Brain Stem answers \"does this action score above \\(\\L","source_id":"thesis_session","maturity":"defined"},{"id":"F0031","source_file":"thesis.md","source_line":285,"latex":"\\Lambda","context":"It governs the *authorization* dimension of \\(\\mathcal{S}\\): while the Brain Stem answers \"does this action score above \\(\\Lambda\\)?\", the Heart answers \"is this action permitted under the active cove","source_id":"thesis_session","maturity":"defined"},{"id":"F0032","source_file":"thesis.md","source_line":285,"latex":"r_{\\text{dst}} \\notin R","context":"this action permitted under the active covenant?\". No action may exit the body graph — i.e., no edge in \\(E\\) may have \\(r_{\\text{dst}} \\notin R\\) — without a Heart pulse. The covenant is a named, ver","source_id":"thesis_session","maturity":"defined"},{"id":"F0033","source_file":"thesis.md","source_line":293,"latex":"\\Lambda","context":"Stem's chain.  **Dependencies:** - Depends on: `ouroboros` (Brain Stem) — covenant evaluation results are sealed with a \\(\\Lambda\\)-gated receipt; a covenant check that fails \\(\\Lambda\\) is itself a g","source_id":"thesis_session","maturity":"defined"},{"id":"F0034","source_file":"thesis.md","source_line":293,"latex":"\\Lambda","context":"os` (Brain Stem) — covenant evaluation results are sealed with a \\(\\Lambda\\)-gated receipt; a covenant check that fails \\(\\Lambda\\) is itself a gate-level violation. - Depends on: `safety-gate layer` (safety wires) — t","source_id":"thesis_session","maturity":"defined"},{"id":"F0035","source_file":"thesis.md","source_line":305,"latex":"\\mathcal{S}","context":"but a verifiable, chain-linked artifact.  ---  ### safety wires — `safety-gate layer`  **Repo:** `szl-holdings/safety-gate layer`  **Formal role in \\(\\mathcal{S}\\):** The safety wires are the attribution trail — the afferent channel tha","source_id":"thesis_session","maturity":"defined"},{"id":"F0036","source_file":"thesis.md","source_line":305,"latex":"\\text{attr}: E \\to A","context":"rent channel that carries signals inward and records *who observed what and when*. Formally, safety wires maintain the mapping \\(\\text{attr}: E \\to A\\), ensuring that every edge in \\(E\\) is attributable to a","source_id":"thesis_session","maturity":"defined"},{"id":"F0037","source_file":"thesis.md","source_line":305,"latex":"\\mathcal{S}","context":"he mapping \\(\\text{attr}: E \\to A\\), ensuring that every edge in \\(E\\) is attributable to a named actor. Without safety wires, \\(\\mathcal{S}\\) degrades: edges carry receipts but not attributions, making the ","source_id":"thesis_session","maturity":"defined"},{"id":"F0038","source_file":"thesis.md","source_line":308,"latex":"a \\in A","context":"egal-accountability sense.  **Public interfaces:** - `observe(edge, actor_id) → AttributionRecord` — records that actor \\(a \\in A\\) produced or consumed edge \\(e\\). - `attribution_trail(region, time_r","source_id":"thesis_session","maturity":"defined"},{"id":"F0039","source_file":"thesis.md","source_line":325,"latex":"\\mathcal{S}","context":"aft-morrow-sogomonian-exec-outcome-attest`.  ---  ### reasoning spine — `reasoning core`  **Repo:** `szl-holdings/reasoning core`  **Formal role in \\(\\mathcal{S}\\):** The reasoning spine is the append-only coordination and protocol bridge","source_id":"thesis_session","maturity":"defined"},{"id":"F0040","source_file":"thesis.md","source_line":325,"latex":"\\langle e_1, e_2, \\ldots, e_n \\rangle \\subseteq E","context":"ordered, hash-verified record of every state transition across the body graph. Formally, `reasoning core` maintains the sequence \\(\\langle e_1, e_2, \\ldots, e_n \\rangle \\subseteq E\\) ordered by timestamp, with","source_id":"thesis_session","maturity":"defined"},{"id":"F0041","source_file":"thesis.md","source_line":339,"latex":"O(\\log n)","context":"(identified in the runtime roadmap) would upgrade the reasoning spine's linear hash-chain to a directed acyclic graph supporting \\(O(\\log n)\\) subset inclusion proofs — enabling privacy-preserving audits for re","source_id":"thesis_session","maturity":"defined"},{"id":"F0042","source_file":"thesis.md","source_line":347,"latex":"\\mathcal{S}","context":"nce in the enterprise segment.  ---  ### Skeleton — `lutar-lean`  **Repo:** `szl-holdings/lutar-lean`  **Formal role in \\(\\mathcal{S}\\):** The Skeleton is the formal scaffold — the Lean 4 axioms and M","source_id":"thesis_session","maturity":"defined"},{"id":"F0043","source_file":"thesis.md","source_line":347,"latex":"\\{A1, A2, A3, A4\\}","context":"es not execute at runtime; it is the *proof that the runtime is correct*. Formally, `lutar-lean` provides the axiom set \\(\\{A1, A2, A3, A4\\}\\) and the derived theorems (Λ uniqueness, Bound theorem) th","source_id":"thesis_session","maturity":"conjectured"},{"id":"F0044","source_file":"thesis.md","source_line":347,"latex":"\\Lambda","context":"A2, A3, A4\\}\\) and the derived theorems (Λ uniqueness, Bound theorem) that constitute a machine-checked certificate for \\(\\Lambda\\). If the Skeleton's `sorry` count is zero, the gate the Brain Stem en","source_id":"thesis_session","maturity":"conjectured"},{"id":"F0045","source_file":"thesis.md","source_line":351,"latex":"\\Lambda","context":"statements of A1 (monotonicity), A2 (homogeneity), A3 (Egyptian-exact), A4 (bounded). - `Uniqueness.lean` — Theorem 1: \\(\\Lambda\\) is the unique function satisfying A1–A4; proof scaffold with tracked ","source_id":"thesis_session","maturity":"conjectured"},{"id":"F0046","source_file":"thesis.md","source_line":367,"latex":"\\mathcal{S}","context":"*Repos:** `szl-holdings/counsel` (governance UI), `szl-holdings/terra` (dashboards and visualization)  **Formal role in \\(\\mathcal{S}\\):** The Hands are the tooling and visualization surfaces — the co","source_id":"thesis_session","maturity":"defined"},{"id":"F0047","source_file":"thesis.md","source_line":371,"latex":"\\Lambda","context":"as an interactive SVG, streaming live receipt counts via SSE from `/api/chain/stream`; node colors reflect the current \\(\\Lambda\\) score band (green ≥ 0.95, amber 0.90–0.95, red < 0.90). The planned \"","source_id":"thesis_session","maturity":"defined"},{"id":"F0048","source_file":"thesis.md","source_line":386,"latex":"\\mathcal{S}","context":"*is* the system.  ---  ### Full Body — `ouroboros-thesis`  **Repo:** `szl-holdings/ouroboros-thesis`  **Formal role in \\(\\mathcal{S}\\):** The Full Body is the public-record thesis — the DOI-pinned, ve","source_id":"thesis_session","maturity":"defined"},{"id":"F0049","source_file":"thesis.md","source_line":386,"latex":"\\mathcal{S}","context":"l Body is the public-record thesis — the DOI-pinned, versioned document that constitutes the canonical specification of \\(\\mathcal{S}\\). Formally, `ouroboros-thesis` defines the normative description ","source_id":"thesis_session","maturity":"defined"},{"id":"F0050","source_file":"thesis.md","source_line":405,"latex":"\\mathcal{S}","context":"d identity anchoring), `szl-holdings/szl-cookbook` (reference implementations / developer onboarding)  **Formal role in \\(\\mathcal{S}\\):** The Vessels and Chakras collectively form the trust mesh and ","source_id":"thesis_session","maturity":"defined"},{"id":"F0051","source_file":"thesis.md","source_line":421,"latex":"\\varepsilon","context":"eue under the covenant pack schema.  ---  ## Cross-Region Contracts  Every edge in \\(E\\) carries a **receipt envelope** \\(\\varepsilon\\). The envelope is a typed, signed, content-addressed record that ","source_id":"thesis_session","maturity":"defined"},{"id":"F0052","source_file":"thesis.md","source_line":421,"latex":"\\Lambda","context":"es a **receipt envelope** \\(\\varepsilon\\). The envelope is a typed, signed, content-addressed record that provides: the \\(\\Lambda\\) score vector, the dual-witness closure status (\\(\\rho\\)), the actor ","source_id":"thesis_session","maturity":"defined"},{"id":"F0053","source_file":"thesis.md","source_line":479,"latex":"\\Lambda","context":"_lambda(axes) → Receipt` — any MCP-compatible client (Claude Desktop, Cursor, enterprise agent frameworks) can call the \\(\\Lambda\\) gate as a typed tool and receive a signed receipt in the tool respon","source_id":"thesis_session","maturity":"defined"},{"id":"F0054","source_file":"thesis.md","source_line":507,"latex":"\\mathcal{S}","context":"the 8-Region Model Structurally Surpasses the Leaders  Each leading framework or protocol is a partial instantiation of \\(\\mathcal{S}\\). The gap is structural: the missing region is not a feature that","source_id":"thesis_session","maturity":"defined"},{"id":"F0055","source_file":"thesis.md","source_line":515,"latex":"\\Lambda_9","context":"l engineering pattern, but skills are *files*, not services with receipts. A Brain Stem can issue a decision that fails \\(\\Lambda_9\\) moralGrounding; in the Managed Agents architecture there is no mec","source_id":"thesis_session","maturity":"defined"},{"id":"F0056","source_file":"thesis.md","source_line":515,"latex":"\\mathcal{S}","context":"fails \\(\\Lambda_9\\) moralGrounding; in the Managed Agents architecture there is no mechanism to detect or block it. In \\(\\mathcal{S}\\), that decision never exits the Brain Stem.  **Mastra** (22K+ GitH","source_id":"thesis_session","maturity":"defined"},{"id":"F0057","source_file":"thesis.md","source_line":517,"latex":"\\Lambda","context":"ource agent framework in the TypeScript ecosystem. Mastra has no Skeleton: there are no Lean 4 proofs. It has no formal \\(\\Lambda\\) gate — behavioral constraints are implemented as runtime checks with","source_id":"thesis_session","maturity":"defined"},{"id":"F0058","source_file":"thesis.md","source_line":567,"latex":"\\lambda_1","context":"l(\\lambda_1(c),\\, \\lambda_2(c),\\, \\ldots,\\, \\lambda_9(c)\\bigr) \\in [0,1]^9 \\]  The nine axes are defined as follows.  **\\(\\lambda_1\\): moralGrounding.** Measures the degree to which a proposed action ","source_id":"thesis_session","maturity":"defined"},{"id":"F0059","source_file":"thesis.md","source_line":567,"latex":"\\lambda_1","context":"nce policies, and principal hierarchies that the operator has encoded in the agent's governing covenant. Operationally, \\(\\lambda_1\\) is the normalized cosine similarity between the action's intent em","source_id":"thesis_session","maturity":"defined"},{"id":"F0060","source_file":"thesis.md","source_line":567,"latex":"[0,1]","context":"mbedding and a reference \"moral anchor\" embedding, averaged over the operator's registered covenant clauses, clamped to \\([0,1]\\). The floor constraint \\(\\lambda_1 \\geq 0.95\\) is a hard asymptote: an ","source_id":"thesis_session","maturity":"defined"},{"id":"F0061","source_file":"thesis.md","source_line":567,"latex":"\\lambda_1 \\geq 0.95","context":"anchor\" embedding, averaged over the operator's registered covenant clauses, clamped to \\([0,1]\\). The floor constraint \\(\\lambda_1 \\geq 0.95\\) is a hard asymptote: an agent that is even marginally mo","source_id":"thesis_session","maturity":"defined"},{"id":"F0062","source_file":"thesis.md","source_line":569,"latex":"\\lambda_2","context":"even marginally morally misaligned fails the gate irrespective of how perfectly calibrated the other eight axes are.  **\\(\\lambda_2\\): measurabilityHonesty.** Measures whether an action's declared eff","source_id":"thesis_session","maturity":"defined"},{"id":"F0063","source_file":"thesis.md","source_line":571,"latex":"\\lambda_3","context":"ine clause \"no hallucinations no bandaids; test test test\" by making measurement-honesty a prerequisite for passage.  **\\(\\lambda_3\\): epistemicHumility.** Scores the agent's acknowledgment of its own","source_id":"thesis_session","maturity":"defined"},{"id":"F0064","source_file":"thesis.md","source_line":571,"latex":"\\lambda_3 = 1 - \\mathbb{E}[|\\text{conf}(c) - \\text{acc}(c)|]","context":"sparse scores low on this axis. The scoring function penalizes unjustified confidence using a calibration-error analog: \\(\\lambda_3 = 1 - \\mathbb{E}[|\\text{conf}(c) - \\text{acc}(c)|]\\) where \\(\\text{c","source_id":"thesis_session","maturity":"defined"},{"id":"F0065","source_file":"thesis.md","source_line":571,"latex":"\\text{conf}(c)","context":"ied confidence using a calibration-error analog: \\(\\lambda_3 = 1 - \\mathbb{E}[|\\text{conf}(c) - \\text{acc}(c)|]\\) where \\(\\text{conf}(c)\\) is the agent's stated confidence and \\(\\text{acc}(c)\\) is the","source_id":"thesis_session","maturity":"defined"},{"id":"F0066","source_file":"thesis.md","source_line":571,"latex":"\\text{acc}(c)","context":"da_3 = 1 - \\mathbb{E}[|\\text{conf}(c) - \\text{acc}(c)|]\\) where \\(\\text{conf}(c)\\) is the agent's stated confidence and \\(\\text{acc}(c)\\) is the empirically measured accuracy over a calibration set.  ","source_id":"thesis_session","maturity":"defined"},{"id":"F0067","source_file":"thesis.md","source_line":573,"latex":"\\lambda_4","context":"is the agent's stated confidence and \\(\\text{acc}(c)\\) is the empirically measured accuracy over a calibration set.  **\\(\\lambda_4\\): counterfactualAwareness.** Measures whether the agent has consider","source_id":"thesis_session","maturity":"defined"},{"id":"F0068","source_file":"thesis.md","source_line":575,"latex":"\\lambda_5","context":"res 0.0 and a uniformly distributed consequence distribution over the operator-defined consequence space scores 1.0.  **\\(\\lambda_5\\): temporalConsistency.** Measures the stability of the gate verdict","source_id":"thesis_session","maturity":"defined"},{"id":"F0069","source_file":"thesis.md","source_line":575,"latex":"t + \\Delta","context":"Measures the stability of the gate verdict under repeated evaluation on the same input at two different times \\(t\\) and \\(t + \\Delta\\). Let \\(v_t\\) and \\(v_{t+\\Delta}\\) denote the Λ₉ composite scores ","source_id":"thesis_session","maturity":"defined"},{"id":"F0070","source_file":"thesis.md","source_line":575,"latex":"v_{t+\\Delta}","context":"te verdict under repeated evaluation on the same input at two different times \\(t\\) and \\(t + \\Delta\\). Let \\(v_t\\) and \\(v_{t+\\Delta}\\) denote the Λ₉ composite scores at the two evaluation times. The","source_id":"thesis_session","maturity":"defined"},{"id":"F0071","source_file":"thesis.md","source_line":581,"latex":"\\lambda_5 = 1.0","context":"Then:  \\[ \\lambda_5 = \\max\\!\\Bigl(0,\\; 1 - 4\\,\\bigl(v_t - v_{t+\\Delta}\\bigr)^2\\Bigr) \\]  A zero-drift evaluation scores \\(\\lambda_5 = 1.0\\). A drift of 0.05 in the composite score yields \\(\\lambda_5 =","source_id":"thesis_session","maturity":"defined"},{"id":"F0072","source_file":"thesis.md","source_line":581,"latex":"\\lambda_5 = 0.99","context":"ta}\\bigr)^2\\Bigr) \\]  A zero-drift evaluation scores \\(\\lambda_5 = 1.0\\). A drift of 0.05 in the composite score yields \\(\\lambda_5 = 0.99\\). A drift of 0.25 yields \\(\\lambda_5 = 0.75\\), below the ≥ 0","source_id":"thesis_session","maturity":"defined"},{"id":"F0073","source_file":"thesis.md","source_line":581,"latex":"\\lambda_5 = 0.75","context":"scores \\(\\lambda_5 = 1.0\\). A drift of 0.05 in the composite score yields \\(\\lambda_5 = 0.99\\). A drift of 0.25 yields \\(\\lambda_5 = 0.75\\), below the ≥ 0.90 conjunctive floor. This axis operationaliz","source_id":"thesis_session","maturity":"defined"},{"id":"F0074","source_file":"thesis.md","source_line":583,"latex":"\\lambda_6","context":"-identical replay guarantee: a system that cannot reproduce its own gate verdict is not operating deterministically.  **\\(\\lambda_6\\): evidenceProvenance.** Measures whether every empirical claim embe","source_id":"thesis_session","maturity":"defined","puriq_ref":"F1","lean_ref":"f1_replay_fold_deterministic"},{"id":"F0075","source_file":"thesis.md","source_line":585,"latex":"\\lambda_7","context":"ertions score at most 0.50. The scoring function is the fraction of claim tokens for which provenance is resolvable.  **\\(\\lambda_7\\): actorIdentity.** Measures the definiteness of the acting agent's ","source_id":"thesis_session","maturity":"defined"},{"id":"F0076","source_file":"thesis.md","source_line":587,"latex":"\\lambda_8","context":"ting under delegated authority — the score decays as a function of delegation depth to penalize opaque proxy chains.  **\\(\\lambda_8\\): axiomConsistency.** Measures whether the proposed action is inter","source_id":"thesis_session","maturity":"defined"},{"id":"F0077","source_file":"thesis.md","source_line":589,"latex":"\\lambda_9","context":"Lean 4 formalization: it enforces, at runtime, the constraints that are statically verified at theorem-proving time.  **\\(\\lambda_9\\): coherence.