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     <div class="nav-item" data-view="threatgraph" onclick="go('threatgraph')"><span class="ico">⩟</span>Threat Graph</div>
     <div class="nav-item" data-view="deploy" onclick="go('deploy')"><span class="ico">⧈</span>Deploy Posture</div>
     <div class="nav-item" data-view="warboard" onclick="go('warboard')"><span class="ico">✪</span>Warhacker Proofs</div>
-    <div class="side-foot">Trust score = research conjecture<br>5 formulas formally proven<br>SLSA Build L2 · 5 services<br>Verifiable receipts · honest by design</div>
+    <div class="side-foot">Trust score (Λ) = Conjecture 1 (+conditional-proven)<br>5 locked-proven + 80+ experimental CI-green<br>SLSA Build L2 · 5 services<br>Verifiable receipts · honest by design</div>
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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 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_dsse_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},"wave6":{"campaign":"prove-wave-6 (graph substrate)","pull_request":"https://github.com/szl-holdings/lutar-lean/pull/189","commit_ci_green":"dc7ae26d","ci_status":"GREEN (Lean kernel check + lake build+numbers + doctrine + DCO)","count":11,"axioms":"0 new","new_proven_ids":["F-G1","F-G2","F-G3","F-G4","F-G5","F-G6"],"headline":"Frechet/Kuratowski embedding core, GNN<=1-WL ceiling, spectral contraction, Lambda-graph iso-invariance, bounded-frontier DAG termination, relabel-invariance","maturity":"experimental-CI-green","locked_kernel":"749/14/163 @ c7c0ba17 UNCHANGED; experimental scope"},"wave7":{"campaign":"prove-wave-7","pull_request":"https://github.com/szl-holdings/lutar-lean/pull/190","commit_ci_green":"d6a232ba","ci_status":"GREEN","count":10,"axioms":"0 new","new_proven_ci_green":["W7-1a","W7-1","W7-5a","W7-5b","W7-5"],"new_proven_bare_lean":["W7-4a","W7-4b","W7-4c","W7-6a","W7-6"],"headline":"conformal rank-count/p-value + Doob two-sided audit envelope + degree-sum iso-invariance + PAC-Bayes routing envelope","maturity":"experimental-CI-green","locked_kernel":"749/14/163 @ c7c0ba17 UNCHANGED; experimental scope"},"agentic_loop":{"campaign":"prove-agentic-loop (the governed RAG->MCP->kernel->receipt loop, proven as a SYSTEM)","pull_request":"https://github.com/szl-holdings/lutar-lean/pull/188","commit_ci_green":"2ede47a2","ci_status":"GREEN","namespace":"Lutar.Agentic.Pipeline (EXPERIMENTAL_SCOPES; NOT imported into Lutar.lean)","theorems":28,"axiom_free":14,"lean_core_only":10,"axiom_gated":4,"declared_axiom":"hashFn_collision_resistant (P5 only; NIST FIPS 180-4)","properties":{"P1":"receipt-completeness","P2":"gate-soundness","P3":"non-interference (Goguen-Meseguer 1982, axiom-free core)","P4":"replay-determinism (axiom-free)","P5":"tamper-evidence (axiom-gated)","P6":"monotone auditability"},"headline":"the RAG->MCP->kernel loop is proven end-to-end; P3 (poisoned input can't flip the verdict) is the Cannonico bullseye","maturity":"experimental-CI-green (P5 axiom-gated)","locked_kernel":"749/14/163 @ c7c0ba17 UNCHANGED; experimental scope"},"coder_formulas":{"campaign":"prove-coder (a11oy Code governed coder formulas)","pull_request":"https://github.com/szl-holdings/lutar-lean/pull/193","commit_ci_green":"29e33534","ci_status":"GREEN (bare-lean sorry-free + CI build/numbers/doctrine/DCO)","theorems":27,"axiom_free":5,"lean_core_only":23,"axiom_gated":1,"declared_axiom":"codeHash_collision_resistant (1 only; standard, disclosed)","areas":{"CS1":"sandbox containment (extends P2)","CS2":"bounded exec/termination (extends F-G5)","CR3":"router envelope + argmin stability (W7-5/C20)","CV4":"consensus/Byzantine majority (C10)","CC5":"conformal code-confidence <1 (W5-3/W7-4)","CK6":"receipt-log compression (Kraft/Shannon C8/C9)","NI7":"code-context non-interference (extends P3) — poisoned dependency can't flip DENY->ALLOW"},"headline":"27 theorems innovated for the governed coder; kernel-verified two ways","maturity":"experimental-CI-green (1 axiom-gated)","locked_kernel":"749/14/163 @ c7c0ba17 UNCHANGED; experimental scope"},"lambda_setalpha_setdelta":{"campaign":"lambda-uniqueness Set alpha + Set delta (conditional uniqueness within strengthened axiom classes)","pull_request":"https://github.com/szl-holdings/lutar-lean/pull/192","commit_ci_green":"5f0bb5ee","ci_status":"GREEN (build + lake+numbers + doctrine + DCO)","results":22,"headline_theorems_approx":12,"declared_bridge_axioms":["setAlpha_cauchy","KS_theorem_1_1","setDelta_stage2"],"impostor_deaths_axiom_free":10,"what_proven":"Lambda (geometric mean) is UNIQUE within Set alpha {A1,A2,A3,A4,A5' multiplicativity} (cond. on setAlpha_cauchy) and within Set delta {d1..d4,d5' multiplicativity} (cond. on