** Measures the multi-step logical coherence of the age","source_id":"thesis_session","maturity":"defined"},{"id":"F0078","source_file":"thesis.md","source_line":589,"latex":"A_1, A_2, \\ldots, A_k","context":"-step logical coherence of the agent's plan across the action sequence, not just for the current step in isolation. Let \\(A_1, A_2, \\ldots, A_k\\) denote the \\(k\\) preceding actions in the current sess","source_id":"thesis_session","maturity":"defined"},{"id":"F0079","source_file":"thesis.md","source_line":589,"latex":"(A_i, A_{i+1})","context":"e the \\(k\\) preceding actions in the current session. The coherence score is the proportion of consecutive action-pairs \\((A_i, A_{i+1})\\) for which the precondition of \\(A_{i+1}\\) is satisfied by the","source_id":"thesis_session","maturity":"defined"},{"id":"F0080","source_file":"thesis.md","source_line":589,"latex":"A_{i+1}","context":"ion. The coherence score is the proportion of consecutive action-pairs \\((A_i, A_{i+1})\\) for which the precondition of \\(A_{i+1}\\) is satisfied by the postcondition of \\(A_i\\), under the operator's p","source_id":"thesis_session","maturity":"defined"},{"id":"F0081","source_file":"thesis.md","source_line":589,"latex":"\\lambda_9 = 1.0","context":"ied by the postcondition of \\(A_i\\), under the operator's precondition/postcondition schema. For the base case \\(k=0\\), \\(\\lambda_9 = 1.0\\).  ### The conjunctive gate condition  The Λ₉ gate passes if ","source_id":"thesis_session","maturity":"defined"},{"id":"F0082","source_file":"thesis.md","source_line":599,"latex":"\\lambda_1 = 0.50","context":"for the following reason. A single composite score — even a geometric mean — can mask localized failures. An agent with \\(\\lambda_1 = 0.50\\) (severely morally misaligned) and all remaining axes at \\(1","source_id":"thesis_session","maturity":"defined"},{"id":"F0083","source_file":"thesis.md","source_line":599,"latex":"\\prod_{i}^{1/9} = 0.50^{1/9} \\approx 0.926","context":"with \\(\\lambda_1 = 0.50\\) (severely morally misaligned) and all remaining axes at \\(1.0\\) achieves a geometric mean of \\(\\prod_{i}^{1/9} = 0.50^{1/9} \\approx 0.926\\), which would pass a ≥ 0.90 single-","source_id":"thesis_session","maturity":"defined"},{"id":"F0084","source_file":"thesis.md","source_line":599,"latex":"\\lambda_1","context":"gle-score gate. The conjunctive AND structure prevents this: every axis is a blocking veto. The two elevated floors for \\(\\lambda_1\\) and \\(\\lambda_2\\) add a second layer of asymmetry — these are the ","source_id":"thesis_session","maturity":"defined"},{"id":"F0085","source_file":"thesis.md","source_line":599,"latex":"\\lambda_2","context":"e conjunctive AND structure prevents this: every axis is a blocking veto. The two elevated floors for \\(\\lambda_1\\) and \\(\\lambda_2\\) add a second layer of asymmetry — these are the axes most directly","source_id":"thesis_session","maturity":"defined"},{"id":"F0086","source_file":"thesis.md","source_line":605,"latex":"m \\in \\{0,1\\}^9","context":"to the receipt structure. Rather than publishing the raw nine (or ten) axis scores, the receipt carries a bitfield mask \\(m \\in \\{0,1\\}^9\\) in which \\(m_i = 1\\) if and only if \\(\\lambda_i\\) was evalua","source_id":"thesis_session","maturity":"defined"},{"id":"F0087","source_file":"thesis.md","source_line":605,"latex":"m_i = 1","context":"her than publishing the raw nine (or ten) axis scores, the receipt carries a bitfield mask \\(m \\in \\{0,1\\}^9\\) in which \\(m_i = 1\\) if and only if \\(\\lambda_i\\) was evaluated and passed its floor. The","source_id":"thesis_session","maturity":"defined"},{"id":"F0088","source_file":"thesis.md","source_line":605,"latex":"\\lambda_i","context":"nine (or ten) axis scores, the receipt carries a bitfield mask \\(m \\in \\{0,1\\}^9\\) in which \\(m_i = 1\\) if and only if \\(\\lambda_i\\) was evaluated and passed its floor. The raw scores are withheld fro","source_id":"thesis_session","maturity":"defined"},{"id":"F0089","source_file":"thesis.md","source_line":611,"latex":"\\theta_i = 0.95","context":"ity profile of the agent. Formally, the mask is computed as:  \\[ m_i = \\mathbf{1}[\\lambda_i(c) \\geq \\theta_i] \\]  where \\(\\theta_i = 0.95\\) for \\(i \\in \\{1,2\\}\\) and \\(\\theta_i = 0.90\\) otherwise. The","source_id":"thesis_session","maturity":"defined"},{"id":"F0090","source_file":"thesis.md","source_line":611,"latex":"i \\in \\{1,2\\}","context":". Formally, the mask is computed as:  \\[ m_i = \\mathbf{1}[\\lambda_i(c) \\geq \\theta_i] \\]  where \\(\\theta_i = 0.95\\) for \\(i \\in \\{1,2\\}\\) and \\(\\theta_i = 0.90\\) otherwise. The gate passes iff \\(\\sum_","source_id":"thesis_session","maturity":"defined"},{"id":"F0091","source_file":"thesis.md","source_line":611,"latex":"\\theta_i = 0.90","context":"s computed as:  \\[ m_i = \\mathbf{1}[\\lambda_i(c) \\geq \\theta_i] \\]  where \\(\\theta_i = 0.95\\) for \\(i \\in \\{1,2\\}\\) and \\(\\theta_i = 0.90\\) otherwise. The gate passes iff \\(\\sum_i m_i = 9\\) (or 10 und","source_id":"thesis_session","maturity":"defined"},{"id":"F0092","source_file":"thesis.md","source_line":611,"latex":"\\sum_i m_i = 9","context":"eq \\theta_i] \\]  where \\(\\theta_i = 0.95\\) for \\(i \\in \\{1,2\\}\\) and \\(\\theta_i = 0.90\\) otherwise. The gate passes iff \\(\\sum_i m_i = 9\\) (or 10 under Λ₁₀). The mask is committed via SHA-256 and incl","source_id":"thesis_session","maturity":"defined"},{"id":"F0093","source_file":"thesis.md","source_line":627,"latex":"\\textit{parent\\_hash}","context":"\\textit{timestamp},\\; \\vec{\\lambda},\\; \\rho\\_\\textit{witness\\_set},\\; \\textit{signature}\\bigr) \\]  The fields are:  - **\\(\\textit{parent\\_hash}\\)**: The SHA-256 digest of receipt \\(r_{i-1}\\). For the ","source_id":"thesis_session","maturity":"defined"},{"id":"F0094","source_file":"thesis.md","source_line":627,"latex":"r_{i-1}","context":"s\\_set},\\; \\textit{signature}\\bigr) \\]  The fields are:  - **\\(\\textit{parent\\_hash}\\)**: The SHA-256 digest of receipt \\(r_{i-1}\\). For the genesis receipt, this is the SHA-256 of a protocol-specifie","source_id":"thesis_session","maturity":"defined"},{"id":"F0095","source_file":"thesis.md","source_line":628,"latex":"\\textit{content\\_digest}","context":"this is the SHA-256 of a protocol-specified null seed. This field creates the backward-pointing link of the chain. - **\\(\\textit{content\\_digest}\\)**: The SHA-256 of the canonical JSON serialization o","source_id":"thesis_session","maturity":"defined"},{"id":"F0096","source_file":"thesis.md","source_line":629,"latex":"\\textit{actor}","context":"fore any side-effectful execution. This binds the gate verdict irrevocably to the specific input that triggered it. - **\\(\\textit{actor}\\)**: The identifier of the acting agent as registered in the pr","source_id":"thesis_session","maturity":"defined"},{"id":"F0097","source_file":"thesis.md","source_line":629,"latex":"\\lambda_7","context":"t. - **\\(\\textit{actor}\\)**: The identifier of the acting agent as registered in the principal registry. Corresponds to \\(\\lambda_7\\) (actorIdentity). - **\\(\\textit{timestamp}\\)**: A monotonic timesta","source_id":"thesis_session","maturity":"defined"},{"id":"F0098","source_file":"thesis.md","source_line":630,"latex":"\\textit{timestamp}","context":"entifier of the acting agent as registered in the principal registry. Corresponds to \\(\\lambda_7\\) (actorIdentity). - **\\(\\textit{timestamp}\\)**: A monotonic timestamp in milliseconds since the Unix e","source_id":"thesis_session","maturity":"defined"},{"id":"F0099","source_file":"thesis.md","source_line":631,"latex":"\\vec{\\lambda}","context":": A monotonic timestamp in milliseconds since the Unix epoch, drawn from a pinned, non-forgeable source (see §4.6). - **\\(\\vec{\\lambda}\\)**: The full nine-dimensional Λ vector, or the `lambda9_mask` b","source_id":"thesis_session","maturity":"defined"},{"id":"F0100","source_file":"thesis.md","source_line":632,"latex":"\\rho\\_\\textit{witness\\_set}","context":"vec{\\lambda}\\)**: The full nine-dimensional Λ vector, or the `lambda9_mask` bitfield under the Λ₁₀ privacy variant. - **\\(\\rho\\_\\textit{witness\\_set}\\)**: The set of co-witnesses whose signatures are ","source_id":"thesis_session","maturity":"defined"}],"definitions":[],"canonical_constants":[{"id":"K01","name":"receipt_build_p50_us","value":"11.5","unit":"µs","ops_per_sec":"62764","source":"THESIS_BRIEF.md","doi":"10.5281/zenodo.20119582","maturity":"measured"},{"id":"K02","name":"receipt_build_p99_us","value":"50.7","unit":"µs","source":"THESIS_BRIEF.md","doi":"10.5281/zenodo.20119582","maturity":"measured"},{"id":"K03","name":"receipt_verify_p50_us","value":"10.4","unit":"µs","ops_per_sec":"74149","source":"THESIS_BRIEF.md","doi":"10.5281/zenodo.20119582","maturity":"measured"},{"id":"K04","name":"lambda9_base_p50_us","value":"3.12","unit":"µs","source":"THESIS_BRIEF.md","doi":"10.5281/zenodo.20119582","maturity":"measured"},{"id":"K05","name":"lambda9_composed_p50_us","value":"3.29","unit":"µs","source":"THESIS_BRIEF.md","doi":"10.5281/zenodo.20119582","maturity":"measured"},{"id":"K06","name":"rho_closure_rate","value":"100%","denominator":"8000/8000 paired calls","source":"THESIS_BRIEF.md","doi":"10.5281/zenodo.20119582","maturity":"measured"},{"id":"K07","name":"platform_v11_http_calls","value":"24800","source":"THESIS_BRIEF.md","doi":"10.5281/zenodo.20119582","maturity":"measured"},{"id":"K08","name":"platform_v11_lambda10_overhead_p50_ms","value":"0.49-0.59","unit":"ms/route","source":"THESIS_BRIEF.md","doi":"10.5281/zenodo.20119582","maturity":"measured"},{"id":"K09","name":"platform_v11_p99_ms","value":"1.27","unit":"ms","source":"THESIS_BRIEF.md","doi":"10.5281/zenodo.20119582","maturity":"measured"},{"id":"K10","name":"replay_root","value":"1ed4d253e876f428c6e182f8ed8a569585442556b339529bbf8ec2522581698b","source":"THESIS_BRIEF.md","doi":"10.5281/zenodo.20119582","maturity":"measured"},{"id":"K11","name":"test_count_production","value":"218/218","source":"THESIS_BRIEF.md","doi":"10.5281/zenodo.20119582","maturity":"measured"},{"id":"K12","name":"test_count_demo","value":"37/37","source":"replit_payload_build","commit":"demo","maturity":"measured"},{"id":"K13","name":"bekenstein_indicator_fire_rate","value":"49.5%","source":"thesis.md §4.5","doi":"10.5281/zenodo.20119582","maturity":"measured"}],"extracted_constants":[{"id":"C0001","name":"receipt_build_p50_us","value":"11.5","raw":"receipt build p50 = 11.5 µs","context":"0).** A production Rust runtime with 218/218 tests passing, receipt build p50 = 11.5 µs (62,764 ops/sec), receipt verify p50 = 10.4 µs (74,149 ops/sec","source_file":"thesis.md","source_line":83,"source_id":"thesis_session"},{"id":"C0003","name":"receipt_verify_p50_us","value":"10.4","raw":"receipt verify p50 = 10.4 µs","context":"ests passing, receipt build p50 = 11.5 µs (62,764 ops/sec), receipt verify p50 = 10.4 µs (74,149 ops/sec), and 100% ρ-closure on 8,000/8,000 paired ca","source_file":"thesis.md","source_line":83,"source_id":"thesis_session"},{"id":"C0008","name":"receipt_build_p99_us","value":"50.7","raw":"p99 = 50.7 µs","context":"→ Receipt` — constructs a receipt envelope; p50 = 11.5 µs, p99 = 50.7 µs, throughput 62,764 ops/sec. - `verify_receipt(receipt) → bool` — verifies byt","source_file":"thesis.md","source_line":269,"source_id":"thesis_session"},{"id":"C0009","name":"ops_per_sec","value":"62764","raw":"62,764 ops/sec","context":"me with 218/218 tests passing, receipt build p50 = 11.5 µs (62,764 ops/sec), receipt verify p50 = 10.4 µs (74,149 ops/sec), and 100% ρ-closure on 8,00","source_file":"thesis.md","source_line":83,"source_id":"thesis_session"},{"id":"C0010","name":"ops_per_sec","value":"74149","raw":"74,149 ops/sec","context":"0 = 11.5 µs (62,764 ops/sec), receipt verify p50 = 10.4 µs (74,149 ops/sec), and 100% ρ-closure on 8,000/8,000 paired calls [9]. The runtime enforces ","source_file":"thesis.md","source_line":83,"source_id":"thesis_session"},{"id":"C0023","name":"ops_per_sec","value":"200000","raw":"200,000 ops/sec","context":"arget for the Merkle-DAG upgrade is **5 µs build p50** at **200,000 ops/sec**. This is a 2.3× improvement in latency and a 3.2× improvement in through","source_file":"thesis.md","source_line":2100,"source_id":"thesis_session"},{"id":"C0027","name":"lambda9_base_p50_us","value":"3.12","raw":"Λ₉ base p50 = 3.12 µs","context":"9]. The runtime enforces a 9-axis conjunctive quality gate (Λ₉ base p50 = 3.12 µs) and a Λ₁₀ platform layer with 0.49–0.59 ms/route overhead validated","source_file":"thesis.md","source_line":83,"source_id":"thesis_session"},{"id":"C0029","name":"tests_passed","value":"218","raw":"218/218 passing","context":"ify-p50 with 100% ρ-closure on 8,000/8,000 paired calls and 218/218 passing tests. We propose `lambda9_mask` as a privacy-preserving extension to SCIT","source_file":"thesis.md","source_line":27,"source_id":"thesis_session"},{"id":"C0031","name":"tests_passed","value":"37","raw":"37/37 tests","context":"nt invocations of the same input. The demo payload confirms 37/37 tests passing in the Replit environment (33 `ouroboros` core + 4 `a11oy` covenant), ","source_file":"thesis.md","source_line":249,"source_id":"thesis_session"},{"id":"C0044","name":"http_calls","value":"24800","raw":"24,800 HTTP calls","context":"orm layer with 0.49–0.59 ms/route overhead validated across 24,800 HTTP calls.  2. **Lean 4 formal axioms and proofs (`lutar-lean`).** A Mathlib-groun","source_file":"thesis.md","source_line":83,"source_id":"thesis_session"},{"id":"C0053","name":"lambda_p50_us","value":"11.5","raw":"p50 = 11.5 µs (62,764 ops/sec), receipt verify p50 = 10.4 µs (74,149 ops/sec), and 100% ρ-closure on 8,000/8,000 paired calls [9]. The runtime enforces a 9-axis conjunctive quality gate (Λ","context":"tion Rust runtime with 218/218 tests passing, receipt build p50 = 11.5 µs (62,764 ops/sec), receipt verify p50 = 10.4 µs (74,149 ops/sec), and 100% ρ-","source_file":"thesis.md","source_line":83,"source_id":"thesis_session"},{"id":"C0054","name":"lambda_p50_us","value":"3.12","raw":"p50 = 3.12 µs) and a Λ","context":"runtime enforces a 9-axis conjunctive quality gate (Λ₉ base p50 = 3.12 µs) and a Λ₁₀ platform layer with 0.49–0.59 ms/route overhead validated across ","source_file":"thesis.md","source_line":83,"source_id":"thesis_session"},{"id":"C0055","name":"receipt_build_p99_us","value":"50.7","raw":"p99 = 50.7 µs","context":"bers - **218/218 tests** - Receipt build p50 = **11.5 µs**, p99 = 50.7 µs (62,764 ops/sec) - Receipt verify p50 = **10.4 µs** (74,149 ops/sec) - Λ₉ ba","source_file":"THESIS_BRIEF.md","source_line":57,"source_id":"thesis_brief"},{"id":"C0056","name":"ops_per_sec","value":"62764","raw":"62,764 ops/sec","context":"8 tests** - Receipt build p50 = **11.5 µs**, p99 = 50.7 µs (62,764 ops/sec) - Receipt verify p50 = **10.4 µs** (74,149 ops/sec) - Λ₉ base p50 = 3.12 µ","source_file":"THESIS_BRIEF.md","source_line":57,"source_id":"thesis_brief"},{"id":"C0057","name":"ops_per_sec","value":"74149","raw":"74,149 ops/sec","context":"0.7 µs (62,764 ops/sec) - Receipt verify p50 = **10.4 µs** (74,149 ops/sec) - Λ₉ base p50 = 3.12 µs / composed p50 = 3.29 µs - 100% ρ-closure on **8,0","source_file":"THESIS_BRIEF.md","source_line":58,"source_id":"thesis_brief"},{"id":"C0058","name":"lambda9_base_p50_us","value":"3.12","raw":"Λ₉ base p50 = 3.12 µs","context":"/sec) - Receipt verify p50 = **10.4 µs** (74,149 ops/sec) - Λ₉ base p50 = 3.12 µs / composed p50 = 3.29 µs - 100% ρ-closure on **8,000/8,000 paired ca","source_file":"THESIS_BRIEF.md","source_line":59,"source_id":"thesis_brief"},{"id":"C0059","name":"tests_passed","value":"218","raw":"218/218 tests","context":"boros v6.3.0 (released 2026-05-13) — production numbers - **218/218 tests** - Receipt build p50 = **11.5 µs**, p99 = 50.7 µs (62,764 ops/sec) - Receip","source_file":"THESIS_BRIEF.md","source_line":56,"source_id":"thesis_brief"},{"id":"C0060","name":"tests_passed","value":"37","raw":"37/37 tests","context":"plit demo payload (verified live 2026-05-15 at 11:22 EDT) - 37/37 tests passing (33 ouroboros core + 4 a11oy covenant) - `bash scripts/doctrine-check.","source_file":"THESIS_BRIEF.md","source_line":68,"source_id":"thesis_brief"},{"id":"C0061","name":"http_calls","value":"24800","raw":"24,800 HTTP calls","context":"ρ-closure on **8,000/8,000 paired calls** - Platform v11: **24,800 HTTP calls validated**, Λ₁₀ overhead 0.49–0.59 ms/route, p99 ≤ 1.27 ms - Apache-2.0","source_file":"THESIS_BRIEF.md","source_line":61,"source_id":"thesis_brief"},{"id":"C0062","name":"receipt_build_p50_us","value":"11.5","raw":"Receipt build p50 = 11.5 µs","context":"e not. | 12–18 months — they have a runtime, not a kernel | Receipt build p50 = 11.5 µs · v11 DOI [`zenodo.20119582`](https://doi.org/10.5281/zenodo.2","source_file":"master_evolution_memo.md","source_line":81,"source_id":"master_memo"},{"id":"C0064","name":"receipt_build_p99_us","value":"50.7","raw":"p99 = 50.7 µs","context":"218 / 218 passing** | | Receipt build | p50 = **11.5 µs** · p99 = 50.7 µs · 62,764 ops/sec | | Receipt verify | p50 = **10.4 µs** · 74,149 ops/sec | |","source_file":"master_evolution_memo.md","source_line":36,"source_id":"master_memo"},{"id":"C0065","name":"ops_per_sec","value":"62764","raw":"62,764 ops/sec","context":"g** | | Receipt build | p50 = **11.5 µs** · p99 = 50.7 µs · 62,764 ops/sec | | Receipt verify | p50 = **10.4 µs** · 74,149 ops/sec | | Λ₉ base | p50 =","source_file":"master_evolution_memo.md","source_line":36,"source_id":"master_memo"},{"id":"C0066","name":"ops_per_sec","value":"74149","raw":"74,149 ops/sec","context":"s · 62,764 ops/sec | | Receipt verify | p50 = **10.4 µs** · 74,149 ops/sec | | Λ₉ base | p50 = 3.12 µs | | Λ₉ composed | p50 = **3.29 µs** | | ρ-closu","source_file":"master_evolution_memo.md","source_line":37,"source_id":"master_memo"},{"id":"C0067","name":"tests_passed","value":"37","raw":"37/37 tests","context":"ic-facing Replit demo (`replit_a11oy_demo`) currently shows 37/37 tests passing. The upstream runtime is **218/218**. Every Series A diligence visitor","source_file":"master_evolution_memo.md","source_line":141,"source_id":"master_memo"},{"id":"C0068","name":"tests_passed","value":"218","raw":"218/218 tests","context":"astructure.  **Success metric:** the Replit demo URL shows \"218/218 tests · v6.3.0 · OpenSSF 8.2\" with the same badge as the canonical repo, refreshed","source_file":"master_evolution_memo.md","source_line":152,"source_id":"master_memo"},{"id":"C0070","name":"receipt_build_p50_us","value":"11.5","raw":"Receipt build p50=11.5 µs","context":"rg/doc/draft-morrow-sogomonian-exec-outcome-attest/00/)). | Receipt build p50=11.5 µs, 218/218 tests, v11 DOI: [10.5281/zenodo.20119582](https://doi.o","source_file":"pm_memo.md","source_line":54,"source_id":"pm_memo"},{"id":"C0072","name":"ops_per_sec","value":"62764","raw":"62,764 ops/sec","context":"Claim:** Receipt build p50 = 11.5 µs, verify p50 = 10.4 µs, 62,764 ops/sec, 218/218 runtime tests, ρ-closure 8,000/8,000, byte-identical replay root `","source_file":"pm_memo.md","source_line":81,"source_id":"pm_memo"},{"id":"C0073","name":"tests_passed","value":"218","raw":"218/218 tests","context":"ian-exec-outcome-attest/00/)). | Receipt build p50=11.5 µs, 218/218 tests, v11 DOI: [10.5281/zenodo.20119582](https://doi.org/10.5281/zenodo.20119582)","source_file":"pm_memo.md","source_line":54,"source_id":"pm_memo"},{"id":"C0076","name":"tests_passed","value":"37","raw":"37/37 tests","context":"arity + Public Scorecard  **Thesis:** The Replit demo shows 37/37 tests (ouroboros 33 + a11oy 4). The live runtime is 218/218. This delta undersells t","source_file":"pm_memo.md","source_line":135,"source_id":"pm_memo"},{"id":"C0077","name":"http_calls","value":"24800","raw":"24,800 HTTP calls","context":"ships a Λ₉-gated resource. | Ouroboros v6.3.0 platform v11: 24,800 HTTP calls, Λ₁₀ overhead 0.49–0.59 ms/route | | **Mastra** ([mastra.ai](https://mas","source_file":"pm_memo.md","source_line":57,"source_id":"pm_memo"},{"id":"C0078","name":"receipt_build_p50_us","value":"11.5","raw":"Receipt build p50 = 11.5 µs","context":"-witness guarantee baked into `ouroboros`'s runtime kernel. Receipt build p50 = 11.5 µs; verify p50 = 10.4 µs; 100% ρ-closure on 8,000/8,000 paired ca","source_file":"cto_memo.md","source_line":78,"source_id":"cto_memo"},{"id":"C0079","name":"ops_per_sec","value":"62764","raw":"62,764 ops/sec","context":"in · p50 = 11.5 µs build / 10.4 µs verify · 218/218 tests · 62,764 ops/sec | | `a11oy` | Covenant policy + approval queue | **HEART** (consent + pulse","source_file":"cto_memo.md","source_line":18,"source_id":"cto_memo"},{"id":"C0080","name":"tests_passed","value":"218","raw":"218/218 tests","context":"ss · receipt chain · p50 = 11.5 µs build / 10.4 µs verify · 218/218 tests · 62,764 ops/sec | | `a11oy` | Covenant policy + approval queue | **HEART** ","source_file":"cto_memo.md","source_line":18,"source_id":"cto_memo"},{"id":"C0081","name":"ops_per_sec","value":"62764","raw":"62,764 ops/sec","context":"218 / 218 passing | 100% | | Receipt build p50 | 11.5 µs | 62,764 ops/sec | | Receipt build p99 | 50.7 µs | — | | Receipt verify p50 | 10.4 µs | 74,14","source_file":"runtime_memo.md","source_line":20,"source_id":"runtime_memo"},{"id":"C0082","name":"ops_per_sec","value":"74149","raw":"74,149 ops/sec","context":"build p99 | 50.7 µs | — | | Receipt verify p50 | 10.4 µs | 74,149 ops/sec | | Λ₉ base p50 | 3.12 µs | — | | Λ₉ composed p50 | 3.29 µs | — | | ρ-closur","source_file":"runtime_memo.md","source_line":22,"source_id":"runtime_memo"},{"id":"C0083","name":"tests_passed","value":"218","raw":"218/218 tests","context":"ary (5 lines)  The ouroboros v6.3.0 runtime is confirmed at 218/218 tests, receipt build p50 11.5 µs, Λ₉ composed p50 3.29 µs, and 100% ρ-closure — al","source_file":"runtime_memo.md","source_line":404,"source_id":"runtime_memo"},{"id":"C0084","name":"http_calls","value":"11","raw":"11 HTTP calls","context":"9 µs | — | | ρ-closure | 8,000 / 8,000 | 100% | | Platform v11 HTTP calls | 24,800 | — | | Λ overhead p50 per route | 0.49–0.59 ms | — | | Λ overhead ","source_file":"runtime_memo.md","source_line":26,"source_id":"runtime_memo"},{"id":"C0085","name":"ops_per_sec","value":"74149","raw":"74,149 ops/sec","context":"pt verify p50 | **10.4 µs** | | Receipt verify throughput | 74,149 ops/sec | | Λ₉ base p50 | 3.12 µs | | Λ₉ composed p50 | 3.29 µs | | ρ-closure | 100","source_file":"data_memo.md","source_line":419,"source_id":"data_memo"}],"dois":[{"doi":"10.5281/zenodo.19944926","url":"https://doi.org/10.5281/zenodo.19944926","source_file":"thesis.md","source_line":18,"source_id":"thesis_session"},{"doi":"10.5281/zenodo.20119582","url":"https://doi.org/10.5281/zenodo.20119582","source_file":"thesis.md","source_line":19,"source_id":"thesis_session"},{"doi":"10.5281/zenodo.19867281","url":"https://doi.org/10.5281/zenodo.19867281","source_file":"thesis.md","source_line":1740,"source_id":"thesis_session"},{"doi":"10.5281/zenodo.19934129","url":"https://doi.org/10.5281/zenodo.19934129","source_file":"thesis.md","source_line":1741,"source_id":"thesis_session"},{"doi":"10.5281/zenodo.19983066","url":"https://doi.org/10.5281/zenodo.19983066","source_file":"thesis.md","source_line":1743,"source_id":"thesis_session"},{"doi":"10.5281/zenodo.20020841","url":"https://doi.org/10.5281/zenodo.20020841","source_file":"thesis.md","source_line":1744,"source_id":"thesis_session"},{"doi":"10.5281/zenodo.20020845","url":"https://doi.org/10.5281/zenodo.20020845","source_file":"thesis.md","source_line":1745,"source_id":"thesis_session"},{"doi":"10.5281/zenodo.20020846","url":"https://doi.org/10.5281/zenodo.20020846","source_file":"thesis.md","source_line":1746,"source_id":"thesis_session"},{"doi":"10.5281/zenodo.20020848","url":"https://doi.org/10.5281/zenodo.20020848","source_file":"thesis.md","source_line":1747,"source_id":"thesis_session"},{"doi":"10.5281/zenodo.20020849","url":"https://doi.org/10.5281/zenodo.20020849","source_file":"thesis.md","source_line":1748,"source_id":"thesis_session"},{"doi":"10.5281/zenodo.20053148","url":"https://doi.org/10.5281/zenodo.20053148","source_file":"thesis.md","source_line":1749,"source_id":"thesis_session"},{"doi":"10.5281/zenodo.20053163","url":"https://doi.org/10.5281/zenodo.20053163","source_file":"thesis.md","source_line":1750,"source_id":"thesis_session"},{"doi":"10.5281/zenodo.20162352","url":"https://doi.org/10.5281/zenodo.20162352","source_file":"thesis.md","source_line":1752,"source_id":"thesis_session"}],"doctrine_clauses":[{"id":"DC1","clause":"Byline must be 'Lutar, Stephen P.' — never 'Jr.' or 'Stephen Paul'","source":"THESIS_BRIEF.md"},{"id":"DC2","clause":"8 forbidden patterns: see doctrine.json (FP-1..FP-8)","source":"PM_LEAD_CHARTER_V2.md"},{"id":"DC3","clause":"License allow-list: Apache-2.0, MIT, BSD-3-Clause, CC-BY-4.0","source":"THESIS_BRIEF.md"},{"id":"DC4","clause":"ORCID: 0009-0001-0110-4173","source":"THESIS_BRIEF.md"},{"id":"DC5","clause":"9-axis Λ >= 0.90 conjunctive AND; moralGrounding + measurabilityHonesty >= 0.95","source":"THESIS_BRIEF.md"},{"id":"DC6","clause":"Public-only ingestion: no private data, no proprietary code","source":"THESIS_BRIEF.md"},{"id":"DC7","clause":"5x byte-identical replay (deterministic)","source":"THESIS_BRIEF.md"},{"id":"DC8","clause":"No hallucinations; every empirical claim cites a verifiable artifact","source":"THESIS_BRIEF.md"}],"source_files":["thesis.md","THESIS_BRIEF.md","master_evolution_memo.md","pm_memo.md","cto_memo.md","runtime_memo.md","governance_memo.md","data_memo.md","anatomy_memo.md"],"zenodo_corpus":["10.5281/zenodo.19867281","10.5281/zenodo.19934129","10.5281/zenodo.19944926","10.5281/zenodo.19983066","10.5281/zenodo.20020841","10.5281/zenodo.20020846","10.5281/zenodo.20020845","10.5281/zenodo.20020848","10.5281/zenodo.20020849","10.5281/zenodo.20053148","10.5281/zenodo.20053163","10.5281/zenodo.20119582","10.5281/zenodo.20162352"],"proof_summary":{"locked_proven":5,"locked_ids":["F1","F11","F12","F18","F19"],"experimental_sorry_free":21,"axiom_gated":3,"axiom_gated_detail":{"f13_tamper_evident":"hash_collision_resistant","f14_sigenv_verifiable":"ecdsa_unforgeable","f15_inclusion_binding":"h2_collision_resistant"},"conjecture":["F23"],"note":"Locked kernel proven=5; experimental scope Lutar/Puriq/Formulas has 21 sorry-free (excluded from locked count); F23 = Conjecture 1, NOT a theorem.","lean_repo":"szl-holdings/lutar-lean","lean_files":["Lutar/Puriq/Formulas/PuriqFormulaLean.lean","Lutar/Puriq/Formulas/F23_Uniqueness.lean"],"verification":"bare `lean` 4.13.0, 0 errors, 1 sorry (F23 only); #print axioms shows no sorryAx in any proved theorem.","source_report":"team/PROOFS_WAVE2_REPORT.md","wave3":{"campaign":"prove-wave-3 (C1-C20 research candidates)","source_report":"team/PROVE_WAVE3_REPORT.md","lean_repo":"szl-holdings/lutar-lean","commit_proofs":"775093f0f8ef7f530272c38d513c28fdaec3366b","commit_root_wiring":"02e44c30657c9986475ff7373113728f4ba38f67","lean_files":["Lutar/Wave3/Consensus.lean","Lutar/Wave3/MerkleKraft.lean","Lutar/Wave3/InfoEstim.lean","Lutar/Wave3/Tier1Mathlib.lean (CI-pending, not wired into lake build)"],"verification":"Mathlib-free modules bare-`lean` 4.13.0 verified sorry-free (0 errors); #print axioms ledger shows no sorryAx. Tier1Mathlib (C1/C2/C6) is Mathlib-dependent and CI-pending, NOT compiled in sandbox.","new_proven_sorry_free":19,"new_proven_ids":["C8","C9","C10","C11","C12","C17","C20"],"new_axiom_gated":4,"new_axiom_gated_detail":{"c13_md_step_cr":"compression_collision_resistant","c13a_md_append_cr":"compression_collision_resistant","c14_merkle_binding":"node_collision_resistant, leaf_collision_resistant, domain_separation","c14b_no_second_preimage":"domain_separation (structural tag only, no hardness)"},"ci_pending":["C1","C2","C6"],"ci_pending_detail":"C1 tsirelson_inequality, C2 CHSH_inequality_of_comm, C6 ConvexOn.map_sum_le re-exports; Mathlib-dependent, awaiting green lake build.","maturity":{"C1":"ci-pending","C2":"ci-pending","C3":"mathlib-available-not-instantiated","C4":"mathlib-available-not-instantiated","C5":"mathlib-available-not-instantiated","C6":"ci-pending","C7":"axiom-gated (A6_bisymmetric); Lambda still Conjecture 1","C8":"proven","C9":"proven (Mathlib-free fragment; full L>=H is Mathlib target)","C10":"proven","C11":"proven","C12":"proven (bivalence core; full FLP not claimed)","C13":"axiom-gated","C14":"axiom-gated","C15":"lean-exists-not-ported","C16":"not-attempted","C17":"proven (Mathlib-free scalar core; full matrix-PSD is Mathlib target)","C18":"lean-exists-not-ported","C19":"not-attempted","C20":"proven (Mathlib-free order-preservation core; tight 1/2-Lipschitz is Mathlib target)"},"lambda_status":"F23 = Conjecture 1 (UNCHANGED). C7 is conditional only, via the DECLARED axiom A6_bisymmetric in F23_Uniqueness.lean; unconditional uniqueness is FALSE under A1-A5 (maxAgg_ne_Lambda).","locked_kernel":"749/14/163 @ c7c0ba17 (Doctrine v11) UNCHANGED; wave3 is experimental and counter-excluded from the locked count.","headline":"+19 sorry-free (Lean-core axioms only, bare-lean verified), +4 axiom-gated (declared idealizations), 3 Mathlib re-exports CI-pending, Lambda still Conjecture 1."},"wave4":{"campaign":"prove-wave-4 (conditional Lambda uniqueness on the WEAKER block-consistency axiom)","source_report":"team/PROVE_WAVE4_REPORT.md","candidate_research":"team/RESEARCH_WAVE4/CANDIDATE_FORMULAS_V4.md","lean_repo":"szl-holdings/lutar-lean","commit_final":"043c3df4bcbe55c60f1ce2d5c59b91284a7cc1d4","commit_ci_green_lambda":"52d9bf542bcb1adb8a0a5a5de694f2ca96bf9b68","lean_files":["Lutar/Wave4/LambdaBlockConsistency.lean (Mathlib-dependent, CI-green: lake build + kernel check success @ 043c3df)","Lutar/Wave4/LambdaBisymmetryWitness.lean (bare-`lean` 4.13.0 verified sorry-free, ZERO axioms; also CI-green)","Lutar/Wave3/Tier1Mathlib.lean (CI-PENDING, NOT wired into the compiled root)"],"ci_status":"build + lake build + numbers + check/doctrine all GREEN @ 043c3df; only doi-title-gate fails (PRE-EXISTING live-network README DOI check, unrelated to wave4).","verification":"LambdaBlockConsistency kernel-checked by lutar-lean CI lake build (green). LambdaBisymmetryWitness bare-`lean` verified: all 6 theorems 'do not depend on any axioms'. Every theorem carries #print axioms.","new_proven_ci_green":{"lambda_unique_under_block":"CLOSED, conditional on declared axiom A6'_block_consistent; #print axioms = [A6'_block_consistent, propext, Quot.sound, Classical.choice]","lambda_factors":"CLOSED, AXIOM-FREE (Mathlib core only): Lambda factors with exponents 1/k, so A6' is non-vacuous","unconditional_lambda_is_false":"CLOSED (= maxAgg_ne_Lambda): unconditional Lambda uniqueness is FALSE under A1-A5"},"witness_theorems_zero_axiom":["Fmax_not_strict","Fmin_not_strict","geo_separates_where_max_collapses","geo_bisym_product_eq","geo_fourth_root_consistent","geo_inner_products_consistent"],"lambda_axiom_set":"{A1,A2,A3,A4,A5} + A6'_block_consistent (single DECLARED, disclosed, NON-core axiom).","lambda_weakest_axiom":"Cleanest published: Aczel-Saaty 1983 (doi:10.1016/0022-2496(83)90028-7) = reciprocity + positive homogeneity (A2 already assumed). Weakest governance-natural & formalized: Csato 2018 block-consistency / aggregation-invariance (doi:10.1007/s10726-018-9589-3, arXiv:1706.07256), WEAKER than the prior A6_bisymmetric.","lambda_status":"F23 = Conjecture 1 (UNCHANGED, unconditional). Conditional uniqueness now CI-green on the WEAKER A6'_block_consistent (lambda_unique_under_block), superseding the stronger A6_bisymmetric route. Unconditional uniqueness FALSE (maxAgg_ne_Lambda). NEVER conflated.","ci_pending":["C1","C2","C6"],"ci_pending_detail":"C1 tsirelson_inequality / C2 CHSH_inequality_of_comm / C6 ConvexOn.map_sum_le re-exports. Signatures verified VERBATIM vs pinned Mathlib d731765, but wiring Tier1Mathlib into the compiled root reproducibly red-lights lake build (bisected: a4299fb/52d9bf5 un-wired = green). Exact error not retrievable (CI log download proxy-blocked). File stays in-tree, NOT imported; NOT claimed proven.","locked_kernel":"749/14/163 @ c7c0ba17 UNCHANGED","locked_proven":5,"canonical_numbers":{"declarations":1182,"axioms_raw":20,"axioms_unique":19,"new_axiom":"A6'_block_consistent (declared, disclosed, NON-core, NOT in locked kernel)","sorries_raw":308,"sorries_noncomment":256,"drift_gate":"PASS"},"citations":["Aczel 1948","Aczel-Saaty 1983 doi:10.1016/0022-2496(83)90028-7","Csato 2018 doi:10.1007/s10726-018-9589-3 arXiv:1706.07256","Kolmogorov 1930","Maksa-Munnich-Mokken","Burai-Kiss-Szokol 2021"]},"wave5":{"campaign":"prove-wave-5: un-block C1/C2/C6 Mathlib re-exports (CI-GREEN) + new substrate re-exports (AM-GM/Cauchy-Schwarz) + Mathlib-free discrete substrate guarantees (bare-lean verified)","source_report":"team/PROVE_WAVE5_REPORT.md","lean_repo":"szl-holdings/lutar-lean","branch":"prove-wave5/c1c2c6-rewire-plus-amgm-cs","pull_request":"https://github.com/szl-holdings/lutar-lean/pull/186","commit_ci_green":"0a552a90dd7f3b8b668ae761bf6e39eca17c62f1","ci_run_ids":{"lean_kernel_check":"27053443102 (success)","lake_build_gate_numbers":"27053443099 (success)","doctrine":"27053443200 (success)","dco":"27053443096 (success)"},"ci_status":"build (Lean kernel check) + lake build + numbers + check/doctrine + DCO all GREEN @ 0a552a90 (and @ 099d6caa). Only doi-title-gate + PR-title-lint fail (PRE-EXISTING / cosmetic, unrelated to proofs).","headline":"C1 Tsirelson 2sqrt2 / C2 CHSH<=2 / C6 Jensen are now CI-GREEN (wave-4 had them CI-PENDING). Root cause fixed: dropped the non-load-bearing c1a_tsirelson_constant numeric remark and its two extra SpecialFunctions imports, minimizing Tier1Mathlib's build closure to exactly the two modules that define the instantiated theorems.","ci_green_mathlib_dependent":{"Wave3.Tier1.c1_lutar_omega_tsirelson_ceiling":"C1 Tsirelson 2sqrt2 ceiling (tsirelson_inequality) — PROVEN, CI-green. EPR-Bell governance diagnostic (entangled-agent ceiling).","Wave3.Tier1.c2_lutar_omega_classical_ceiling":"C2 CHSH classical ceiling <=2 (CHSH_inequality_of_comm) — PROVEN, CI-green. Local/independent-prior agent ceiling.","Wave3.Tier1.c6_jensen_forecaster":"C6 finite Jensen (ConvexOn.map_sum_le) — PROVEN, CI-green. Active-inference ELBO-direction conservative forecaster.","Wave5.MathlibCore.w5_1_lambda_le_arith_mean":"W5-1 weighted AM-GM (Real.geom_mean_le_arith_mean_weighted) — PROVEN, CI-green. Lambda (geometric-mean aggregator) <= arithmetic mean: no-inflation guarantee.","Wave5.MathlibCore.w5_1b_lambda2_le_arith_mean":"W5-1b two-point weighted AM-GM — PROVEN, CI-green. Pairwise consensus diagnostic.","Wave5.MathlibCore.w5_2_trust_inner_le_norm":"W5-2 Cauchy-Schwarz (real_inner_le_norm) — PROVEN, CI-green. Trust-vector similarity bound (cosine in [-1,1])."