KS_theorem_1_1+setDelta_stage2). All 10 impostor-deaths AXIOM-FREE.","what_NOT_claimed":"NOT unconditional uniqueness under original A1-A5 (machine-checked FALSE: Round13.maxAgg_ne_Lambda). Lambda STAYS Conjecture 1.","maturity":"conditional (axiom-gated bridge); Lambda = Conjecture 1 unconditionally","locked_kernel":"749/14/163 @ c7c0ba17 UNCHANGED; locked_proven STAYS 5"},"mathlib_bump_c3c4c5":{"campaign":"Mathlib v4.18 bump — concentration/KL re-exports C3/C4/C5","pull_request":"https://github.com/szl-holdings/lutar-lean/pull/187","ci_status":"PROVEN on the Mathlib-v4.18 bump branch (CI-green), PENDING MERGE to main","ids":["C3","C4","C5"],"status_honest":"proven on bump branch (PR#187), pending merge to main — NOT on-main, NOT blocked","maturity":"branch-pending"},"unify_governed_run_sound":{"campaign":"unify governance substrate meta-theorem (monoid-action spine unifying P1/P4/P6 + coder corpus)","pull_request":"https://github.com/szl-holdings/lutar-lean/pull/194","commit_ci_green":"9f9c1bbd","artifact":"Lutar/Unify/GovernanceSubstrate.lean (EXPERIMENTAL scope; NOT wired into Lutar.lean)","spine":"run is a left monoid action of the free monoid (List Hop,++,[]) on St; run_append homomorphism is the unifier","theorems":["run_nil (axiom-free)","run_append","run_singleton (axiom-free)","completeness_additive","determinism_composes","chainEnd_append (axiom-free)","auditability_multiplicative","governed_run_sound"],"headline":"every compositional corpus guarantee is a corollary of one homomorphism; a synthesis (unification) theorem, not new deep pure math","maturity":"experimental-CI-green","locked_kernel":"749/14/163 @ c7c0ba17 UNCHANGED; experimental scope"},"maturity_legend":["locked","experimental-CI-green","branch-pending","axiom-gated","conditional","conjecture"],"experimental_total_note":"LOCKED proven = exactly 5 {F1,F11,F12,F18,F19} @ c7c0ba17 (749/14/163), UNCHANGED. PLUS 80+ experimental kernel-verified theorems (all CI-green, never folded into the locked 5): wave5 (11, PR#186), wave6 (11, PR#189), wave7 (10, PR#190), agentic-loop P1-P6 (28, PR#188), coder formulas (27, PR#193), Lambda Set alpha/delta (22 results / ~12 theorems, PR#192), unify governed_run_sound (PR#194). C3/C4/C5 proven on the Mathlib-v4.18 bump branch (PR#187), pending merge to main. Lambda = Conjecture 1 unconditionally (uniqueness machine-checked FALSE) + PROVEN conditionally under declared strengthened Set alpha/delta axioms (PR#192).","experimental_count_min":80},"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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2.0"],"required_attestors":["system_security_officer","control_systems_engineer","incident_commander"],"lambda_floors":{"moralGrounding":0.99,"actionReversibility":0.99,"scopeContainment":1.0,"informationIntegrity":0.99,"adversarialRobustness":0.99,"temporalConsistency":0.99},"forbidden_inputs":["unauthenticated_control_commands","non_air_gapped_ot_data"],"required_output_formats":["ics_audit_log","json_receipt","nerc_compliance_report"],"retention_days":"1825","primitives_applicable":["A4","A5","A6","A10","A13","T5","T9","T10","TH1"],"acv_range_usd":{"low":1000000.0,"mid":5000000.0,"high":20000000.0}},{"policy_id":"defense","policy_name":"Defense / DoD","version":"0.3.0","regulations":["NIST SP 800-53 Rev 5","CMMC 2.0","FedRAMP High","DISA STIGs"],"required_attestors":["authorizing_official","system_owner","security_control_assessor"],"lambda_floors":{"moralGrounding":0.99,"measurabilityHonesty":0.99,"actionReversibility":0.95,"scopeContainment":0.99,"informationIntegrity":0.99,"consentBoundary":0.95},"forbidden_inputs":["unclassified_cui_without_marking","foreign_national_data"],"required_output_formats":["json_audit_log","nist_oscal"],"retention_days":"7300","primitives_applicable":["A1","A4","A5","A6","A8","A9","A12","A13","T5","T9","T10","TH1"],"acv_range_usd":{"low":500000.0,"mid":2000000.0,"high":5000000.0}},{"policy_id":"financial_services","policy_name":"Financial Services / Banking","version":"0.3.0","regulations":["SR 11-7","OCC 2011-12","MiFID II RTS 6","Basel III"],"required_attestors":["model_risk_officer","chief_risk_officer","internal_audit"],"lambda_floors":{"moralGrounding":0.97,"measurabilityHonesty":0.99,"temporalConsistency":0.99,"informationIntegrity":0.99,"economicGrounding":1.0},"forbidden_inputs":["insider_information","unregistered_model_version"],"required_output_formats":["csv_model_log","json_receipt","pdf_board_report"],"retention_days":"2190","primitives_applicable":["A1","A5","A6","A8","A9","A14","T5","T9","T10","TH1","TH2"],"acv_range_usd":{"low":200000.0,"mid":800000.0,"high":2000000.0}},{"policy_id":"healthcare","policy_name":"Healthcare / Clinical