},"proven_mathlib_free_bare_lean":{"Wave5.DiscreteSubstrate.w5_3a_miscover_le_total":"miscoverage<=sample size. axioms=[propext]. killinchu conformal coverage.","Wave5.DiscreteSubstrate.w5_3b_cover_miscover_partition":"covered+miscovered=total. axioms=[propext, Quot.sound]. coverage=1-miscoverage conservation.","Wave5.DiscreteSubstrate.w5_3c_threshold_count_mono":"stricter threshold selects fewer. axioms=[propext, Quot.sound]. a11oy threshold monotonicity.","Wave5.DiscreteSubstrate.w5_4_collision_of_image_dup":"image-duplicate => hash collision (pigeonhole). axioms=[propext, Classical.choice, Quot.sound]. UDS forgery-detection.","Wave5.DiscreteSubstrate.w5_5_no_early_stop_deflation":"monotone optional-stopping anti-deflation. ZERO axioms. UDS receipt-stream anti-gaming."},"axiom_disclosure":"Mathlib-dependent re-exports use the standard Mathlib trio [propext, Classical.choice, Quot.sound] (NO sorryAx, NO declared Lutar axioms); their #print axioms are emitted in the CI build log (blob log download proxy-blocked here, but the build is green and they are pure term-mode instantiations of axiom-clean Mathlib theorems). Mathlib-free theorems' #print axioms pasted verbatim in PROVE_WAVE5_REPORT.md section 3 (bare lean 4.13.0, exit 0).","not_available_at_pinned_mathlib":"C3 Hoeffding / C4 Azuma (Mathlib.Probability.Moments.SubGaussian) and C5 KL>=0 (Mathlib.InformationTheory.KullbackLeibler.Basic) modules DO NOT EXIST at the pinned rev d7317655 (v4.13.0) — verified HTTP 404. They cannot be re-exported on this toolchain; deferred to a future Mathlib bump. Honestly NOT claimed.","lambda_status":"Lambda (F23) STAYS Conjecture 1 unconditionally. W5-1 AM-GM is a building block Lambda relies on; it does NOT prove uniqueness. Unconditional uniqueness remains FALSE (wave-4 counterexample in-tree).","locked_kernel":"749/14/163 @ c7c0ba17 UNCHANGED. locked_proven=5 UNCHANGED. All wave-5 work is experimental scope (counter-excluded).","canonical_numbers":{"declarations":1189,"axioms_raw":20,"axioms_unique":19,"sorries_raw":308,"sorries_noncomment":256,"delta_decls_from_wave4":"+5 net (1184->1189; -1 c1a, +3 MathlibCore, +5 DiscreteSubstrate vs wave4 baseline 1182 -> 1189)"},"citations":["Tsirelson (1980) doi:10.1007/BF00417500","CHSH (1969) doi:10.1103/PhysRevLett.23.880","Jensen (1906)","Hardy-Littlewood-Polya, Inequalities (1934) [AM-GM]","Cauchy (1821); Schwarz (1888)","Vovk-Gammerman-Shafer (2005); Lei et al. (2018) JASA 113:1094 [conformal]","Dirichlet (1834) [pigeonhole]","Doob (1953) Stochastic Processes [optional stopping]"]},"experimental_sorry_free_note":"wave5 adds 11 kernel-verified experimental theorems (6 Mathlib-dependent CI-green: C1/C2/C6 + W5-1/W5-1b/W5-2; 5 Mathlib-free bare-lean: W5-3a/b/c, W5-4, W5-5). Prior experimental_sorry_free baseline was 21 (wave-2 F-pack ceiling).","wave5_proven_count":{"mathlib_dependent_ci_green":6,"mathlib_free_bare_lean":5,"total_new":11}},"puriq_formulas":[{"id":"F1","name":"Replay-Hash Determinism","statement":"Deterministic step-fold replay: equal logs replay to equal final state; folded state equals last of the explicit replay trace.","maturity":"proven","lean_ref":"f1_replay_fold_deterministic","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean","locked_kernel":true},{"id":"F2","name":"Scheduler Liveness","statement":"Fair round-robin scheduler: every ready organ eventually ticks (strictly-decreasing Nat ranking measure reaches 0).","maturity":"proven","lean_ref":"f2_scheduler_liveness","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean"},{"id":"F3","name":"Organ Boot-Gate Soundness","statement":"If the boot gate permits an organ, its genome is valid (decidable implication).","maturity":"proven","lean_ref":"f3_genome_gate_sound","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean"},{"id":"F4","name":"Receipt-Chain Acyclicity","statement":"Appending the new largest-index node preserves DAG acyclicity (backward-edge invariant).","maturity":"proven","lean_ref":"f4_rcptchain_dag_acyclic","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean"},{"id":"F5","name":"Unay Receipt Recall","statement":"Insert-then-lookup on the same receipt key returns the inserted value (exact-key recall correctness).","maturity":"proven","lean_ref":"f5_unay_recall_correct","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean"},{"id":"F6","name":"LMDB Durability","statement":"Commit-then-restart-then-read returns the committed value; uncommitted writes are lost on crash (WAL model).","maturity":"proven","lean_ref":"f6_lmdb_durability","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean"},{"id":"F7","name":"Chaski FIFO Ordering","statement":"Enqueue-batch-then-drain yields send order; head is the oldest message (true FIFO, no tautology).","maturity":"proven","lean_ref":"f7_chaski_fifo","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean"},{"id":"F8","name":"Wallpa OSS-Only Safety","statement":"Governed-voice admission gate admits only OSS sources; no humanClone or synthetic config is ever admitted.","maturity":"proven","lean_ref":"f8_wallpa_oss_only","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean"},{"id":"F9","name":"Wasi-Rikuq Non-Interference","statement":"Advisory non-interference (Goguen-Meseguer 1982): the low view is unchanged by high inputs.","maturity":"proven","lean_ref":"f9_wasi_rikuq_noninterference","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean"},{"id":"F10","name":"Hatun MCP Idempotency","statement":"MCP request normalizer is idempotent: normalizing twice equals normalizing once.","maturity":"proven","lean_ref":"f10_hatun_mcp_idempotent","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean"},{"id":"F11","name":"Ayni Reciprocity Conservation","statement":"Event-sourcing replay invariant: balance reciprocity is conserved; tit-for-tat parity (Axelrod-Hamilton).","maturity":"proven","lean_ref":"f11_ayni_reciprocity_conservation","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean","locked_kernel":true},{"id":"F12","name":"Kuramoto Phase-Coupling Boundedness","statement":"Discrete additive coupling is bounded and superposes over an organ set. CAVEAT: additive fragment only, NOT nonlinear Kuramoto synchronisation.","maturity":"proven","lean_ref":"f12_kuramoto_superposition","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean","locked_kernel":true},{"id":"F13","name":"Wayra Hash-Chain Verification","statement":"Hash-chain verification is sound by induction: a verified chain has every link consistent.","maturity":"proven","lean_ref":"f13_wayra_chain_verified","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean","declared_axiom":"hash_collision_resistant (tamper-evidence f13_tamper_evident)"},{"id":"F14","name":"Signature Verifiable Attribution","statement":"A signature-envelope signature that verifies attributes the message to the key. AXIOM-GATED on declared `ecdsa_unforgeable`.","maturity":"axiom-gated","lean_ref":"f14_sigenv_verifiable","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean","declared_axiom":"ecdsa_unforgeable"},{"id":"F15","name":"Rekor Merkle Inclusion","statement":"Merkle inclusion checker is sound (structural). Binding form (equal roots => equal leaves) is AXIOM-GATED on declared `h2_collision_resistant`.","maturity":"proven","lean_ref":"f15_rekor_inclusion","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean","declared_axiom":"h2_collision_resistant (binding form f15_inclusion_binding)"},{"id":"F16","name":"Safety-Gate Coverage Completeness","statement":"Immune cross-cut completeness: 8 gates cover all 8 enumerated threats; gate set is exhaustive.","maturity":"proven","lean_ref":"f16_safegate_immune_complete","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean"},{"id":"F17","name":"Three-Vertical Isolation","statement":"The three verticals are pairwise disjoint (isolation by construction).","maturity":"proven","lean_ref":"f17_three_vertical_isolation","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean"},{"id":"F18","name":"Reed-Solomon RS(10,6) Recovery","statement":"RS(10,6) parity arithmetic: data is recoverable iff at least 6 of 10 shards survive (tolerates 4 erasures).","maturity":"proven","lean_ref":"f18_reed_solomon_parity_count","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean","locked_kernel":true},{"id":"F19","name":"Bekenstein Entropy Budget","statement":"Entropy budget is additive and monotone over a region partition; each region <= total. CAVEAT: additive scaffolding only, NOT the full Bekenstein bound S <= 2*pi*k*R*E/(hbar*c).","maturity":"proven","lean_ref":"f19_budget_total_cons","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean","locked_kernel":true},{"id":"F20","name":"Mobile Input Equivalence","statement":"Touch and pointer inputs are equivalent under the normalization map (decidable and sound).","maturity":"proven","lean_ref":"f20_mobile_input_equiv","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean"},{"id":"F21","name":"Genome Validator Totality","statement":"The genome validator is total over Fin 16: every organ validates.","maturity":"proven","lean_ref":"f21_all_organs_valid","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean"},{"id":"F22","name":"Receipt Emit Monotonicity","statement":"Emit appends to the sequence log with strictly increasing sequence numbers (monotone emit).","maturity":"proven","lean_ref":"f22_rcptchain_emit_monotone","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean"},{"id":"F23","name":"Lambda-Aggregator Uniqueness","statement":"CONJECTURE 1 (NOT a theorem). Unconditional uniqueness is FALSE under A1-A5 (maxAgg counterexample). Conditional `lambda_unique_of_factors` IS proved; unconditional uniqueness closes only under declared axiom A6_bisymmetric.","maturity":"conjectured","lean_ref":"f23_lambda_aggregator_sound","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/F23_Uniqueness.lean","declared_axiom":"A6_bisymmetric (optional, only for conditional lambda_unique_under_A6)"}],"vertical_policies":[{"policy_id":"academic","policy_name":"Academic / Research Integrity","version":"0.3.0","regulations":["NIH NOT-OD-23-149","NSF PAPPG Chapter II.E","ORI Standards","COPE 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+<script>window.__KB__={"version":"5.1.0","byline":"Lutar, Stephen P.","orcid":"0009-0001-0110-4173","email":"stephen@szlholdings.com","org":"SZL Holdings","generated_at":"2026-06-06T06:00:00Z","axioms":[{"id":"A1","name":"soundnessAxiom","statement":"For any receipt r, if gate_pass(r) then lambda(r) >= 0.90 conjunctively","source_file":"thesis.md","source_section":"§4.1","maturity":"proven","citation":"https://doi.org/10.5281/zenodo.20119582"},{"id":"A2","name":"moralGroundingFloor","statement":"moralGrounding axis floor = 0.95 (higher than default 0.90)","source_file":"thesis.md","source_section":"§4.1","maturity":"defined","citation":"https://doi.org/10.5281/zenodo.20119582"},{"id":"A3","name":"measurabilityHonestyFloor","statement":"measurabilityHonesty axis floor = 0.95","source_file":"thesis.md","source_section":"§4.1","maturity":"defined","citation":"https://doi.org/10.5281/zenodo.20119582"},{"id":"A4","name":"dualWitnessDisjointness","statement":"For rho-closure: witness_1_id != witness_2_id (enforced by registry at write time)","source_file":"thesis.md","source_section":"§4.3","maturity":"proven","citation":"https://doi.org/10.5281/zenodo.20119582"},{"id":"A5","name":"deterministicReplay","statement":"For canonical JSON + pinned PRNG + frozen registry, 5x replay yields byte-identical roots","source_file":"thesis.md","source_section":"§4.6","maturity":"measured","citation":"https://doi.org/10.5281/zenodo.20119582"},{"id":"A6","name":"hashChainIntegrity","statement":"Every spine entry hash-chain invariant: entry.chain = SHA256(prev_entry)","source_file":"thesis.md","source_section":"§3.4","maturity":"defined","citation":"https://doi.org/10.5281/zenodo.20119582"},{"id":"A7","name":"bekensteinBound","statement":"Receipt chain entropy H(R_n) bounded by information-theoretic limit from registry area","source_file":"thesis.md","source_section":"§4.5","maturity":"conjectured","citation":"https://doi.org/10.5281/zenodo.19944926"},{"id":"A8","name":"ingestDiscipline","statement":"Every ingest requires: source_url + content_hash + license (allow-list) + ORCID","source_file":"thesis.md","source_section":"§7","maturity":"defined","citation":"https://doi.org/10.5281/zenodo.20119582"},{"id":"A9","name":"doctrineCompleteness","statement":"doctrine.json v1.0.0 enumerates all 8 forbidden patterns; SHA-anchored","source_file":"szl-trust/doctrine.json","source_section":"§8","maturity":"defined","citation":"https://github.com/szl-holdings/szl-trust"}],"theorems":[{"id":"TH_L1","name":"Λ_uniqueness","statement":"Conjecture 1: the Lutar Invariant Λ_k (weighted geometric mean with Egyptian unit-fraction weights) is the unique aggregator satisfying axioms A1-A5. NOT a theorem: unconditional uniqueness is FALSE under A1-A5 (machine-checked counterexample maxAgg_ne_Lambda; max-aggregator satisfies A1-A5 yet differs from Λ at (4,1)). The conditional theorem lambda_unique_of_factors (uniqueness GIVEN factorization Φ x = ∏ x_i^α_i) IS fully proved; unconditional uniqueness closes only under a declared bisymmetry axiom A6 (Kolmogorov-Nagumo-Aczel).","source_file":"lutar-lean/Lutar/Round13/Lambda_Uniqueness.lean","maturity":"conjectured","citation":"https://doi.org/10.5281/zenodo.20053148"},{"id":"TH_L2","name":"Λ_min_max_bounds","statement":"Λ_k lies in [0,1] with min=0 iff any axis=0 and max=1 iff all axes=1","source_file":"lutar-lean/Lutar/Bound.lean","maturity":"proven","citation":"https://doi.org/10.5281/zenodo.20053148"},{"id":"TH_L3","name":"bekenstein_soundness","statement":"Bekenstein indicator fires at 49.5% under uniform seed (measured); formal proof pending in lutar-lean","source_file":"lutar-lean (pending PR #12)","maturity":"measured/conjectured","citation":"https://github.com/szl-holdings/lutar-lean"},{"id":"TH_L4","name":"rho_closure_production","statement":"100% rho-closure on 8,000/8,000 paired calls under v11 platform","source_file":"ouroboros v6.3.0 release","maturity":"measured","citation":"https://doi.org/10.5281/zenodo.20119582"}],"formulas":[{"id":"F0001","source_file":"thesis.md","source_line":27,"latex":"\\mathcal{S} = \\langle R, A, E, \\Lambda, \\rho, W \\rangle","context":"ith a doctrine-locked runtime** as a category-defining primitive for verifiable agency. We define the system as a tuple \\( \\mathcal{S} = \\langle R, A, E, \\Lambda, \\rho, W \\rangle \\) over an eight-regi","source_id":"thesis_session","maturity":"defined"},{"id":"F0002","source_file":"thesis.md","source_line":229,"latex":"\\mathtt{szl\\text{-}trust}","context":"d system.  - \\(A\\) — the set of **named actors**. Every actor in \\(A\\) carries a stable identity resolvable to a key in \\(\\mathtt{szl\\text{-}trust}\\). No edge in \\(E\\) may originate from or terminate ","source_id":"thesis_session","maturity":"defined"},{"id":"F0003","source_file":"thesis.md","source_line":231,"latex":"e \\in E","context":"and resolvable — unidentified actors are structurally excluded.  - \\(E\\) — the set of **receipt-bound edges**. An edge \\(e \\in E\\) is a tuple \\((a_{\\text{src}},\\; r_{\\text{src}},\\; r_{\\text{dst}},\\; \\","source_id":"thesis_session","maturity":"defined"},{"id":"F0004","source_file":"thesis.md","source_line":231,"latex":"(a_{\\text{src}},\\; r_{\\text{src}},\\; r_{\\text{dst}},\\; \\varepsilon)","context":"ntified actors are structurally excluded.  - \\(E\\) — the set of **receipt-bound edges**. An edge \\(e \\in E\\) is a tuple \\((a_{\\text{src}},\\; r_{\\text{src}},\\; r_{\\text{dst}},\\; \\varepsilon)\\) where \\(","source_id":"thesis_session","maturity":"defined"},{"id":"F0005","source_file":"thesis.md","source_line":231,"latex":"a_{\\text{src}} \\in A","context":"d edges**. An edge \\(e \\in E\\) is a tuple \\((a_{\\text{src}},\\; r_{\\text{src}},\\; r_{\\text{dst}},\\; \\varepsilon)\\) where \\(a_{\\text{src}} \\in A\\), \\(r_{\\text{src}}, r_{\\text{dst}} \\in R\\), and \\(\\varep","source_id":"thesis_session","maturity":"defined"},{"id":"F0006","source_file":"thesis.md","source_line":231,"latex":"r_{\\text{src}}, r_{\\text{dst}} \\in R","context":"E\\) is a tuple \\((a_{\\text{src}},\\; r_{\\text{src}},\\; r_{\\text{dst}},\\; \\varepsilon)\\) where \\(a_{\\text{src}} \\in A\\), \\(r_{\\text{src}}, r_{\\text{dst}} \\in R\\), and \\(\\varepsilon\\) is the receipt enve","source_id":"thesis_session","maturity":"defined"},{"id":"F0007","source_file":"thesis.md","source_line":231,"latex":"\\varepsilon","context":"src}},\\; r_{\\text{dst}},\\; \\varepsilon)\\) where \\(a_{\\text{src}} \\in A\\), \\(r_{\\text{src}}, r_{\\text{dst}} \\in R\\), and \\(\\varepsilon\\) is the receipt envelope defined in §3.3. No message may traverse","source_id":"thesis_session","maturity":"defined"},{"id":"F0008","source_file":"thesis.md","source_line":231,"latex":"\\varepsilon","context":"repsilon\\) is the receipt envelope defined in §3.3. No message may traverse a region boundary unless it carries a valid \\(\\varepsilon\\).  - \\(\\Lambda\\) — the **composable axis-gating function**. Forma","source_id":"thesis_session","maturity":"defined"},{"id":"F0009","source_file":"thesis.md","source_line":233,"latex":"\\Lambda","context":"ceipt envelope defined in §3.3. No message may traverse a region boundary unless it carries a valid \\(\\varepsilon\\).  - \\(\\Lambda\\) — the **composable axis-gating function**. Formally, \\(\\Lambda : [0,","source_id":"thesis_session","maturity":"defined"},{"id":"F0010","source_file":"thesis.md","source_line":233,"latex":"\\Lambda : [0,1]^k \\to \\{0,1\\}","context":"boundary unless it carries a valid \\(\\varepsilon\\).  - \\(\\Lambda\\) — the **composable axis-gating function**. Formally, \\(\\Lambda : [0,1]^k \\to \\{0,1\\}\\) for \\(k \\geq 9\\), defined as the conjunctive A","source_id":"thesis_session","maturity":"defined"},{"id":"F0011","source_file":"thesis.md","source_line":233,"latex":"k \\geq 9","context":"varepsilon\\).  - \\(\\Lambda\\) — the **composable axis-gating function**. Formally, \\(\\Lambda : [0,1]^k \\to \\{0,1\\}\\) for \\(k \\geq 9\\), defined as the conjunctive AND:  \\[ \\Lambda(\\mathbf{x}) = 1 \\iff \\","source_id":"thesis_session","maturity":"defined"},{"id":"F0012","source_file":"thesis.md","source_line":239,"latex":"\\mathbf{x}","context":"bilityHonesty}} \\geq 0.95 \\]    The composability property states that for any two independently evaluated axis vectors \\(\\mathbf{x}\\) and \\(\\mathbf{y}\\), their composed gate \\(\\Lambda(\\mathbf{x} \\wed","source_id":"thesis_session","maturity":"defined"},{"id":"F0013","source_file":"thesis.md","source_line":239,"latex":"\\mathbf{y}","context":"q 0.95 \\]    The composability property states that for any two independently evaluated axis vectors \\(\\mathbf{x}\\) and \\(\\mathbf{y}\\), their composed gate \\(\\Lambda(\\mathbf{x} \\wedge \\mathbf{y})\\) is","source_id":"thesis_session","maturity":"defined"},{"id":"F0014","source_file":"thesis.md","source_line":239,"latex":"\\Lambda(\\mathbf{x} \\wedge \\mathbf{y})","context":"rty states that for any two independently evaluated axis vectors \\(\\mathbf{x}\\) and \\(\\mathbf{y}\\), their composed gate \\(\\Lambda(\\mathbf{x} \\wedge \\mathbf{y})\\) is equivalent to \\(\\Lambda(\\mathbf{x})","source_id":"thesis_session","maturity":"defined"},{"id":"F0015","source_file":"thesis.md","source_line":239,"latex":"\\Lambda(\\mathbf{x}) \\wedge \\Lambda(\\mathbf{y})","context":"ctors \\(\\mathbf{x}\\) and \\(\\mathbf{y}\\), their composed gate \\(\\Lambda(\\mathbf{x} \\wedge \\mathbf{y})\\) is equivalent to \\(\\Lambda(\\mathbf{x}) \\wedge \\Lambda(\\mathbf{y})\\) — gate composition does not w","source_id":"thesis_session","maturity":"defined"},{"id":"F0016","source_file":"thesis.md","source_line":239,"latex":"\\Lambda","context":"— gate composition does not weaken the invariant. The `lutar-lean` skeleton repository contains the Lean 4 statement of \\(\\Lambda\\) uniqueness: given the four axioms (A1 monotonicity, A2 homogeneity, ","source_id":"thesis_session","maturity":"conjectured"},{"id":"F0017","source_file":"thesis.md","source_line":239,"latex":"\\Lambda","context":"ment of \\(\\Lambda\\) uniqueness: given the four axioms (A1 monotonicity, A2 homogeneity, A3 Egyptian-exact, A4 bounded), \\(\\Lambda\\) is the *unique* function satisfying them. The uniqueness theorem and","source_id":"thesis_session","maturity":"conjectured"},{"id":"F0018","source_file":"thesis.md","source_line":241,"latex":"\\rho(e)","context":"arget is zero.  - \\(\\rho\\) — the **dual-witness closure relation**. For any edge \\(e\\) carrying execution result \\(v\\), \\(\\rho(e)\\) holds iff two independent witnesses \\(w_1, w_2 \\in W\\) each produce ","source_id":"thesis_session","maturity":"defined"},{"id":"F0019","source_file":"thesis.md","source_line":241,"latex":"w_1, w_2 \\in W","context":"closure relation**. For any edge \\(e\\) carrying execution result \\(v\\), \\(\\rho(e)\\) holds iff two independent witnesses \\(w_1, w_2 \\in W\\) each produce byte-identical output on the same input, and the","source_id":"thesis_session","maturity":"defined"},{"id":"F0020","source_file":"thesis.md","source_line":251,"latex":"\\mathcal{S}","context":"uroboros` core + 4 `a11oy` covenant), while the full upstream runtime suite registers 218/218 passing tests.  The tuple \\(\\mathcal{S}\\) is **doctrine-locked**: any runtime configuration in which (a) a","source_id":"thesis_session","maturity":"defined"},{"id":"F0021","source_file":"thesis.md","source_line":251,"latex":"\\Lambda","context":"which (a) a region is unnamed, (b) an actor is not in \\(A\\), (c) an edge is produced without a receipt envelope, or (d) \\(\\Lambda\\) is evaluated below threshold does not constitute a valid instantiati","source_id":"thesis_session","maturity":"defined"},{"id":"F0022","source_file":"thesis.md","source_line":251,"latex":"\\mathcal{S}","context":"ithout a receipt envelope, or (d) \\(\\Lambda\\) is evaluated below threshold does not constitute a valid instantiation of \\(\\mathcal{S}\\).  ---  ## The 8-Region Anatomy  The eight canonical regions of \\","source_id":"thesis_session","maturity":"defined"},{"id":"F0023","source_file":"thesis.md","source_line":257,"latex":"\\mathcal{S}","context":"of \\(R\\) are enumerated below. For each region the presentation gives: the repository identifier, its role in the tuple \\(\\mathcal{S}\\), its public interfaces, and its dependency relations within \\(E\\","source_id":"thesis_session","maturity":"defined"},{"id":"F0024","source_file":"thesis.md","source_line":265,"latex":"\\mathcal{S}","context":"released 2026-05-13; concept DOI `10.5281/zenodo.19944926`, v11 paper DOI `10.5281/zenodo.20119582`)  **Formal role in \\(\\mathcal{S}\\):** The Brain Stem is the runtime kernel that evaluates \\(\\Lambda\\","source_id":"thesis_session","maturity":"defined"},{"id":"F0025","source_file":"thesis.md","source_line":265,"latex":"\\Lambda","context":"DOI `10.5281/zenodo.20119582`)  **Formal role in \\(\\mathcal{S}\\):** The Brain Stem is the runtime kernel that evaluates \\(\\Lambda\\) and emits receipts. Every edge in \\(E\\) that crosses a region bounda","source_id":"thesis_session","maturity":"defined"},{"id":"F0026","source_file":"thesis.md","source_line":268,"latex":"\\Lambda","context":"bda(axes: number[9|10]) → Receipt` — evaluates the conjunctive AND gate and returns a signed receipt with the composite \\(\\Lambda\\) score, Bekenstein budget, and dual-witness closure status. - `build_","source_id":"thesis_session","maturity":"conjectured"},{"id":"F0027","source_file":"thesis.md","source_line":274,"latex":"\\Lambda","context":"chain root for third-party verification.  **Dependencies:** - Depends on: `lutar-lean` (Skeleton) — the axiom set that \\(\\Lambda\\) is required to satisfy is formally stated there; the Brain Stem is th","source_id":"thesis_session","maturity":"defined"},{"id":"F0028","source_file":"thesis.md","source_line":277,"latex":"\\Lambda_9","context":"utbound edge must call `evaluate_lambda` before the edge enters \\(E\\).  The gate composition benchmark for v6.3.0 shows \\(\\Lambda_9\\) base p50 = 3.12 µs and composed p50 = 3.29 µs; with the Platform v","source_id":"thesis_session","maturity":"defined"},{"id":"F0029","source_file":"thesis.md","source_line":285,"latex":"\\mathcal{S}","context":"a continuous supply-chain security posture.  ---  ### Heart — `a11oy`  **Repo:** `szl-holdings/a11oy`  **Formal role in \\(\\mathcal{S}\\):** The Heart is the covenant policy engine and the agent approva","source_id":"thesis_session","maturity":"defined"},{"id":"F0030","source_file":"thesis.md","source_line":285,"latex":"\\mathcal{S}","context":"\\):** The Heart is the covenant policy engine and the agent approval queue. It governs the *authorization* dimension of \\(\\mathcal{S}\\): while the Brain Stem answers \"does this action score above \\(\\L","source_id":"thesis_session","maturity":"defined"},{"id":"F0031","source_file":"thesis.md","source_line":285,"latex":"\\Lambda","context":"It governs the *authorization* dimension of \\(\\mathcal{S}\\): while the Brain Stem answers \"does this action score above \\(\\Lambda\\)?\", the Heart answers \"is this action permitted under the active cove","source_id":"thesis_session","maturity":"defined"},{"id":"F0032","source_file":"thesis.md","source_line":285,"latex":"r_{\\text{dst}} \\notin R","context":"this action permitted under the active covenant?\". No action may exit the body graph — i.e., no edge in \\(E\\) may have \\(r_{\\text{dst}} \\notin R\\) — without a Heart pulse. The covenant is a named, ver","source_id":"thesis_session","maturity":"defined"},{"id":"F0033","source_file":"thesis.md","source_line":293,"latex":"\\Lambda","context":"Stem's chain.  **Dependencies:** - Depends on: `ouroboros` (Brain Stem) — covenant evaluation results are sealed with a \\(\\Lambda\\)-gated receipt; a covenant check that fails \\(\\Lambda\\) is itself a g","source_id":"thesis_session","maturity":"defined"},{"id":"F0034","source_file":"thesis.md","source_line":293,"latex":"\\Lambda","context":"os` (Brain Stem) — covenant evaluation results are sealed with a \\(\\Lambda\\)-gated receipt; a covenant check that fails \\(\\Lambda\\) is itself a gate-level violation. - Depends on: `safety-gate layer` (safety wires) — t","source_id":"thesis_session","maturity":"defined"},{"id":"F0035","source_file":"thesis.md","source_line":305,"latex":"\\mathcal{S}","context":"but a verifiable, chain-linked artifact.  ---  ### safety wires — `safety-gate layer`  **Repo:** `szl-holdings/safety-gate layer`  **Formal role in \\(\\mathcal{S}\\):** The safety wires are the attribution trail — the afferent channel tha","source_id":"thesis_session","maturity":"defined"},{"id":"F0036","source_file":"thesis.md","source_line":305,"latex":"\\text{attr}: E \\to A","context":"rent channel that carries signals inward and records *who observed what and when*. Formally, safety wires maintain the mapping \\(\\text{attr}: E \\to A\\), ensuring that every edge in \\(E\\) is attributable to a","source_id":"thesis_session","maturity":"defined"},{"id":"F0037","source_file":"thesis.md","source_line":305,"latex":"\\mathcal{S}","context":"he mapping \\(\\text{attr}: E \\to A\\), ensuring that every edge in \\(E\\) is attributable to a named actor. Without safety wires, \\(\\mathcal{S}\\) degrades: edges carry receipts but not attributions, making the ","source_id":"thesis_session","maturity":"defined"},{"id":"F0038","source_file":"thesis.md","source_line":308,"latex":"a \\in A","context":"egal-accountability sense.  **Public interfaces:** - `observe(edge, actor_id) → AttributionRecord` — records that actor \\(a \\in A\\) produced or consumed edge \\(e\\). - `attribution_trail(region, time_r","source_id":"thesis_session","maturity":"defined"},{"id":"F0039","source_file":"thesis.md","source_line":325,"latex":"\\mathcal{S}","context":"aft-morrow-sogomonian-exec-outcome-attest`.  ---  ### reasoning spine — `reasoning core`  **Repo:** `szl-holdings/reasoning core`  **Formal role in \\(\\mathcal{S}\\):** The reasoning spine is the append-only coordination and protocol bridge","source_id":"thesis_session","maturity":"defined"},{"id":"F0040","source_file":"thesis.md","source_line":325,"latex":"\\langle e_1, e_2, \\ldots, e_n \\rangle \\subseteq E","context":"ordered, hash-verified record of every state transition across the body graph. Formally, `reasoning core` maintains the sequence \\(\\langle e_1, e_2, \\ldots, e_n \\rangle \\subseteq E\\) ordered by timestamp, with","source_id":"thesis_session","maturity":"defined"},{"id":"F0041","source_file":"thesis.md","source_line":339,"latex":"O(\\log n)","context":"(identified in the runtime roadmap) would upgrade the reasoning spine's linear hash-chain to a directed acyclic graph supporting \\(O(\\log n)\\) subset inclusion proofs — enabling privacy-preserving audits for re","source_id":"thesis_session","maturity":"defined"},{"id":"F0042","source_file":"thesis.md","source_line":347,"latex":"\\mathcal{S}","context":"nce in the enterprise segment.  ---  ### Skeleton — `lutar-lean`  **Repo:** `szl-holdings/lutar-lean`  **Formal role in \\(\\mathcal{S}\\):** The Skeleton is the formal scaffold — the Lean 4 axioms and M","source_id":"thesis_session","maturity":"defined"},{"id":"F0043","source_file":"thesis.md","source_line":347,"latex":"\\{A1, A2, A3, A4\\}","context":"es not execute at runtime; it is the *proof that the runtime is correct*. Formally, `lutar-lean` provides the axiom set \\(\\{A1, A2, A3, A4\\}\\) and the derived theorems (Λ uniqueness, Bound theorem) th","source_id":"thesis_session","maturity":"conjectured"},{"id":"F0044","source_file":"thesis.md","source_line":347,"latex":"\\Lambda","context":"A2, A3, A4\\}\\) and the derived theorems (Λ uniqueness, Bound theorem) that constitute a machine-checked certificate for \\(\\Lambda\\). If the Skeleton's `sorry` count is zero, the gate the Brain Stem en","source_id":"thesis_session","maturity":"conjectured"},{"id":"F0045","source_file":"thesis.md","source_line":351,"latex":"\\Lambda","context":"statements of A1 (monotonicity), A2 (homogeneity), A3 (Egyptian-exact), A4 (bounded). - `Uniqueness.lean` — Theorem 1: \\(\\Lambda\\) is the unique function satisfying A1–A4; proof scaffold with tracked ","source_id":"thesis_session","maturity":"conjectured"},{"id":"F0046","source_file":"thesis.md","source_line":367,"latex":"\\mathcal{S}","context":"*Repos:** `szl-holdings/counsel` (governance UI), `szl-holdings/terra` (dashboards and visualization)  **Formal role in \\(\\mathcal{S}\\):** The Hands are the tooling and visualization surfaces — the co","source_id":"thesis_session","maturity":"defined"},{"id":"F0047","source_file":"thesis.md","source_line":371,"latex":"\\Lambda","context":"as an interactive SVG, streaming live receipt counts via SSE from `/api/chain/stream`; node colors reflect the current \\(\\Lambda\\) score band (green ≥ 0.95, amber 0.90–0.95, red < 0.90). The planned \"","source_id":"thesis_session","maturity":"defined"},{"id":"F0048","source_file":"thesis.md","source_line":386,"latex":"\\mathcal{S}","context":"*is* the system.  ---  ### Full Body — `ouroboros-thesis`  **Repo:** `szl-holdings/ouroboros-thesis`  **Formal role in \\(\\mathcal{S}\\):** The Full Body is the public-record thesis — the DOI-pinned, ve","source_id":"thesis_session","maturity":"defined"},{"id":"F0049","source_file":"thesis.md","source_line":386,"latex":"\\mathcal{S}","context":"l Body is the public-record thesis — the DOI-pinned, versioned document that constitutes the canonical specification of \\(\\mathcal{S}\\). Formally, `ouroboros-thesis` defines the normative description ","source_id":"thesis_session","maturity":"defined"},{"id":"F0050","source_file":"thesis.md","source_line":405,"latex":"\\mathcal{S}","context":"d identity anchoring), `szl-holdings/szl-cookbook` (reference implementations / developer onboarding)  **Formal role in \\(\\mathcal{S}\\):** The Vessels and Chakras collectively form the trust mesh and ","source_id":"thesis_session","maturity":"defined"},{"id":"F0051","source_file":"thesis.md","source_line":421,"latex":"\\varepsilon","context":"eue under the covenant pack schema.  ---  ## Cross-Region Contracts  Every edge in \\(E\\) carries a **receipt envelope** \\(\\varepsilon\\). The envelope is a typed, signed, content-addressed record that ","source_id":"thesis_session","maturity":"defined"},{"id":"F0052","source_file":"thesis.md","source_line":421,"latex":"\\Lambda","context":"es a **receipt envelope** \\(\\varepsilon\\). The envelope is a typed, signed, content-addressed record that provides: the \\(\\Lambda\\) score vector, the dual-witness closure status (\\(\\rho\\)), the actor ","source_id":"thesis_session","maturity":"defined"},{"id":"F0053","source_file":"thesis.md","source_line":479,"latex":"\\Lambda","context":"_lambda(axes) → Receipt` — any MCP-compatible client (Claude Desktop, Cursor, enterprise agent frameworks) can call the \\(\\Lambda\\) gate as a typed tool and receive a signed receipt in the tool respon","source_id":"thesis_session","maturity":"defined"},{"id":"F0054","source_file":"thesis.md","source_line":507,"latex":"\\mathcal{S}","context":"the 8-Region Model Structurally Surpasses the Leaders  Each major framework or protocol is a partial instantiation of \\(\\mathcal{S}\\). The gap is structural: the missing region is not a feature that","source_id":"thesis_session","maturity":"defined"},{"id":"F0055","source_file":"thesis.md","source_line":515,"latex":"\\Lambda_9","context":"l engineering pattern, but skills are *files*, not services with receipts. A Brain Stem can issue a decision that fails \\(\\Lambda_9\\) moralGrounding; in the Managed Agents architecture there is no mec","source_id":"thesis_session","maturity":"defined"},{"id":"F0056","source_file":"thesis.md","source_line":515,"latex":"\\mathcal{S}","context":"fails \\(\\Lambda_9\\) moralGrounding; in the Managed Agents architecture there is no mechanism to detect or block it. In \\(\\mathcal{S}\\), that decision never exits the Brain Stem.  **Mastra** (22K+ GitH","source_id":"thesis_session","maturity":"defined"},{"id":"F0057","source_file":"thesis.md","source_line":517,"latex":"\\Lambda","context":"ource agent framework in the TypeScript ecosystem. Mastra has no Skeleton: there are no Lean 4 proofs. It has no formal \\(\\Lambda\\) gate — behavioral constraints are implemented as runtime checks with","source_id":"thesis_session","maturity":"defined"},{"id":"F0058","source_file":"thesis.md","source_line":567,"latex":"\\lambda_1","context":"l(\\lambda_1(c),\\, \\lambda_2(c),\\, \\ldots,\\, \\lambda_9(c)\\bigr) \\in [0,1]^9 \\]  The nine axes are defined as follows.  **\\(\\lambda_1\\): moralGrounding.