AI","version":"0.3.0","regulations":["HIPAA 45 CFR Part 164","FDA 21 CFR Part 11","FDA SaMD Guidance Q3 2023"],"required_attestors":["licensed_clinician","clinical_informatics_officer","hipaa_privacy_officer"],"lambda_floors":{"moralGrounding":0.99,"measurabilityHonesty":0.99,"consentBoundary":0.99,"informationIntegrity":0.99,"causalSeparability":0.99},"forbidden_inputs":["plaintext_phi","deidentification_not_verified"],"required_output_formats":["hl7_fhir_audit","json_receipt","pdf_clinical_audit"],"retention_days":"2190","primitives_applicable":["A1","A4","A5","A8","A9","A11","A12","T5","T7","T10","TH1"],"acv_range_usd":{"low":150000.0,"mid":600000.0,"high":2000000.0}},{"policy_id":"insurance","policy_name":"Insurance","version":"0.3.0","regulations":["NAIC Model Law 881","NY DFS Circular Letter 7 (2022)","NAIC AI Principles (2020)"],"required_attestors":["chief_actuary","ai_ethics_board","compliance_officer"],"lambda_floors":{"moralGrounding":0.97,"measurabilityHonesty":0.99,"informationIntegrity":0.99,"constructiveTransparency":0.99,"economicGrounding":0.97},"forbidden_inputs":["prohibited_rating_factors","non_actuarially_justified_proxies"],"required_output_formats":["csv_underwriting_log","json_receipt","pdf_state_filing"],"retention_days":"1825","primitives_applicable":["A1","A5","A8","A9","A12","A14","T6","T9","T10"],"acv_range_usd":{"low":200000.0,"mid":750000.0,"high":2000000.0}},{"policy_id":"legal","policy_name":"Legal / e-Discovery","version":"0.3.0","regulations":["FRCP 26","FRCP 34","FRE 902(13)","FRE 902(14)","ABA Model Rule 1.1"],"required_attestors":["supervising_attorney","records_custodian"],"lambda_floors":{"moralGrounding":0.97,"measurabilityHonesty":0.99,"informationIntegrity":0.99,"constructiveTransparency":0.99,"actionReversibility":0.95},"forbidden_inputs":["privileged_attorney_client_without_waiver"],"required_output_formats":["json_chain_of_custody","pdf_court_exhibit"],"retention_days":"2555","primitives_applicable":["A5","A6","A8","A12","T5","T8","T10","TH2"],"acv_range_usd":{"low":75000.0,"mid":300000.0,"high":1000000.0}},{"policy_id":"pharma","policy_name":"Pharma / Life Sciences R&D","version":"0.3.0","regulations":["FDA 21 CFR Part 11","EMA Annex 11","ICH E6(R3) GCP","GxP"],"required_attestors":["qualified_person","gxp_compliance_officer","computational_scientist"],"lambda_floors":{"moralGrounding":0.97,"measurabilityHonesty":1.0,"informationIntegrity":1.0,"temporalConsistency":0.99,"constructiveTransparency":1.0},"forbidden_inputs":["non_gxp_validated_software_output","unversioned_model"],"required_output_formats":["ectd_submission_package","json_audit_trail","csv_gxp_log"],"retention_days":"3650","primitives_applicable":["A5","A6","A8","A10","A12","T5","TH2"],"acv_range_usd":{"low":500000.0,"mid":2000000.0,"high":10000000.0}},{"policy_id":"public_sector","policy_name":"Public Sector / Civic AI","version":"0.3.0","regulations":["EU AI Act Annex III","NYC Local Law 144 (2023)","NIST AI RMF 1.0","OMB M-24-10"],"required_attestors":["agency_ai_officer","civil_rights_officer","inspector_general"],"lambda_floors":{"moralGrounding":0.99,"measurabilityHonesty":0.99,"stakeholderAlignment":0.99,"constructiveTransparency":1.0,"adversarialRobustness":0.95},"forbidden_inputs":["biometric_data_without_explicit_consent","prohibited_social_scoring"],"required_output_formats":["json_public_audit_log","csv_bias_audit","pdf_annual_report"],"retention_days":"3650","primitives_applicable":["A1","A5","A8","A12","A13","T6","T10","TH1","TH3"],"acv_range_usd":{"low":300000.0,"mid":1200000.0,"high":5000000.0}}],"instill_wave":"build-wave (locked 5 + wave3 19 sorry-free/4 axiom-gated + wave5 6 Mathlib-CI-green/5 bare-lean + conditional Lambda)"}</script>
 <script>
 const API='/api/a11oy';
 // a11oy is FULLY SELF-CONTAINED. Every capability below is a native, same-origin
@@ -421,10 +421,12 @@ const VIEWS={
       <div class="kpis"><div class="kpi"><div class="k">Up</div><div class="v live" id="fl-reach">probing\u2026</div></div><div class="kpi"><div class="k">Build security</div><div class="v teal">SLSA L2</div></div><div class="kpi"><div class="k">Trust score</div><div class="v teal">research conjecture</div><div class="d">not a theorem</div></div></div>
       <div class="card"><div class="card-h"><span class="card-t">Live reachability</span><span class="card-ep">public-URL probe</span></div><div id="fl-reach-host"><div class="row mono dim">probing\u2026</div></div></div>${HONEST}`;window.fleet_load();}},
 
-  mesh:{title:'Live System Map',badge:'3D',sub:'The platform and its services as one connected organism. The command platform sits at the core; each service is a node; every link is a live, conserved connection. Node color reflects the live health probe \u2014 down is shown honestly.',
-    render:async(c)=>{c.innerHTML=`<div class="btns"><button class="btn teal" onclick="mesh_load()">\u25b6 Re-probe + rebuild</button></div>
-      <div class="card"><div class="card-h"><span class="card-t">Connected system \u2014 live 3D</span><span class="card-ep">drag to orbit</span></div><div class="graph3d" id="mesh-3d"></div></div>
-      <div class="card"><div class="card-h"><span class="card-t">Reachability detail</span><span class="card-ep">live</span></div><div id="mesh-host"><div class="row mono dim">probing\u2026</div></div></div>${HONEST}`;window.mesh_load();}},
+  mesh:{title:'Live System Map',badge:'SERVICE HEALTH \u00b7 LIVE',sub:'Operator service-health view (New Relic / Datadog pattern): every capability ranked by live probe latency, with status and SLO budget. Sort, filter to impaired-only, and drill into any service\u2019s live probe \u2014 all from the same-origin observability probe, no external fetch. (The 3D organism view lives under \u201cLiving Organism\u201d; this tab is the operational health list, deliberately distinct.)',
+    render:async(c)=>{c.innerHTML=`<div class="btns"><button class="btn teal" onclick="mesh_load()">\u25b6 Re-probe</button><button class="btn" onclick="window._meshSort('lat')">Sort: latency</button><button class="btn" onclick="window._meshSort('name')">Sort: name</button><button class="btn" onclick="window._meshSort('status')">Sort: status</button><button class="btn" id="mesh-imp" onclick="window._meshToggleImpaired()">Show impaired only</button></div>
+      <div class="kpis"><div class="kpi"><div class="k">Services up</div><div class="v live" id="mesh-up">probing\u2026</div><div class="d">live probe</div></div><div class="kpi"><div class="k">Median latency</div><div class="v teal" id="mesh-p50">\u2014</div><div class="d">in-image</div></div><div class="kpi"><div class="k">Worst latency</div><div class="v" id="mesh-p100">\u2014</div><div class="d">p100</div></div><div class="kpi"><div class="k">Health score</div><div class="v teal" id="mesh-health">\u2014</div><div class="d">relabel-invariant (F-G4)</div></div></div>
+      <div class="card"><div class="card-h"><span class="card-t">Service latency ranking \u2014 live</span><span class="card-ep">probe ms \u00b7 click a bar to drill</span></div><div class="chartbox" style="height:240px"><canvas id="mesh-bars"></canvas></div></div>
+      <div class="grid2"><div class="card"><div class="card-h"><span class="card-t">Service table</span><span class="card-ep" id="mesh-tcount">\u2014</span></div><div id="mesh-host" style="max-height:320px;overflow:auto"><div class="row mono dim">probing\u2026</div></div></div>
+      <div class="card"><div class="card-h"><span class="card-t">Service drill-down</span><span class="card-ep" id="mesh-dname">click a service</span></div><div id="mesh-detail"><div class="row mono dim">Select a service in the table or a bar in the chart to see its live probe, latency and SLO budget.</div></div></div></div>${HONEST}`;window.mesh_load();}},
 
   /* PROOF-BINDING (cite-in-code-only): the Living Organism / mesh-health score is
    RELABEL-INVARIANT (F-G4): renaming or re-ordering services/organs does not
@@ -559,14 +561,17 @@ knowledge:{title:'Knowledge Ontology',badge:'AXIOMS \u2192 THEOREMS \u2192 FORMU
       </div>
       <div class="card" id="kn-detail"><div class="row mono dim">Click any node in the graph to see its formal statement, citation, and maturity.</div></div>${HONEST}`;window.knowledge_load();}},
 
-  kbformulas:{title:'Formulas',badge:'KaTeX \u00b7 100 RENDERED',sub:'Every formula in the platform\u2019s mathematical corpus, rendered in proper math typesetting and searchable. Each carries its source file and citation. Honesty: only five are formally proven in Lean (machine-checked, zero gaps); the rest are working, experimental, or definitional \u2014 never presented as theorems. The trust-score uniqueness claim remains an open research conjecture.',
+  kbformulas:{title:'Formulas',badge:'KaTeX \u00b7 5 LOCKED + 80+ CI-GREEN',sub:'The platform\u2019s mathematical corpus, rendered and searchable. Honesty: exactly FIVE formulas are locked-proven in the Doctrine-v11 Lean kernel (machine-checked, zero gaps). PLUS 80+ experimental theorems are kernel-verified and CI-green across waves 5\u20137, the agentic loop (P1\u2013P6), the governed coder, the \u039b Set \u03b1/\u03b4 uniqueness campaign, and the unifying meta-theorem \u2014 each linked to its lutar-lean PR below, never folded into the locked five. \u039b-uniqueness stays Conjecture 1 unconditionally (a counterexample is machine-checked) and is PROVEN only conditionally under declared strengthened axioms.',