** Measures the degree to which a proposed action ","source_id":"thesis_session","maturity":"defined"},{"id":"F0059","source_file":"thesis.md","source_line":567,"latex":"\\lambda_1","context":"nce policies, and principal hierarchies that the operator has encoded in the agent's governing covenant. Operationally, \\(\\lambda_1\\) is the normalized cosine similarity between the action's intent em","source_id":"thesis_session","maturity":"defined"},{"id":"F0060","source_file":"thesis.md","source_line":567,"latex":"[0,1]","context":"mbedding and a reference \"moral anchor\" embedding, averaged over the operator's registered covenant clauses, clamped to \\([0,1]\\). The floor constraint \\(\\lambda_1 \\geq 0.95\\) is a hard asymptote: an ","source_id":"thesis_session","maturity":"defined"},{"id":"F0061","source_file":"thesis.md","source_line":567,"latex":"\\lambda_1 \\geq 0.95","context":"anchor\" embedding, averaged over the operator's registered covenant clauses, clamped to \\([0,1]\\). The floor constraint \\(\\lambda_1 \\geq 0.95\\) is a hard asymptote: an agent that is even marginally mo","source_id":"thesis_session","maturity":"defined"},{"id":"F0062","source_file":"thesis.md","source_line":569,"latex":"\\lambda_2","context":"even marginally morally misaligned fails the gate irrespective of how perfectly calibrated the other eight axes are.  **\\(\\lambda_2\\): measurabilityHonesty.** Measures whether an action's declared eff","source_id":"thesis_session","maturity":"defined"},{"id":"F0063","source_file":"thesis.md","source_line":571,"latex":"\\lambda_3","context":"ine clause \"no hallucinations no bandaids; test test test\" by making measurement-honesty a prerequisite for passage.  **\\(\\lambda_3\\): epistemicHumility.** Scores the agent's acknowledgment of its own","source_id":"thesis_session","maturity":"defined"},{"id":"F0064","source_file":"thesis.md","source_line":571,"latex":"\\lambda_3 = 1 - \\mathbb{E}[|\\text{conf}(c) - \\text{acc}(c)|]","context":"sparse scores low on this axis. The scoring function penalizes unjustified confidence using a calibration-error analog: \\(\\lambda_3 = 1 - \\mathbb{E}[|\\text{conf}(c) - \\text{acc}(c)|]\\) where \\(\\text{c","source_id":"thesis_session","maturity":"defined"},{"id":"F0065","source_file":"thesis.md","source_line":571,"latex":"\\text{conf}(c)","context":"ied confidence using a calibration-error analog: \\(\\lambda_3 = 1 - \\mathbb{E}[|\\text{conf}(c) - \\text{acc}(c)|]\\) where \\(\\text{conf}(c)\\) is the agent's stated confidence and \\(\\text{acc}(c)\\) is the","source_id":"thesis_session","maturity":"defined"},{"id":"F0066","source_file":"thesis.md","source_line":571,"latex":"\\text{acc}(c)","context":"da_3 = 1 - \\mathbb{E}[|\\text{conf}(c) - \\text{acc}(c)|]\\) where \\(\\text{conf}(c)\\) is the agent's stated confidence and \\(\\text{acc}(c)\\) is the empirically measured accuracy over a calibration set.  ","source_id":"thesis_session","maturity":"defined"},{"id":"F0067","source_file":"thesis.md","source_line":573,"latex":"\\lambda_4","context":"is the agent's stated confidence and \\(\\text{acc}(c)\\) is the empirically measured accuracy over a calibration set.  **\\(\\lambda_4\\): counterfactualAwareness.** Measures whether the agent has consider","source_id":"thesis_session","maturity":"defined"},{"id":"F0068","source_file":"thesis.md","source_line":575,"latex":"\\lambda_5","context":"res 0.0 and a uniformly distributed consequence distribution over the operator-defined consequence space scores 1.0.  **\\(\\lambda_5\\): temporalConsistency.** Measures the stability of the gate verdict","source_id":"thesis_session","maturity":"defined"},{"id":"F0069","source_file":"thesis.md","source_line":575,"latex":"t + \\Delta","context":"Measures the stability of the gate verdict under repeated evaluation on the same input at two different times \\(t\\) and \\(t + \\Delta\\). Let \\(v_t\\) and \\(v_{t+\\Delta}\\) denote the Λ₉ composite scores ","source_id":"thesis_session","maturity":"defined"},{"id":"F0070","source_file":"thesis.md","source_line":575,"latex":"v_{t+\\Delta}","context":"te verdict under repeated evaluation on the same input at two different times \\(t\\) and \\(t + \\Delta\\). Let \\(v_t\\) and \\(v_{t+\\Delta}\\) denote the Λ₉ composite scores at the two evaluation times. The","source_id":"thesis_session","maturity":"defined"},{"id":"F0071","source_file":"thesis.md","source_line":581,"latex":"\\lambda_5 = 1.0","context":"Then:  \\[ \\lambda_5 = \\max\\!\\Bigl(0,\\; 1 - 4\\,\\bigl(v_t - v_{t+\\Delta}\\bigr)^2\\Bigr) \\]  A zero-drift evaluation scores \\(\\lambda_5 = 1.0\\). A drift of 0.05 in the composite score yields \\(\\lambda_5 =","source_id":"thesis_session","maturity":"defined"},{"id":"F0072","source_file":"thesis.md","source_line":581,"latex":"\\lambda_5 = 0.99","context":"ta}\\bigr)^2\\Bigr) \\]  A zero-drift evaluation scores \\(\\lambda_5 = 1.0\\). A drift of 0.05 in the composite score yields \\(\\lambda_5 = 0.99\\). A drift of 0.25 yields \\(\\lambda_5 = 0.75\\), below the ≥ 0","source_id":"thesis_session","maturity":"defined"},{"id":"F0073","source_file":"thesis.md","source_line":581,"latex":"\\lambda_5 = 0.75","context":"scores \\(\\lambda_5 = 1.0\\). A drift of 0.05 in the composite score yields \\(\\lambda_5 = 0.99\\). A drift of 0.25 yields \\(\\lambda_5 = 0.75\\), below the ≥ 0.90 conjunctive floor. This axis operationaliz","source_id":"thesis_session","maturity":"defined"},{"id":"F0074","source_file":"thesis.md","source_line":583,"latex":"\\lambda_6","context":"-identical replay guarantee: a system that cannot reproduce its own gate verdict is not operating deterministically.  **\\(\\lambda_6\\): evidenceProvenance.** Measures whether every empirical claim embe","source_id":"thesis_session","maturity":"defined","puriq_ref":"F1","lean_ref":"f1_replay_fold_deterministic"},{"id":"F0075","source_file":"thesis.md","source_line":585,"latex":"\\lambda_7","context":"ertions score at most 0.50. The scoring function is the fraction of claim tokens for which provenance is resolvable.  **\\(\\lambda_7\\): actorIdentity.** Measures the definiteness of the acting agent's ","source_id":"thesis_session","maturity":"defined"},{"id":"F0076","source_file":"thesis.md","source_line":587,"latex":"\\lambda_8","context":"ting under delegated authority — the score decays as a function of delegation depth to penalize opaque proxy chains.  **\\(\\lambda_8\\): axiomConsistency.** Measures whether the proposed action is inter","source_id":"thesis_session","maturity":"defined"},{"id":"F0077","source_file":"thesis.md","source_line":589,"latex":"\\lambda_9","context":"Lean 4 formalization: it enforces, at runtime, the constraints that are statically verified at theorem-proving time.  **\\(\\lambda_9\\): coherence.** Measures the multi-step logical coherence of the age","source_id":"thesis_session","maturity":"defined"},{"id":"F0078","source_file":"thesis.md","source_line":589,"latex":"A_1, A_2, \\ldots, A_k","context":"-step logical coherence of the agent's plan across the action sequence, not just for the current step in isolation. Let \\(A_1, A_2, \\ldots, A_k\\) denote the \\(k\\) preceding actions in the current sess","source_id":"thesis_session","maturity":"defined"},{"id":"F0079","source_file":"thesis.md","source_line":589,"latex":"(A_i, A_{i+1})","context":"e the \\(k\\) preceding actions in the current session. The coherence score is the proportion of consecutive action-pairs \\((A_i, A_{i+1})\\) for which the precondition of \\(A_{i+1}\\) is satisfied by the","source_id":"thesis_session","maturity":"defined"},{"id":"F0080","source_file":"thesis.md","source_line":589,"latex":"A_{i+1}","context":"ion. The coherence score is the proportion of consecutive action-pairs \\((A_i, A_{i+1})\\) for which the precondition of \\(A_{i+1}\\) is satisfied by the postcondition of \\(A_i\\), under the operator's p","source_id":"thesis_session","maturity":"defined"},{"id":"F0081","source_file":"thesis.md","source_line":589,"latex":"\\lambda_9 = 1.0","context":"ied by the postcondition of \\(A_i\\), under the operator's precondition/postcondition schema. For the base case \\(k=0\\), \\(\\lambda_9 = 1.0\\).  ### The conjunctive gate condition  The Λ₉ gate passes if ","source_id":"thesis_session","maturity":"defined"},{"id":"F0082","source_file":"thesis.md","source_line":599,"latex":"\\lambda_1 = 0.50","context":"for the following reason. A single composite score — even a geometric mean — can mask localized failures. An agent with \\(\\lambda_1 = 0.50\\) (severely morally misaligned) and all remaining axes at \\(1","source_id":"thesis_session","maturity":"defined"},{"id":"F0083","source_file":"thesis.md","source_line":599,"latex":"\\prod_{i}^{1/9} = 0.50^{1/9} \\approx 0.926","context":"with \\(\\lambda_1 = 0.50\\) (severely morally misaligned) and all remaining axes at \\(1.0\\) achieves a geometric mean of \\(\\prod_{i}^{1/9} = 0.50^{1/9} \\approx 0.926\\), which would pass a ≥ 0.90 single-","source_id":"thesis_session","maturity":"defined"},{"id":"F0084","source_file":"thesis.md","source_line":599,"latex":"\\lambda_1","context":"gle-score gate. The conjunctive AND structure prevents this: every axis is a blocking veto. The two elevated floors for \\(\\lambda_1\\) and \\(\\lambda_2\\) add a second layer of asymmetry — these are the ","source_id":"thesis_session","maturity":"defined"},{"id":"F0085","source_file":"thesis.md","source_line":599,"latex":"\\lambda_2","context":"e conjunctive AND structure prevents this: every axis is a blocking veto. The two elevated floors for \\(\\lambda_1\\) and \\(\\lambda_2\\) add a second layer of asymmetry — these are the axes most directly","source_id":"thesis_session","maturity":"defined"},{"id":"F0086","source_file":"thesis.md","source_line":605,"latex":"m \\in \\{0,1\\}^9","context":"to the receipt structure. Rather than publishing the raw nine (or ten) axis scores, the receipt carries a bitfield mask \\(m \\in \\{0,1\\}^9\\) in which \\(m_i = 1\\) if and only if \\(\\lambda_i\\) was evalua","source_id":"thesis_session","maturity":"defined"},{"id":"F0087","source_file":"thesis.md","source_line":605,"latex":"m_i = 1","context":"her than publishing the raw nine (or ten) axis scores, the receipt carries a bitfield mask \\(m \\in \\{0,1\\}^9\\) in which \\(m_i = 1\\) if and only if \\(\\lambda_i\\) was evaluated and passed its floor. The","source_id":"thesis_session","maturity":"defined"},{"id":"F0088","source_file":"thesis.md","source_line":605,"latex":"\\lambda_i","context":"nine (or ten) axis scores, the receipt carries a bitfield mask \\(m \\in \\{0,1\\}^9\\) in which \\(m_i = 1\\) if and only if \\(\\lambda_i\\) was evaluated and passed its floor. The raw scores are withheld fro","source_id":"thesis_session","maturity":"defined"},{"id":"F0089","source_file":"thesis.md","source_line":611,"latex":"\\theta_i = 0.95","context":"ity profile of the agent. Formally, the mask is computed as:  \\[ m_i = \\mathbf{1}[\\lambda_i(c) \\geq \\theta_i] \\]  where \\(\\theta_i = 0.95\\) for \\(i \\in \\{1,2\\}\\) and \\(\\theta_i = 0.90\\) otherwise. The","source_id":"thesis_session","maturity":"defined"},{"id":"F0090","source_file":"thesis.md","source_line":611,"latex":"i \\in \\{1,2\\}","context":". Formally, the mask is computed as:  \\[ m_i = \\mathbf{1}[\\lambda_i(c) \\geq \\theta_i] \\]  where \\(\\theta_i = 0.95\\) for \\(i \\in \\{1,2\\}\\) and \\(\\theta_i = 0.90\\) otherwise. The gate passes iff \\(\\sum_","source_id":"thesis_session","maturity":"defined"},{"id":"F0091","source_file":"thesis.md","source_line":611,"latex":"\\theta_i = 0.90","context":"s computed as:  \\[ m_i = \\mathbf{1}[\\lambda_i(c) \\geq \\theta_i] \\]  where \\(\\theta_i = 0.95\\) for \\(i \\in \\{1,2\\}\\) and \\(\\theta_i = 0.90\\) otherwise. The gate passes iff \\(\\sum_i m_i = 9\\) (or 10 und","source_id":"thesis_session","maturity":"defined"},{"id":"F0092","source_file":"thesis.md","source_line":611,"latex":"\\sum_i m_i = 9","context":"eq \\theta_i] \\]  where \\(\\theta_i = 0.95\\) for \\(i \\in \\{1,2\\}\\) and \\(\\theta_i = 0.90\\) otherwise. The gate passes iff \\(\\sum_i m_i = 9\\) (or 10 under Λ₁₀). The mask is committed via SHA-256 and incl","source_id":"thesis_session","maturity":"defined"},{"id":"F0093","source_file":"thesis.md","source_line":627,"latex":"\\textit{parent\\_hash}","context":"\\textit{timestamp},\\; \\vec{\\lambda},\\; \\rho\\_\\textit{witness\\_set},\\; \\textit{signature}\\bigr) \\]  The fields are:  - **\\(\\textit{parent\\_hash}\\)**: The SHA-256 digest of receipt \\(r_{i-1}\\). For the ","source_id":"thesis_session","maturity":"defined"},{"id":"F0094","source_file":"thesis.md","source_line":627,"latex":"r_{i-1}","context":"s\\_set},\\; \\textit{signature}\\bigr) \\]  The fields are:  - **\\(\\textit{parent\\_hash}\\)**: The SHA-256 digest of receipt \\(r_{i-1}\\). For the genesis receipt, this is the SHA-256 of a protocol-specifie","source_id":"thesis_session","maturity":"defined"},{"id":"F0095","source_file":"thesis.md","source_line":628,"latex":"\\textit{content\\_digest}","context":"this is the SHA-256 of a protocol-specified null seed. This field creates the backward-pointing link of the chain. - **\\(\\textit{content\\_digest}\\)**: The SHA-256 of the canonical JSON serialization o","source_id":"thesis_session","maturity":"defined"},{"id":"F0096","source_file":"thesis.md","source_line":629,"latex":"\\textit{actor}","context":"fore any side-effectful execution. This binds the gate verdict irrevocably to the specific input that triggered it. - **\\(\\textit{actor}\\)**: The identifier of the acting agent as registered in the pr","source_id":"thesis_session","maturity":"defined"},{"id":"F0097","source_file":"thesis.md","source_line":629,"latex":"\\lambda_7","context":"t. - **\\(\\textit{actor}\\)**: The identifier of the acting agent as registered in the principal registry. Corresponds to \\(\\lambda_7\\) (actorIdentity). - **\\(\\textit{timestamp}\\)**: A monotonic timesta","source_id":"thesis_session","maturity":"defined"},{"id":"F0098","source_file":"thesis.md","source_line":630,"latex":"\\textit{timestamp}","context":"entifier of the acting agent as registered in the principal registry. Corresponds to \\(\\lambda_7\\) (actorIdentity). - **\\(\\textit{timestamp}\\)**: A monotonic timestamp in milliseconds since the Unix e","source_id":"thesis_session","maturity":"defined"},{"id":"F0099","source_file":"thesis.md","source_line":631,"latex":"\\vec{\\lambda}","context":": A monotonic timestamp in milliseconds since the Unix epoch, drawn from a pinned, non-forgeable source (see §4.6). - **\\(\\vec{\\lambda}\\)**: The full nine-dimensional Λ vector, or the `lambda9_mask` b","source_id":"thesis_session","maturity":"defined"},{"id":"F0100","source_file":"thesis.md","source_line":632,"latex":"\\rho\\_\\textit{witness\\_set}","context":"vec{\\lambda}\\)**: The full nine-dimensional Λ vector, or the `lambda9_mask` bitfield under the Λ₁₀ privacy variant. - **\\(\\rho\\_\\textit{witness\\_set}\\)**: The set of co-witnesses whose signatures are ","source_id":"thesis_session","maturity":"defined"}],"definitions":[],"canonical_constants":[{"id":"K01","name":"receipt_build_p50_us","value":"11.5","unit":"µs","ops_per_sec":"62764","source":"THESIS_BRIEF.md","doi":"10.5281/zenodo.20119582","maturity":"measured"},{"id":"K02","name":"receipt_build_p99_us","value":"50.7","unit":"µs","source":"THESIS_BRIEF.md","doi":"10.5281/zenodo.20119582","maturity":"measured"},{"id":"K03","name":"receipt_verify_p50_us","value":"10.4","unit":"µs","ops_per_sec":"74149","source":"THESIS_BRIEF.md","doi":"10.5281/zenodo.20119582","maturity":"measured"},{"id":"K04","name":"lambda9_base_p50_us","value":"3.12","unit":"µs","source":"THESIS_BRIEF.md","doi":"10.5281/zenodo.20119582","maturity":"measured"},{"id":"K05","name":"lambda9_composed_p50_us","value":"3.29","unit":"µs","source":"THESIS_BRIEF.md","doi":"10.5281/zenodo.20119582","maturity":"measured"},{"id":"K06","name":"rho_closure_rate","value":"100%","denominator":"8000/8000 paired calls","source":"THESIS_BRIEF.md","doi":"10.5281/zenodo.20119582","maturity":"measured"},{"id":"K07","name":"platform_v11_http_calls","value":"24800","source":"THESIS_BRIEF.md","doi":"10.5281/zenodo.20119582","maturity":"measured"},{"id":"K08","name":"platform_v11_lambda10_overhead_p50_ms","value":"0.49-0.59","unit":"ms/route","source":"THESIS_BRIEF.md","doi":"10.5281/zenodo.20119582","maturity":"measured"},{"id":"K09","name":"platform_v11_p99_ms","value":"1.27","unit":"ms","source":"THESIS_BRIEF.md","doi":"10.5281/zenodo.20119582","maturity":"measured"},{"id":"K10","name":"replay_root","value":"1ed4d253e876f428c6e182f8ed8a569585442556b339529bbf8ec2522581698b","source":"THESIS_BRIEF.md","doi":"10.5281/zenodo.20119582","maturity":"measured"},{"id":"K11","name":"test_count_production","value":"218/218","source":"THESIS_BRIEF.md","doi":"10.5281/zenodo.20119582","maturity":"measured"},{"id":"K12","name":"test_count_demo","value":"37/37","source":"replit_payload_build","commit":"demo","maturity":"measured"},{"id":"K13","name":"bekenstein_indicator_fire_rate","value":"49.5%","source":"thesis.md §4.5","doi":"10.5281/zenodo.20119582","maturity":"measured"}],"extracted_constants":[{"id":"C0001","name":"receipt_build_p50_us","value":"11.5","raw":"receipt build p50 = 11.5 µs","context":"0).