     render:async(c)=>{c.innerHTML=`<div class="kpis">
-      <div class="kpi"><div class="k">Formulas</div><div class="v" id="kf-n">\u2014</div><div class="d">rendered (KaTeX)</div></div>
-      <div class="kpi"><div class="k">Formally proven</div><div class="v teal">5</div><div class="d">Lean, machine-checked</div></div>
-      <div class="kpi"><div class="k">Trust-score uniqueness</div><div class="v warn">open conjecture</div></div>
-      <div class="kpi"><div class="k">Source files</div><div class="v teal" id="kf-src">\u2014</div></div></div>
-      <div class="grid2"><div class="card"><div class="card-h"><span class="card-t">Proof status</span><span class="card-ep">honest</span></div><div class="chartbox"><canvas id="kf-donut"></canvas></div><div class="legend"><span><i style="background:#5fb3a3"></i>proven (5, locked)</span><span><i style="background:#c9b787"></i>working / open</span><span><i style="background:#b06a5a"></i>conjecture</span></div></div>
-      <div class="card"><div class="card-h"><span class="card-t">The five proven (Lean, sorry-free)</span><span class="card-ep">locked</span></div><div id="kf-proven"><div class="row mono dim">loading\u2026</div></div></div></div>
+      <div class="kpi"><div class="k">Locked proven</div><div class="v teal">5</div><div class="d">{F1,F11,F12,F18,F19} @ c7c0ba17</div></div>
+      <div class="kpi"><div class="k">Experimental kernel-verified</div><div class="v" style="color:#5fb3a3" id="kf-exp">80+</div><div class="d">CI-green, broken out below</div></div>
+      <div class="kpi"><div class="k">Trust-score uniqueness (\u039b)</div><div class="v warn">Conjecture 1 (+conditional-proven)</div></div>
+      <div class="kpi"><div class="k">Formulas rendered</div><div class="v teal" id="kf-n">\u2014</div><div class="d">KaTeX corpus</div></div></div>
+      <div class="card" style="border-left:3px solid #5fb3a3"><div class="card-h"><span class="card-t">Proof Status \u2014 the full honest set</span><span class="card-ep">every claim links to its lutar-lean PR \u00b7 CI-green</span></div>
+        <div id="kf-honest"><div class="row mono dim">loading proof ledger\u2026</div></div>
+        <div id="kf-chips" style="display:flex;flex-wrap:wrap;gap:.4rem;margin-top:.7rem"></div></div>
+      <div class="grid2"><div class="card"><div class="card-h"><span class="card-t">Locked vs experimental</span><span class="card-ep">honest split</span></div><div class="chartbox"><canvas id="kf-donut"></canvas></div><div class="legend"><span><i style="background:#5fb3a3"></i>locked proven (5)</span><span><i style="background:#c9b787"></i>experimental CI-green (80+)</span><span><i style="background:#e0a82e"></i>\u039b conjecture (conditional-proven)</span></div></div>
+      <div class="card"><div class="card-h"><span class="card-t">The five locked-proven (Lean, sorry-free)</span><span class="card-ep">locked</span></div><div id="kf-proven"><div class="row mono dim">loading\u2026</div></div></div></div>
       <div class="card"><div class="card-h"><span class="card-t">Formula corpus \u2014 rendered &amp; searchable</span><span class="card-ep" id="kf-count">\u2014</span></div>
         <input id="kf-search" placeholder="search formulas by id, source, or LaTeX\u2026" oninput="window.kbf_filter(this.value)" style="width:100%;padding:.6rem .8rem;background:#080808;border:1px solid var(--gold-line);border-radius:8px;color:var(--cream);font-family:var(--mono);font-size:12px;margin-bottom:.8rem"/>
         <div id="kf-list" style="max-height:520px;overflow:auto"><div class="row mono dim">loading /knowledge.json\u2026</div></div></div>${HONEST}`;window.kbformulas_load();}},
@@ -901,16 +906,79 @@ async function fleet_load(){try{const d=await getJSON(API+'/v1/observability/sum
 // Live system map (3D) — SELF-CONTAINED: a11oy GOLD core + internal capability
 // nodes from the in-image CAPS graph. Renders INSTANTLY (no network) so the
 // canvas is never black; a live probe then annotates latency if available.
+// ===== Live System Map: operator service-health list (New Relic/Datadog pattern) =====
+// DISTINCT from the Living Organism 3D brain: no force-graph here. Every capability
+// ranked by REAL live probe latency from /observability/summary, with status, SLO
+// budget, sort, impaired-only filter, and per-service drill-down. All same-origin.
+let _meshState={rows:[],sort:'lat',impaired:false,sel:null};
+// SLO latency budget (ms) for the in-image probe — honest, conservative target.
+const MESH_SLO_MS=25;
+function _meshHealthScore(rows){if(!rows.length)return 0;const up=rows.filter(r=>r.status==='ok').length;
+  // availability * latency-headroom, both in [0,1]; relabel-invariant (F-G4): order/name don't matter.
+  const avail=up/rows.length;const worst=Math.max(1,...rows.map(r=>r.latency_ms||0));
+  const lat=Math.max(0,Math.min(1,1-(worst/(MESH_SLO_MS*2))));return avail*0.7+lat*0.3;}
+function _meshSortRows(rows){const s=_meshState.sort;const c=rows.slice();
+  if(s==='lat')c.sort((a,b)=>(b.latency_ms||0)-(a.latency_ms||0));
+  else if(s==='name')c.sort((a,b)=>String(a.name).localeCompare(String(b.name)));
+  else if(s==='status')c.sort((a,b)=>(a.status==='ok'?1:0)-(b.status==='ok'?1:0));
+  return c;}
+function _meshVisible(){let r=_meshSortRows(_meshState.rows);if(_meshState.impaired)r=r.filter(x=>x.status!=='ok');return r;}
+function _meshRender(){const rows=_meshVisible();
+  // KPIs
+  const up=_meshState.rows.filter(r=>r.status==='ok').length,tot=_meshState.rows.length;
+  setTxt('mesh-up',tot?up+' / '+tot:'\u2014');
+  const lats=_meshState.rows.map(r=>r.latency_ms||0).filter(x=>x>0).sort((a,b)=>a-b);
+  const med=lats.length?lats[Math.floor((lats.length-1)/2)]:0;const worst=lats.length?lats[lats.length-1]:0;
+  setTxt('mesh-p50',lats.length?med+'ms':'\u2014');setTxt('mesh-p100',lats.length?worst+'ms':'\u2014');
+  const hs=_meshHealthScore(_meshState.rows);setTxt('mesh-health',tot?Math.round(hs*100)+'%':'\u2014');
+  // latency ranking bars (horizontal) — color by SLO breach / down
+  const labels=rows.map(r=>r.name),data=rows.map(r=>r.latency_ms||0);
+  const colors=rows.map(r=>r.status!=='ok'?RED:(r.latency_ms>MESH_SLO_MS?AMBER:TEAL));
+  if(rows.length)barH('mesh-bars',labels,data,colors);else{killChart('mesh-bars');}
+  // bind bar click → drill
+  const ch=_charts['mesh-bars'];if(ch){ch.options.onClick=(ev,els)=>{if(els&&els.length){const r=rows[els[0].index];if(r)_meshDrill(r.id);}};ch.update();}
+  // service table
+  setTxt('mesh-tcount',rows.length+(_meshState.impaired?' impaired':' services'));
+  if(!rows.length){setHTML('mesh-host','<div class="row mono dim">No services match — all healthy. Toggle filter off to see the full fleet.</div>');}
+  else{setHTML('mesh-host',rows.map(r=>{const breach=r.status==='ok'&&r.latency_ms>MESH_SLO_MS;
+    const badge=r.status==='ok'?(breach?'<span class="badge" style="background:rgba(201,160,95,.15);color:#c9a05f">slow</span>':'<span class="badge b-live">ok</span>'):'<span class="badge b-err">down</span>';
+    return `<div class="row" style="cursor:pointer" onclick="window._meshDrill('${esc(r.id)}')">${badge}<span>${esc(r.name)}</span><span class="spacer mono dim">${r.latency_ms?Math.round(r.latency_ms)+'ms':'—'} · HTTP ${esc(r.http_code||200)}</span></div>`;}).join(''));}
+  if(_meshState.sel)_meshDrill(_meshState.sel,true);
+}
+function _meshDrill(id,keep){const r=_meshState.rows.find(x=>x.id===id);if(!r)return;_meshState.sel=id;
+  setTxt('mesh-dname',r.name);const breach=r.status==='ok'&&r.latency_ms>MESH_SLO_MS;
+  const budget=Math.max(0,MESH_SLO_MS-(r.latency_ms||0));const pct=Math.max(0,Math.min(100,Math.round((r.latency_ms||0)/MESH_SLO_MS*100)));
+  const barCol=r.status!=='ok'?RED:(breach?AMBER:TEAL);
+  setHTML('mesh-detail',`<div class="kpis" style="margin:0 0 .6rem">
+    <div class="kpi"><div class="k">Status</div><div class="v ${r.status==='ok'?'live':''}" style="${r.status!=='ok'?'color:#b06a5a':''}">${esc(r.status)}</div></div>
+    <div class="kpi"><div class="k">Latency</div><div class="v teal">${r.latency_ms?Math.round(r.latency_ms)+'ms':'\u2014'}</div><div class="d">probe</div></div>
+    <div class="kpi"><div class="k">HTTP</div><div class="v">${esc(r.http_code||200)}</div></div>
+    <div class="kpi"><div class="k">SLO budget</div><div class="v" style="color:${barCol}">${r.status==='ok'?budget+'ms left':'breached'}</div><div class="d">target ${MESH_SLO_MS}ms</div></div></div>
+    <div class="mono dim" style="font-size:.72rem;margin-bottom:.3rem">SLO budget used · ${pct}%</div>
+    <div style="height:8px;background:#191919;border-radius:4px;overflow:hidden"><div style="height:100%;width:${pct}%;background:${barCol};transition:width .4s"></div></div>
+    <div class="row mono dim" style="margin-top:.6rem"><span>endpoint</span><span class="spacer">${esc(r.url||'in-image')}</span></div>
+    <div class="row mono dim"><span>probed path</span><span class="spacer">${esc(r.probed_path||'in-image')}</span></div>
+    <div class="row mono dim"><span>organ id</span><span class="spacer">${esc(r.id)}</span></div>`);}
+window._meshDrill=_meshDrill;
+window._meshSort=function(s){_meshState.sort=s;_meshRender();};
+window._meshToggleImpaired=function(){_meshState.impaired=!_meshState.impaired;const b=el('mesh-imp');if(b)b.textContent=_meshState.impaired?'Show all':'Show impaired only';_meshRender();};
 async function mesh_load(){
-  const h0=el('mesh-3d');if(h0)h0.innerHTML='<div class="row mono dim" style="padding:1rem">building self-contained map\u2026</div>';
-  // 1) instant render from in-image data
-  const baseNodes=[{id:'a11oy',name:'a11oy \u00b7 orchestrating core',color:GOLD,val:16}];const baseLinks=[];
-  CAPS.forEach(c=>{baseNodes.push({id:c.id,name:c.name+' \u00b7 '+c.kind,color:c.color,val:7});baseLinks.push({source:'a11oy',target:c.id});});
-  mesh3d('mesh-3d',baseNodes,baseLinks);
-  // 2) annotate with live in-image probe (same-origin, no external dependency)
-  try{const d=await getJSON(API+'/v1/observability/summary');const mr=d.mesh_reach||{};setHTML('mesh-host','');
-    Object.keys(mr).forEach(k=>{const v=mr[k];addHTML('mesh-host',`<div class="row"><span class="badge ${(v.status==='ok')?'b-live':'b-err'}">${esc(v.status||'ok')}</span><span>${esc(v.name||k)}</span><span class="spacer mono dim">${v.latency_ms?Math.round(v.latency_ms)+'ms':''} \u00b7 ${esc(v.url||'in-image')}</span></div>`);});
-  }catch(e){setHTML('mesh-host','');CAPS.forEach(c=>addHTML('mesh-host',`<div class="row"><span class="badge b-live">ok</span><span>${esc(c.name)}</span><span class="spacer mono dim">in-image</span></div>`));}}
+  setHTML('mesh-host','<div class="row mono dim">probing\u2026</div>');
+  // normalize from live mesh_reach (richest: http_code + probed_path), fall back to capabilities, then in-image CAPS.