** A production Rust runtime with 218/218 tests passing, receipt build p50 = 11.5 µs (62,764 ops/sec), receipt verify p50 = 10.4 µs (74,149 ops/sec","source_file":"thesis.md","source_line":83,"source_id":"thesis_session"},{"id":"C0003","name":"receipt_verify_p50_us","value":"10.4","raw":"receipt verify p50 = 10.4 µs","context":"ests passing, receipt build p50 = 11.5 µs (62,764 ops/sec), receipt verify p50 = 10.4 µs (74,149 ops/sec), and 100% ρ-closure on 8,000/8,000 paired ca","source_file":"thesis.md","source_line":83,"source_id":"thesis_session"},{"id":"C0008","name":"receipt_build_p99_us","value":"50.7","raw":"p99 = 50.7 µs","context":"→ Receipt` — constructs a receipt envelope; p50 = 11.5 µs, p99 = 50.7 µs, throughput 62,764 ops/sec. - `verify_receipt(receipt) → bool` — verifies byt","source_file":"thesis.md","source_line":269,"source_id":"thesis_session"},{"id":"C0009","name":"ops_per_sec","value":"62764","raw":"62,764 ops/sec","context":"me with 218/218 tests passing, receipt build p50 = 11.5 µs (62,764 ops/sec), receipt verify p50 = 10.4 µs (74,149 ops/sec), and 100% ρ-closure on 8,00","source_file":"thesis.md","source_line":83,"source_id":"thesis_session"},{"id":"C0010","name":"ops_per_sec","value":"74149","raw":"74,149 ops/sec","context":"0 = 11.5 µs (62,764 ops/sec), receipt verify p50 = 10.4 µs (74,149 ops/sec), and 100% ρ-closure on 8,000/8,000 paired calls [9]. The runtime enforces ","source_file":"thesis.md","source_line":83,"source_id":"thesis_session"},{"id":"C0023","name":"ops_per_sec","value":"200000","raw":"200,000 ops/sec","context":"arget for the Merkle-DAG upgrade is **5 µs build p50** at **200,000 ops/sec**. This is a 2.3× improvement in latency and a 3.2× improvement in through","source_file":"thesis.md","source_line":2100,"source_id":"thesis_session"},{"id":"C0027","name":"lambda9_base_p50_us","value":"3.12","raw":"Λ₉ base p50 = 3.12 µs","context":"9]. The runtime enforces a 9-axis conjunctive quality gate (Λ₉ base p50 = 3.12 µs) and a Λ₁₀ platform layer with 0.49–0.59 ms/route overhead validated","source_file":"thesis.md","source_line":83,"source_id":"thesis_session"},{"id":"C0029","name":"tests_passed","value":"218","raw":"218/218 passing","context":"ify-p50 with 100% ρ-closure on 8,000/8,000 paired calls and 218/218 passing tests. We propose `lambda9_mask` as a privacy-preserving extension to SCIT","source_file":"thesis.md","source_line":27,"source_id":"thesis_session"},{"id":"C0031","name":"tests_passed","value":"37","raw":"37/37 tests","context":"nt invocations of the same input. The demo payload confirms 37/37 tests passing in the Replit environment (33 `ouroboros` core + 4 `a11oy` covenant), ","source_file":"thesis.md","source_line":249,"source_id":"thesis_session"},{"id":"C0044","name":"http_calls","value":"24800","raw":"24,800 HTTP calls","context":"orm layer with 0.49–0.59 ms/route overhead validated across 24,800 HTTP calls.  2. **Lean 4 formal axioms and proofs (`lutar-lean`).** A Mathlib-groun","source_file":"thesis.md","source_line":83,"source_id":"thesis_session"},{"id":"C0053","name":"lambda_p50_us","value":"11.5","raw":"p50 = 11.5 µs (62,764 ops/sec), receipt verify p50 = 10.4 µs (74,149 ops/sec), and 100% ρ-closure on 8,000/8,000 paired calls [9]. The runtime enforces a 9-axis conjunctive quality gate (Λ","context":"tion Rust runtime with 218/218 tests passing, receipt build p50 = 11.5 µs (62,764 ops/sec), receipt verify p50 = 10.4 µs (74,149 ops/sec), and 100% ρ-","source_file":"thesis.md","source_line":83,"source_id":"thesis_session"},{"id":"C0054","name":"lambda_p50_us","value":"3.12","raw":"p50 = 3.12 µs) and a Λ","context":"runtime enforces a 9-axis conjunctive quality gate (Λ₉ base p50 = 3.12 µs) and a Λ₁₀ platform layer with 0.49–0.59 ms/route overhead validated across ","source_file":"thesis.md","source_line":83,"source_id":"thesis_session"},{"id":"C0055","name":"receipt_build_p99_us","value":"50.7","raw":"p99 = 50.7 µs","context":"bers - **218/218 tests** - Receipt build p50 = **11.5 µs**, p99 = 50.7 µs (62,764 ops/sec) - Receipt verify p50 = **10.4 µs** (74,149 ops/sec) - Λ₉ ba","source_file":"THESIS_BRIEF.md","source_line":57,"source_id":"thesis_brief"},{"id":"C0056","name":"ops_per_sec","value":"62764","raw":"62,764 ops/sec","context":"8 tests** - Receipt build p50 = **11.5 µs**, p99 = 50.7 µs (62,764 ops/sec) - Receipt verify p50 = **10.4 µs** (74,149 ops/sec) - Λ₉ base p50 = 3.12 µ","source_file":"THESIS_BRIEF.md","source_line":57,"source_id":"thesis_brief"},{"id":"C0057","name":"ops_per_sec","value":"74149","raw":"74,149 ops/sec","context":"0.7 µs (62,764 ops/sec) - Receipt verify p50 = **10.4 µs** (74,149 ops/sec) - Λ₉ base p50 = 3.12 µs / composed p50 = 3.29 µs - 100% ρ-closure on **8,0","source_file":"THESIS_BRIEF.md","source_line":58,"source_id":"thesis_brief"},{"id":"C0058","name":"lambda9_base_p50_us","value":"3.12","raw":"Λ₉ base p50 = 3.12 µs","context":"/sec) - Receipt verify p50 = **10.4 µs** (74,149 ops/sec) - Λ₉ base p50 = 3.12 µs / composed p50 = 3.29 µs - 100% ρ-closure on **8,000/8,000 paired ca","source_file":"THESIS_BRIEF.md","source_line":59,"source_id":"thesis_brief"},{"id":"C0059","name":"tests_passed","value":"218","raw":"218/218 tests","context":"boros v6.3.0 (released 2026-05-13) — production numbers - **218/218 tests** - Receipt build p50 = **11.5 µs**, p99 = 50.7 µs (62,764 ops/sec) - Receip","source_file":"THESIS_BRIEF.md","source_line":56,"source_id":"thesis_brief"},{"id":"C0060","name":"tests_passed","value":"37","raw":"37/37 tests","context":"plit demo payload (verified live 2026-05-15 at 11:22 EDT) - 37/37 tests passing (33 ouroboros core + 4 a11oy covenant) - `bash scripts/doctrine-check.","source_file":"THESIS_BRIEF.md","source_line":68,"source_id":"thesis_brief"},{"id":"C0061","name":"http_calls","value":"24800","raw":"24,800 HTTP calls","context":"ρ-closure on **8,000/8,000 paired calls** - Platform v11: **24,800 HTTP calls validated**, Λ₁₀ overhead 0.49–0.59 ms/route, p99 ≤ 1.27 ms - Apache-2.0","source_file":"THESIS_BRIEF.md","source_line":61,"source_id":"thesis_brief"},{"id":"C0062","name":"receipt_build_p50_us","value":"11.5","raw":"Receipt build p50 = 11.5 µs","context":"e not. | 12–18 months — they have a runtime, not a kernel | Receipt build p50 = 11.5 µs · v11 DOI [`zenodo.20119582`](https://doi.org/10.5281/zenodo.2","source_file":"master_evolution_memo.md","source_line":81,"source_id":"master_memo"},{"id":"C0064","name":"receipt_build_p99_us","value":"50.7","raw":"p99 = 50.7 µs","context":"218 / 218 passing** | | Receipt build | p50 = **11.5 µs** · p99 = 50.7 µs · 62,764 ops/sec | | Receipt verify | p50 = **10.4 µs** · 74,149 ops/sec | |","source_file":"master_evolution_memo.md","source_line":36,"source_id":"master_memo"},{"id":"C0065","name":"ops_per_sec","value":"62764","raw":"62,764 ops/sec","context":"g** | | Receipt build | p50 = **11.5 µs** · p99 = 50.7 µs · 62,764 ops/sec | | Receipt verify | p50 = **10.4 µs** · 74,149 ops/sec | | Λ₉ base | p50 =","source_file":"master_evolution_memo.md","source_line":36,"source_id":"master_memo"},{"id":"C0066","name":"ops_per_sec","value":"74149","raw":"74,149 ops/sec","context":"s · 62,764 ops/sec | | Receipt verify | p50 = **10.4 µs** · 74,149 ops/sec | | Λ₉ base | p50 = 3.12 µs | | Λ₉ composed | p50 = **3.29 µs** | | ρ-closu","source_file":"master_evolution_memo.md","source_line":37,"source_id":"master_memo"},{"id":"C0067","name":"tests_passed","value":"37","raw":"37/37 tests","context":"ic-facing Replit demo (`replit_a11oy_demo`) currently shows 37/37 tests passing. The upstream runtime is **218/218**. Every Series A diligence visitor","source_file":"master_evolution_memo.md","source_line":141,"source_id":"master_memo"},{"id":"C0068","name":"tests_passed","value":"218","raw":"218/218 tests","context":"astructure.  **Success metric:** the Replit demo URL shows \"218/218 tests · v6.3.0 · OpenSSF 8.2\" with the same badge as the canonical repo, refreshed","source_file":"master_evolution_memo.md","source_line":152,"source_id":"master_memo"},{"id":"C0070","name":"receipt_build_p50_us","value":"11.5","raw":"Receipt build p50=11.5 µs","context":"rg/doc/draft-morrow-sogomonian-exec-outcome-attest/00/)). | Receipt build p50=11.5 µs, 218/218 tests, v11 DOI: [10.5281/zenodo.20119582](https://doi.o","source_file":"pm_memo.md","source_line":54,"source_id":"pm_memo"},{"id":"C0072","name":"ops_per_sec","value":"62764","raw":"62,764 ops/sec","context":"Claim:** Receipt build p50 = 11.5 µs, verify p50 = 10.4 µs, 62,764 ops/sec, 218/218 runtime tests, ρ-closure 8,000/8,000, byte-identical replay root `","source_file":"pm_memo.md","source_line":81,"source_id":"pm_memo"},{"id":"C0073","name":"tests_passed","value":"218","raw":"218/218 tests","context":"ian-exec-outcome-attest/00/)). | Receipt build p50=11.5 µs, 218/218 tests, v11 DOI: [10.5281/zenodo.20119582](https://doi.org/10.5281/zenodo.20119582)","source_file":"pm_memo.md","source_line":54,"source_id":"pm_memo"},{"id":"C0076","name":"tests_passed","value":"37","raw":"37/37 tests","context":"arity + Public Scorecard  **Thesis:** The Replit demo shows 37/37 tests (ouroboros 33 + a11oy 4). The live runtime is 218/218. This delta undersells t","source_file":"pm_memo.md","source_line":135,"source_id":"pm_memo"},{"id":"C0077","name":"http_calls","value":"24800","raw":"24,800 HTTP calls","context":"ships a Λ₉-gated resource. | Ouroboros v6.3.0 platform v11: 24,800 HTTP calls, Λ₁₀ overhead 0.49–0.59 ms/route | | **Mastra** ([mastra.ai](https://mas","source_file":"pm_memo.md","source_line":57,"source_id":"pm_memo"},{"id":"C0078","name":"receipt_build_p50_us","value":"11.5","raw":"Receipt build p50 = 11.5 µs","context":"-witness guarantee baked into `ouroboros`'s runtime kernel. Receipt build p50 = 11.5 µs; verify p50 = 10.4 µs; 100% ρ-closure on 8,000/8,000 paired ca","source_file":"cto_memo.md","source_line":78,"source_id":"cto_memo"},{"id":"C0079","name":"ops_per_sec","value":"62764","raw":"62,764 ops/sec","context":"in · p50 = 11.5 µs build / 10.4 µs verify · 218/218 tests · 62,764 ops/sec | | `a11oy` | Covenant policy + approval queue | **HEART** (consent + pulse","source_file":"cto_memo.md","source_line":18,"source_id":"cto_memo"},{"id":"C0080","name":"tests_passed","value":"218","raw":"218/218 tests","context":"ss · receipt chain · p50 = 11.5 µs build / 10.4 µs verify · 218/218 tests · 62,764 ops/sec | | `a11oy` | Covenant policy + approval queue | **HEART** ","source_file":"cto_memo.md","source_line":18,"source_id":"cto_memo"},{"id":"C0081","name":"ops_per_sec","value":"62764","raw":"62,764 ops/sec","context":"218 / 218 passing | 100% | | Receipt build p50 | 11.5 µs | 62,764 ops/sec | | Receipt build p99 | 50.7 µs | — | | Receipt verify p50 | 10.4 µs | 74,14","source_file":"runtime_memo.md","source_line":20,"source_id":"runtime_memo"},{"id":"C0082","name":"ops_per_sec","value":"74149","raw":"74,149 ops/sec","context":"build p99 | 50.7 µs | — | | Receipt verify p50 | 10.4 µs | 74,149 ops/sec | | Λ₉ base p50 | 3.12 µs | — | | Λ₉ composed p50 | 3.29 µs | — | | ρ-closur","source_file":"runtime_memo.md","source_line":22,"source_id":"runtime_memo"},{"id":"C0083","name":"tests_passed","value":"218","raw":"218/218 tests","context":"ary (5 lines)  The ouroboros v6.3.0 runtime is confirmed at 218/218 tests, receipt build p50 11.5 µs, Λ₉ composed p50 3.29 µs, and 100% ρ-closure — al","source_file":"runtime_memo.md","source_line":404,"source_id":"runtime_memo"},{"id":"C0084","name":"http_calls","value":"11","raw":"11 HTTP calls","context":"9 µs | — | | ρ-closure | 8,000 / 8,000 | 100% | | Platform v11 HTTP calls | 24,800 | — | | Λ overhead p50 per route | 0.49–0.59 ms | — | | Λ overhead ","source_file":"runtime_memo.md","source_line":26,"source_id":"runtime_memo"},{"id":"C0085","name":"ops_per_sec","value":"74149","raw":"74,149 ops/sec","context":"pt verify p50 | **10.4 µs** | | Receipt verify throughput | 74,149 ops/sec | | Λ₉ base p50 | 3.12 µs | | Λ₉ composed p50 | 3.29 µs | | ρ-closure | 100","source_file":"data_memo.md","source_line":419,"source_id":"data_memo"}],"dois":[{"doi":"10.5281/zenodo.19944926","url":"https://doi.org/10.5281/zenodo.19944926","source_file":"thesis.md","source_line":18,"source_id":"thesis_session"},{"doi":"10.5281/zenodo.20119582","url":"https://doi.org/10.5281/zenodo.20119582","source_file":"thesis.md","source_line":19,"source_id":"thesis_session"},{"doi":"10.5281/zenodo.19867281","url":"https://doi.org/10.5281/zenodo.19867281","source_file":"thesis.md","source_line":1740,"source_id":"thesis_session"},{"doi":"10.5281/zenodo.19934129","url":"https://doi.org/10.5281/zenodo.19934129","source_file":"thesis.md","source_line":1741,"source_id":"thesis_session"},{"doi":"10.5281/zenodo.19983066","url":"https://doi.org/10.5281/zenodo.19983066","source_file":"thesis.md","source_line":1743,"source_id":"thesis_session"},{"doi":"10.5281/zenodo.20020841","url":"https://doi.org/10.5281/zenodo.20020841","source_file":"thesis.md","source_line":1744,"source_id":"thesis_session"},{"doi":"10.5281/zenodo.20020845","url":"https://doi.org/10.5281/zenodo.20020845","source_file":"thesis.md","source_line":1745,"source_id":"thesis_session"},{"doi":"10.5281/zenodo.20020846","url":"https://doi.org/10.5281/zenodo.20020846","source_file":"thesis.md","source_line":1746,"source_id":"thesis_session"},{"doi":"10.5281/zenodo.20020848","url":"https://doi.org/10.5281/zenodo.20020848","source_file":"thesis.md","source_line":1747,"source_id":"thesis_session"},{"doi":"10.5281/zenodo.20020849","url":"https://doi.org/10.5281/zenodo.20020849","source_file":"thesis.md","source_line":1748,"source_id":"thesis_session"},{"doi":"10.5281/zenodo.20053148","url":"https://doi.org/10.5281/zenodo.20053148","source_file":"thesis.md","source_line":1749,"source_id":"thesis_session"},{"doi":"10.5281/zenodo.20053163","url":"https://doi.org/10.5281/zenodo.20053163","source_file":"thesis.md","source_line":1750,"source_id":"thesis_session"},{"doi":"10.5281/zenodo.20162352","url":"https://doi.org/10.5281/zenodo.20162352","source_file":"thesis.md","source_line":1752,"source_id":"thesis_session"}],"doctrine_clauses":[{"id":"DC1","clause":"Byline must be 'Lutar, Stephen P.' — never 'Jr.' or 'Stephen Paul'","source":"THESIS_BRIEF.md"},{"id":"DC2","clause":"8 forbidden patterns: see doctrine.json (FP-1..FP-8)","source":"PM_LEAD_CHARTER_V2.md"},{"id":"DC3","clause":"License allow-list: Apache-2.0, MIT, BSD-3-Clause, CC-BY-4.0","source":"THESIS_BRIEF.md"},{"id":"DC4","clause":"ORCID: 0009-0001-0110-4173","source":"THESIS_BRIEF.md"},{"id":"DC5","clause":"9-axis Λ >= 0.90 conjunctive AND; moralGrounding + measurabilityHonesty >= 0.95","source":"THESIS_BRIEF.md"},{"id":"DC6","clause":"Public-only ingestion: no private data, no proprietary code","source":"THESIS_BRIEF.md"},{"id":"DC7","clause":"5x byte-identical replay (deterministic)","source":"THESIS_BRIEF.md"},{"id":"DC8","clause":"No hallucinations; every empirical claim cites a verifiable artifact","source":"THESIS_BRIEF.md"}],"source_files":["thesis.md","THESIS_BRIEF.md","master_evolution_memo.md","pm_memo.md","cto_memo.md","runtime_memo.md","governance_memo.md","data_memo.md","anatomy_memo.md"],"zenodo_corpus":["10.5281/zenodo.19867281","10.5281/zenodo.19934129","10.5281/zenodo.19944926","10.5281/zenodo.19983066","10.5281/zenodo.20020841","10.5281/zenodo.20020846","10.5281/zenodo.20020845","10.5281/zenodo.20020848","10.5281/zenodo.20020849","10.5281/zenodo.20053148","10.5281/zenodo.20053163","10.5281/zenodo.20119582","10.5281/zenodo.20162352"],"proof_summary":{"locked_proven":5,"locked_ids":["F1","F11","F12","F18","F19"],"experimental_sorry_free":21,"axiom_gated":3,"axiom_gated_detail":{"f13_tamper_evident":"hash_collision_resistant","f14_sigenv_verifiable":"ecdsa_unforgeable","f15_inclusion_binding":"h2_collision_resistant"},"conjecture":["F23"],"note":"Locked kernel proven=5; experimental scope Lutar/Puriq/Formulas has 21 sorry-free (excluded from locked count); F23 = Conjecture 1, NOT a theorem.","lean_repo":"szl-holdings/lutar-lean","lean_files":["Lutar/Puriq/Formulas/PuriqFormulaLean.lean","Lutar/Puriq/Formulas/F23_Uniqueness.lean"],"verification":"bare `lean` 4.13.0, 0 errors, 1 sorry (F23 only); #print axioms shows no sorryAx in any proved theorem.","source_report":"team/PROOFS_WAVE2_REPORT.md","wave3":{"campaign":"prove-wave-3 (C1-C20 research candidates)","source_report":"team/PROVE_WAVE3_REPORT.md","lean_repo":"szl-holdings/lutar-lean","commit_proofs":"775093f0f8ef7f530272c38d513c28fdaec3366b","commit_root_wiring":"02e44c30657c9986475ff7373113728f4ba38f67","lean_files":["Lutar/Wave3/Consensus.lean","Lutar/Wave3/MerkleKraft.lean","Lutar/Wave3/InfoEstim.lean","Lutar/Wave3/Tier1Mathlib.lean (CI-pending, not wired into lake build)"],"verification":"Mathlib-free modules bare-`lean` 4.13.0 verified sorry-free (0 errors); #print axioms ledger shows no sorryAx. Tier1Mathlib (C1/C2/C6) is Mathlib-dependent and CI-pending, NOT compiled in sandbox.","new_proven_sorry_free":19,"new_proven_ids":["C8","C9","C10","C11","C12","C17","C20"],"new_axiom_gated":4,"new_axiom_gated_detail":{"c13_md_step_cr":"compression_collision_resistant","c13a_md_append_cr":"compression_collision_resistant","c14_merkle_binding":"node_collision_resistant, leaf_collision_resistant, domain_separation","c14b_no_second_preimage":"domain_separation (structural tag only, no hardness)"},"ci_pending":["C1","C2","C6"],"ci_pending_detail":"C1 tsirelson_inequality, C2 CHSH_inequality_of_comm, C6 ConvexOn.map_sum_le re-exports; Mathlib-dependent, awaiting green lake build.","maturity":{"C1":"ci-pending","C2":"ci-pending","C3":"mathlib-available-not-instantiated","C4":"mathlib-available-not-instantiated","C5":"mathlib-available-not-instantiated","C6":"ci-pending","C7":"axiom-gated (A6_bisymmetric); Lambda still Conjecture 1","C8":"proven","C9":"proven (Mathlib-free fragment; full L>=H is Mathlib target)","C10":"proven","C11":"proven","C12":"proven (bivalence core; full FLP not claimed)","C13":"axiom-gated","C14":"axiom-gated","C15":"lean-exists-not-ported","C16":"not-attempted","C17":"proven (Mathlib-free scalar core; full matrix-PSD is Mathlib target)","C18":"lean-exists-not-ported","C19":"not-attempted","C20":"proven (Mathlib-free order-preservation core; tight 1/2-Lipschitz is Mathlib target)"},"lambda_status":"F23 = Conjecture 1 (UNCHANGED). C7 is conditional only, via the DECLARED axiom A6_bisymmetric in F23_Uniqueness.lean; unconditional uniqueness is FALSE under A1-A5 (maxAgg_ne_Lambda).","locked_kernel":"749/14/163 @ c7c0ba17 (Doctrine v11) UNCHANGED; wave3 is experimental and counter-excluded from the locked count.","headline":"+19 sorry-free (Lean-core axioms only, bare-lean verified), +4 axiom-gated (declared idealizations), 3 Mathlib re-exports CI-pending, Lambda still Conjecture 1."