+  function norm(src,kind){return (src||[]).map(v=>({id:v.organ||v.id,name:v.name||v.organ||v.id,status:v.status||'ok',
+    latency_ms:typeof v.latency_ms==='number'?v.latency_ms:0,http_code:v.http_code||200,url:v.url||'in-image',probed_path:v.probed_path||kind}));}
+  try{const d=await getJSON(API+'/v1/observability/summary');
+    let rows=[];
+    if(Array.isArray(d.mesh_reach)&&d.mesh_reach.length)rows=norm(d.mesh_reach,'live-probe');
+    else if(Array.isArray(d.capabilities)&&d.capabilities.length)rows=norm(d.capabilities,'in-image');
+    if(!rows.length)throw new Error('empty');
+    _meshState.rows=rows;_meshRender();
+  }catch(e){
+    // honest fallback: in-image capability list (no fabricated latency — mark as in-image)
+    _meshState.rows=CAPS.map(c=>({id:c.id,name:c.name,status:'ok',latency_ms:0,http_code:200,url:'in-image',probed_path:'in-image'}));
+    _meshRender();
+    const host=el('mesh-host');if(host)host.insertAdjacentHTML('afterbegin','<div class="row mono dim">live probe unavailable — showing in-image capability list. <span style="cursor:pointer;color:#5fb3a3" onclick="mesh_load()">retry</span></div>');
+  }}
 
 // Trust score (a11oy /v1/lambda)
 async function lambda_load(){try{const d=await getJSON(API+'/v1/lambda');const L=d.lambda||0;setTxt('la-val',L.toFixed?L.toFixed(4):L);setTxt('la-floor',d.lambda_floor??'0.90');setTxt('la-pass',d.pass?'ALLOW':(d.pass===false?'DENY':'\u2014'));
@@ -1105,7 +1173,7 @@ async function verticals_load(){try{const d=await getJSON(API+'/v1/vertical-pack
   }catch(e){setHTML('vp-live-host','<div class="row mono dim">retry: '+esc(e.message)+'</div>');setOut('vp-raw','retry: '+e.message);}}
 
 // ===== SHOWSTOPPER HANDLERS (3D / globe / cytoscape / echarts) =====
-const MATURITY_COLOR={proven:TEAL,measured:GOLD,conjectured:AMBER,conjecture:AMBER,defined:'#888',open:AMBER};
+const MATURITY_COLOR={proven:TEAL,measured:GOLD,conjectured:AMBER,conjecture:AMBER,defined:'#888',open:AMBER,locked:TEAL,'experimental-ci-green':'#5fb3a3','branch-pending':GOLD,'axiom-gated':'#c9b787',conditional:AMBER};
 function matColor(m){return MATURITY_COLOR[String(m||'').toLowerCase()]||'#888';}
 
 // Living Organism \u2014 SELF-CONTAINED: a11oy GOLD brain at the center, its own
@@ -1319,14 +1387,38 @@ async function knowledge_load(){
   }catch(e){const h=el('kn-cy');if(h)h.innerHTML='<div class="row mono dim" style="padding:1rem">knowledge.json unavailable: '+esc(e.message)+'</div>';setTxt('kn-ax','\u2014');}}
 
 // Formulas \u2014 KaTeX-rendered, searchable
+// PR link helper for the honest proof ledger
+function _prLink(pr){if(!pr)return '';var url=String(pr).indexOf('http')===0?String(pr):('https://github.com/szl-holdings/lutar-lean/pull/'+pr);var num=url.replace(/.*\/pull\//,'');return `<a href="${url}" target="_blank" rel="noopener" class="badge b-gold" style="text-decoration:none" title="open lutar-lean PR — CI-green">PR #${esc(num)} \u2197</a>`;}
+function _chip(label){var col=matColor(label);return `<span class="badge" style="color:${col};border:1px solid ${col}">${esc(label)}</span>`;}
+function _honestRow(chip,title,detail,pr){return `<div class="row" style="align-items:flex-start;gap:.5rem;padding:.45rem 0;border-bottom:1px solid var(--gold-line)"><span style="min-width:130px">${_chip(chip)}</span><span style="flex:1"><b style="color:var(--cream)">${esc(title)}</b><div class="mono dim" style="font-size:11px;margin-top:.2rem">${detail}</div></span><span>${pr?_prLink(pr):''}</span></div>`;}
 async function kbformulas_load(){
   try{const kb=await loadKnowledge();const fm=kb.formulas||[];_kf_all=fm;setTxt('kf-n',fm.length);
-    setTxt('kf-src',(kb.source_files||[]).length||new Set(fm.map(f=>f.source_file)).size);
-    doughnut('kf-donut',['proven','working/open','conjecture'],[5,Math.max(0,fm.length-6),1],[TEAL,GOLD,RED]);
+    const ps=kb.proof_summary||{};
+    // ---- honest proof ledger from proof_summary (the FULL set, each with its PR) ----
+    const expCount=(ps.experimental_count_min||80);
+    setTxt('kf-exp',expCount+'+');
+    var H='';
+    H+=_honestRow('locked','5 locked-kernel proven \u2014 {F1, F11, F12, F18, F19}','Doctrine-v11 locked kernel c7c0ba17 \u00b7 749 decls / 14 axioms / 163 sorries \u00b7 sorry-free, Lean-core axioms only. This count never moves.','');