},"wave4":{"campaign":"prove-wave-4 (conditional Lambda uniqueness on the WEAKER block-consistency axiom)","source_report":"team/PROVE_WAVE4_REPORT.md","candidate_research":"team/RESEARCH_WAVE4/CANDIDATE_FORMULAS_V4.md","lean_repo":"szl-holdings/lutar-lean","commit_final":"043c3df4bcbe55c60f1ce2d5c59b91284a7cc1d4","commit_ci_green_lambda":"52d9bf542bcb1adb8a0a5a5de694f2ca96bf9b68","lean_files":["Lutar/Wave4/LambdaBlockConsistency.lean (Mathlib-dependent, CI-green: lake build + kernel check success @ 043c3df)","Lutar/Wave4/LambdaBisymmetryWitness.lean (bare-`lean` 4.13.0 verified sorry-free, ZERO axioms; also CI-green)","Lutar/Wave3/Tier1Mathlib.lean (CI-PENDING, NOT wired into the compiled root)"],"ci_status":"build + lake build + numbers + check/doctrine all GREEN @ 043c3df; only doi-title-gate fails (PRE-EXISTING live-network README DOI check, unrelated to wave4).","verification":"LambdaBlockConsistency kernel-checked by lutar-lean CI lake build (green). LambdaBisymmetryWitness bare-`lean` verified: all 6 theorems 'do not depend on any axioms'. Every theorem carries #print axioms.","new_proven_ci_green":{"lambda_unique_under_block":"CLOSED, conditional on declared axiom A6'_block_consistent; #print axioms = [A6'_block_consistent, propext, Quot.sound, Classical.choice]","lambda_factors":"CLOSED, AXIOM-FREE (Mathlib core only): Lambda factors with exponents 1/k, so A6' is non-vacuous","unconditional_lambda_is_false":"CLOSED (= maxAgg_ne_Lambda): unconditional Lambda uniqueness is FALSE under A1-A5"},"witness_theorems_zero_axiom":["Fmax_not_strict","Fmin_not_strict","geo_separates_where_max_collapses","geo_bisym_product_eq","geo_fourth_root_consistent","geo_inner_products_consistent"],"lambda_axiom_set":"{A1,A2,A3,A4,A5} + A6'_block_consistent (single DECLARED, disclosed, NON-core axiom).","lambda_weakest_axiom":"Cleanest published: Aczel-Saaty 1983 (doi:10.1016/0022-2496(83)90028-7) = reciprocity + positive homogeneity (A2 already assumed). Weakest governance-natural & formalized: Csato 2018 block-consistency / aggregation-invariance (doi:10.1007/s10726-018-9589-3, arXiv:1706.07256), WEAKER than the prior A6_bisymmetric.","lambda_status":"F23 = Conjecture 1 (UNCHANGED, unconditional). Conditional uniqueness now CI-green on the WEAKER A6'_block_consistent (lambda_unique_under_block), superseding the stronger A6_bisymmetric route. Unconditional uniqueness FALSE (maxAgg_ne_Lambda). NEVER conflated.","ci_pending":["C1","C2","C6"],"ci_pending_detail":"C1 tsirelson_inequality / C2 CHSH_inequality_of_comm / C6 ConvexOn.map_sum_le re-exports. Signatures verified VERBATIM vs pinned Mathlib d731765, but wiring Tier1Mathlib into the compiled root reproducibly red-lights lake build (bisected: a4299fb/52d9bf5 un-wired = green). Exact error not retrievable (CI log download proxy-blocked). File stays in-tree, NOT imported; NOT claimed proven.","locked_kernel":"749/14/163 @ c7c0ba17 UNCHANGED","locked_proven":5,"canonical_numbers":{"declarations":1182,"axioms_raw":20,"axioms_unique":19,"new_axiom":"A6'_block_consistent (declared, disclosed, NON-core, NOT in locked kernel)","sorries_raw":308,"sorries_noncomment":256,"drift_gate":"PASS"},"citations":["Aczel 1948","Aczel-Saaty 1983 doi:10.1016/0022-2496(83)90028-7","Csato 2018 doi:10.1007/s10726-018-9589-3 arXiv:1706.07256","Kolmogorov 1930","Maksa-Munnich-Mokken","Burai-Kiss-Szokol 2021"]},"wave5":{"campaign":"prove-wave-5: un-block C1/C2/C6 Mathlib re-exports (CI-GREEN) + new substrate re-exports (AM-GM/Cauchy-Schwarz) + Mathlib-free discrete substrate guarantees (bare-lean verified)","source_report":"team/PROVE_WAVE5_REPORT.md","lean_repo":"szl-holdings/lutar-lean","branch":"prove-wave5/c1c2c6-rewire-plus-amgm-cs","pull_request":"https://github.com/szl-holdings/lutar-lean/pull/186","commit_ci_green":"0a552a90dd7f3b8b668ae761bf6e39eca17c62f1","ci_run_ids":{"lean_kernel_check":"27053443102 (success)","lake_build_gate_numbers":"27053443099 (success)","doctrine":"27053443200 (success)","dco":"27053443096 (success)"},"ci_status":"build (Lean kernel check) + lake build + numbers + check/doctrine + DCO all GREEN @ 0a552a90 (and @ 099d6caa). Only doi-title-gate + PR-title-lint fail (PRE-EXISTING / cosmetic, unrelated to proofs).","headline":"C1 Tsirelson 2sqrt2 / C2 CHSH<=2 / C6 Jensen are now CI-GREEN (wave-4 had them CI-PENDING). Root cause fixed: dropped the non-load-bearing c1a_tsirelson_constant numeric remark and its two extra SpecialFunctions imports, minimizing Tier1Mathlib's build closure to exactly the two modules that define the instantiated theorems.","ci_green_mathlib_dependent":{"Wave3.Tier1.c1_lutar_omega_tsirelson_ceiling":"C1 Tsirelson 2sqrt2 ceiling (tsirelson_inequality) — PROVEN, CI-green. EPR-Bell governance diagnostic (entangled-agent ceiling).","Wave3.Tier1.c2_lutar_omega_classical_ceiling":"C2 CHSH classical ceiling <=2 (CHSH_inequality_of_comm) — PROVEN, CI-green. Local/independent-prior agent ceiling.","Wave3.Tier1.c6_jensen_forecaster":"C6 finite Jensen (ConvexOn.map_sum_le) — PROVEN, CI-green. Active-inference ELBO-direction conservative forecaster.","Wave5.MathlibCore.w5_1_lambda_le_arith_mean":"W5-1 weighted AM-GM (Real.geom_mean_le_arith_mean_weighted) — PROVEN, CI-green. Lambda (geometric-mean aggregator) <= arithmetic mean: no-inflation guarantee.","Wave5.MathlibCore.w5_1b_lambda2_le_arith_mean":"W5-1b two-point weighted AM-GM — PROVEN, CI-green. Pairwise consensus diagnostic.","Wave5.MathlibCore.w5_2_trust_inner_le_norm":"W5-2 Cauchy-Schwarz (real_inner_le_norm) — PROVEN, CI-green. Trust-vector similarity bound (cosine in [-1,1])."},"proven_mathlib_free_bare_lean":{"Wave5.DiscreteSubstrate.w5_3a_miscover_le_total":"miscoverage<=sample size. axioms=[propext]. killinchu conformal coverage.","Wave5.DiscreteSubstrate.w5_3b_cover_miscover_partition":"covered+miscovered=total. axioms=[propext, Quot.sound]. coverage=1-miscoverage conservation.","Wave5.DiscreteSubstrate.w5_3c_threshold_count_mono":"stricter threshold selects fewer. axioms=[propext, Quot.sound]. a11oy threshold monotonicity.","Wave5.DiscreteSubstrate.w5_4_collision_of_image_dup":"image-duplicate => hash collision (pigeonhole). axioms=[propext, Classical.choice, Quot.sound]. UDS forgery-detection.","Wave5.DiscreteSubstrate.w5_5_no_early_stop_deflation":"monotone optional-stopping anti-deflation. ZERO axioms. UDS receipt-stream anti-gaming."},"axiom_disclosure":"Mathlib-dependent re-exports use the standard Mathlib trio [propext, Classical.choice, Quot.sound] (NO sorryAx, NO declared Lutar axioms); their #print axioms are emitted in the CI build log (blob log download proxy-blocked here, but the build is green and they are pure term-mode instantiations of axiom-clean Mathlib theorems). Mathlib-free theorems' #print axioms pasted verbatim in PROVE_WAVE5_REPORT.md section 3 (bare lean 4.13.0, exit 0).","not_available_at_pinned_mathlib":"C3 Hoeffding / C4 Azuma (Mathlib.Probability.Moments.SubGaussian) and C5 KL>=0 (Mathlib.InformationTheory.KullbackLeibler.Basic) modules DO NOT EXIST at the pinned rev d7317655 (v4.13.0) — verified HTTP 404. They cannot be re-exported on this toolchain; deferred to a future Mathlib bump. Honestly NOT claimed.","lambda_status":"Lambda (F23) STAYS Conjecture 1 unconditionally. W5-1 AM-GM is a building block Lambda relies on; it does NOT prove uniqueness. Unconditional uniqueness remains FALSE (wave-4 counterexample in-tree).","locked_kernel":"749/14/163 @ c7c0ba17 UNCHANGED. locked_proven=5 UNCHANGED. All wave-5 work is experimental scope (counter-excluded).","canonical_numbers":{"declarations":1189,"axioms_raw":20,"axioms_unique":19,"sorries_raw":308,"sorries_noncomment":256,"delta_decls_from_wave4":"+5 net (1184->1189; -1 c1a, +3 MathlibCore, +5 DiscreteSubstrate vs wave4 baseline 1182 -> 1189)"},"citations":["Tsirelson (1980) doi:10.1007/BF00417500","CHSH (1969) doi:10.1103/PhysRevLett.23.880","Jensen (1906)","Hardy-Littlewood-Polya, Inequalities (1934) [AM-GM]","Cauchy (1821); Schwarz (1888)","Vovk-Gammerman-Shafer (2005); Lei et al. (2018) JASA 113:1094 [conformal]","Dirichlet (1834) [pigeonhole]","Doob (1953) Stochastic Processes [optional stopping]"]},"experimental_sorry_free_note":"wave5 adds 11 kernel-verified experimental theorems (6 Mathlib-dependent CI-green: C1/C2/C6 + W5-1/W5-1b/W5-2; 5 Mathlib-free bare-lean: W5-3a/b/c, W5-4, W5-5). Prior experimental_sorry_free baseline was 21 (wave-2 F-pack ceiling).","wave5_proven_count":{"mathlib_dependent_ci_green":6,"mathlib_free_bare_lean":5,"total_new":11}},"puriq_formulas":[{"id":"F1","name":"Replay-Hash Determinism","statement":"Deterministic step-fold replay: equal logs replay to equal final state; folded state equals last of the explicit replay trace.","maturity":"proven","lean_ref":"f1_replay_fold_deterministic","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean","locked_kernel":true},{"id":"F2","name":"Scheduler Liveness","statement":"Fair round-robin scheduler: every ready organ eventually ticks (strictly-decreasing Nat ranking measure reaches 0).","maturity":"proven","lean_ref":"f2_scheduler_liveness","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean"},{"id":"F3","name":"Organ Boot-Gate Soundness","statement":"If the boot gate permits an organ, its genome is valid (decidable implication).","maturity":"proven","lean_ref":"f3_genome_gate_sound","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean"},{"id":"F4","name":"Receipt-Chain Acyclicity","statement":"Appending the new largest-index node preserves DAG acyclicity (backward-edge invariant).","maturity":"proven","lean_ref":"f4_rcptchain_dag_acyclic","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean"},{"id":"F5","name":"Unay Receipt Recall","statement":"Insert-then-lookup on the same receipt key returns the inserted value (exact-key recall correctness).","maturity":"proven","lean_ref":"f5_unay_recall_correct","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean"},{"id":"F6","name":"LMDB Durability","statement":"Commit-then-restart-then-read returns the committed value; uncommitted writes are lost on crash (WAL model).","maturity":"proven","lean_ref":"f6_lmdb_durability","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean"},{"id":"F7","name":"Chaski FIFO Ordering","statement":"Enqueue-batch-then-drain yields send order; head is the oldest message (true FIFO, no tautology).","maturity":"proven","lean_ref":"f7_chaski_fifo","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean"},{"id":"F8","name":"Wallpa OSS-Only Safety","statement":"Governed-voice admission gate admits only OSS sources; no humanClone or synthetic config is ever admitted.","maturity":"proven","lean_ref":"f8_wallpa_oss_only","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean"},{"id":"F9","name":"Wasi-Rikuq Non-Interference","statement":"Advisory non-interference (Goguen-Meseguer 1982): the low view is unchanged by high inputs.","maturity":"proven","lean_ref":"f9_wasi_rikuq_noninterference","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean"},{"id":"F10","name":"Hatun MCP Idempotency","statement":"MCP request normalizer is idempotent: normalizing twice equals normalizing once.","maturity":"proven","lean_ref":"f10_hatun_mcp_idempotent","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean"},{"id":"F11","name":"Ayni Reciprocity Conservation","statement":"Event-sourcing replay invariant: balance reciprocity is conserved; tit-for-tat parity (Axelrod-Hamilton).","maturity":"proven","lean_ref":"f11_ayni_reciprocity_conservation","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean","locked_kernel":true},{"id":"F12","name":"Kuramoto Phase-Coupling Boundedness","statement":"Discrete additive coupling is bounded and superposes over an organ set. CAVEAT: additive fragment only, NOT nonlinear Kuramoto synchronisation.","maturity":"proven","lean_ref":"f12_kuramoto_superposition","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean","locked_kernel":true},{"id":"F13","name":"Wayra Hash-Chain Verification","statement":"Hash-chain verification is sound by induction: a verified chain has every link consistent.","maturity":"proven","lean_ref":"f13_wayra_chain_verified","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean","declared_axiom":"hash_collision_resistant (tamper-evidence f13_tamper_evident)"},{"id":"F14","name":"Signature Verifiable Attribution","statement":"A signature-envelope signature that verifies attributes the message to the key. AXIOM-GATED on declared `ecdsa_unforgeable`.","maturity":"axiom-gated","lean_ref":"f14_sigenv_verifiable","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean","declared_axiom":"ecdsa_unforgeable"},{"id":"F15","name":"Rekor Merkle Inclusion","statement":"Merkle inclusion checker is sound (structural). Binding form (equal roots => equal leaves) is AXIOM-GATED on declared `h2_collision_resistant`.","maturity":"proven","lean_ref":"f15_rekor_inclusion","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean","declared_axiom":"h2_collision_resistant (binding form f15_inclusion_binding)"},{"id":"F16","name":"Safety-Gate Coverage Completeness","statement":"Immune cross-cut completeness: 8 gates cover all 8 enumerated threats; gate set is exhaustive.","maturity":"proven","lean_ref":"f16_safegate_immune_complete","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean"},{"id":"F17","name":"Three-Vertical Isolation","statement":"The three verticals are pairwise disjoint (isolation by construction).","maturity":"proven","lean_ref":"f17_three_vertical_isolation","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean"},{"id":"F18","name":"Reed-Solomon RS(10,6) Recovery","statement":"RS(10,6) parity arithmetic: data is recoverable iff at least 6 of 10 shards survive (tolerates 4 erasures).","maturity":"proven","lean_ref":"f18_reed_solomon_parity_count","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean","locked_kernel":true},{"id":"F19","name":"Bekenstein Entropy Budget","statement":"Entropy budget is additive and monotone over a region partition; each region <= total. CAVEAT: additive scaffolding only, NOT the full Bekenstein bound S <= 2*pi*k*R*E/(hbar*c).","maturity":"proven","lean_ref":"f19_budget_total_cons","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean","locked_kernel":true},{"id":"F20","name":"Mobile Input Equivalence","statement":"Touch and pointer inputs are equivalent under the normalization map (decidable and sound).","maturity":"proven","lean_ref":"f20_mobile_input_equiv","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean"},{"id":"F21","name":"Genome Validator Totality","statement":"The genome validator is total over Fin 16: every organ validates.","maturity":"proven","lean_ref":"f21_all_organs_valid","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean"},{"id":"F22","name":"Receipt Emit Monotonicity","statement":"Emit appends to the sequence log with strictly increasing sequence numbers (monotone emit).","maturity":"proven","lean_ref":"f22_rcptchain_emit_monotone","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/PuriqFormulaLean.lean"},{"id":"F23","name":"Lambda-Aggregator Uniqueness","statement":"CONJECTURE 1 (NOT a theorem). Unconditional uniqueness is FALSE under A1-A5 (maxAgg counterexample). Conditional `lambda_unique_of_factors` IS proved; unconditional uniqueness closes only under declared axiom A6_bisymmetric.","maturity":"conjectured","lean_ref":"f23_lambda_aggregator_sound","lean_repo":"szl-holdings/lutar-lean","lean_file":"Lutar/Puriq/Formulas/F23_Uniqueness.lean","declared_axiom":"A6_bisymmetric (optional, only for conditional lambda_unique_under_A6)"}],"vertical_policies":[{"policy_id":"academic","policy_name":"Academic / Research Integrity","version":"0.3.0","regulations":["NIH NOT-OD-23-149","NSF PAPPG Chapter II.E","ORI Standards","COPE 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 <script>
 const API='/api/a11oy';
 // a11oy is FULLY SELF-CONTAINED. Every capability below is a native, same-origin