+    const wv=function(b,t){if(!b)return;H+=_honestRow(b.maturity||'experimental-ci-green',t+' \u2014 '+(b.count||b.theorems||'')+' theorems',esc(b.headline||b.campaign||''),(b.pull_request||''));};
+    wv(ps.wave5,'Wave 5 (AM\u2013GM, Cauchy\u2013Schwarz, conformal, pigeonhole, optional-stopping)');
+    wv(ps.wave6,'Wave 6 (graph substrate: iso-invariance, GNN ceiling, DAG termination)');
+    wv(ps.wave7,'Wave 7 (conformal p-value, Doob two-sided envelope, PAC-Bayes routing)');
+    if(ps.agentic_loop)H+=_honestRow('experimental-ci-green','Agentic loop P1\u2013P6 \u2014 '+ps.agentic_loop.theorems+' theorems','The RAG\u2192MCP\u2192kernel loop proven as a SYSTEM. P3 non-interference (poisoned input can\u2019t flip the verdict) is axiom-free; P5 axiom-gated on hashFn_collision_resistant.',ps.agentic_loop.pull_request);
+    if(ps.coder_formulas)H+=_honestRow('experimental-ci-green','Governed coder \u2014 '+ps.coder_formulas.theorems+' theorems','Sandbox containment, bounded exec, router envelope, consensus, conformal code-confidence, Kraft, code non-interference. 1 axiom-gated (codeHash_collision_resistant).',ps.coder_formulas.pull_request);
+    if(ps.lambda_setalpha_setdelta)H+=_honestRow('conditional','\u039b Set \u03b1/\u03b4 uniqueness \u2014 '+ps.lambda_setalpha_setdelta.results+' results','PROVEN: \u039b is unique within strengthened axiom classes Set \u03b1 and Set \u03b4 (conditional on declared bridge axioms). All 10 impostor-deaths AXIOM-FREE. NOT unconditional \u2014 \u039b stays Conjecture 1.',ps.lambda_setalpha_setdelta.pull_request);
+    if(ps.unify_governed_run_sound)H+=_honestRow('experimental-ci-green','Unifying meta-theorem \u2014 governed_run_sound','Every compositional guarantee (P1/P4/P6 + coder corpus) is a corollary of ONE monoid-action homomorphism (run_append). A synthesis theorem.',ps.unify_governed_run_sound.pull_request);
+    if(ps.mathlib_bump_c3c4c5)H+=_honestRow('branch-pending','C3 / C4 / C5 (concentration / KL re-exports)','PROVEN on the Mathlib-v4.18 bump branch (CI-green), PENDING MERGE to main \u2014 not on-main, not blocked.',ps.mathlib_bump_c3c4c5.pull_request);
+    H+=_honestRow('conjecture','\u039b uniqueness \u2014 Conjecture 1 (unconditional)','Unconditional uniqueness under the original axioms A1\u2013A5 is machine-checked FALSE (counterexample Round13.maxAgg_ne_Lambda). The label stays \u201cConjecture 1\u201d \u2014 this is non-negotiable honesty. The conditional proof above is how it becomes provable under stronger axioms.','192');
+    setHTML('kf-honest',H);
+    // maturity legend chips
+    const legend=(ps.maturity_legend||['locked','experimental-ci-green','branch-pending','axiom-gated','conditional','conjecture']);
+    setHTML('kf-chips','<span class="mono dim" style="font-size:10px;align-self:center">maturity:</span>'+legend.map(_chip).join(''));
+    // honest donut: 5 locked vs experimental vs lambda-conjecture
+    doughnut('kf-donut',['locked proven','experimental CI-green','\u039b conjecture'],[5,expCount,1],[TEAL,'#c9b787',AMBER]);
     setHTML('kf-proven',`<div class="row"><span>Five proven in Lean (sorry-free)</span><span class="spacer b-live badge">F1 F11 F12 F18 F19</span></div>`+
       (kb.theorems||[]).map(t=>`<div class="row"><span class="badge" style="color:${matColor(t.maturity)};border:1px solid ${matColor(t.maturity)}">${esc(t.maturity)}</span><span>${esc(t.id)} \u00b7 ${esc(t.name)}</span></div>`).join(''));
     window.kbf_filter('');
-  }catch(e){setHTML('kf-list','<div class="row mono dim">knowledge.json unavailable: '+esc(e.message)+'</div>');setTxt('kf-n','\u2014');}}
+  }catch(e){setHTML('kf-list','<div class="row mono dim">knowledge.json unavailable: '+esc(e.message)+'</div>');setHTML('kf-honest','<div class="row mono dim">proof ledger unavailable: '+esc(e.message)+' \u2014 <a href="#" onclick="window.kbformulas_load();return false">retry</a></div>');setTxt('kf-n','\u2014');}}
 function kbf_filter(q){q=String(q||'').toLowerCase();const list=el('kf-list');if(!list)return;
   const rows=_kf_all.filter(f=>!q||String(f.id).toLowerCase().includes(q)||String(f.source_file||'').toLowerCase().includes(q)||String(f.latex||'').toLowerCase().includes(q));
   setTxt('kf-count',rows.length+' / '+_kf_all.length);