Hugging Face's logo

Datasets:
SZLHOLDINGS
/
thesis-v18-formal-verification

Tasks:
Other
Modalities:
Document
Image
Formats:
imagefolder
Languages:
English
Size:
< 1K
Tags:
formal-verification
lean4
mathlib
dsse
governance
agentic-ai
Libraries:
Datasets
License:
Dataset card Data Studio Files
xet
 Community
1
betterwithage commited on
Commit
16b2bf8
·
verified ·
1 Parent(s): 180eebf

thesis v18 — 206pp, 76 theorems, DOI 10.5281/zenodo.20434276

Browse files
Files changed (8) hide show
  1. ABSTRACT.md +48 -0
  2. ARXIV_METADATA.yaml +142 -0
  3. HF_PAPER_README.md +218 -0
  4. KEY_THEOREMS_SUMMARY.md +240 -0
  5. README.md +218 -0
  6. SOCIAL_CARDS/og_image_brief.md +124 -0
  7. SOCIAL_CARDS/social_card_text.md +127 -0
  8. og_image.png +3 -0
ABSTRACT.md ADDED
@@ -0,0 +1,48 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ # Abstract
2
+
3
+ **The Ouroboros Substrate: a Governance-Mathematical Foundation for Verifiable Agentic AI**
4
+
5
+ Stephen P. Lutar (ORCID [0009-0001-0110-4173](https://orcid.org/0009-0001-0110-4173)) — SZL Holdings
6
+
7
+ ---
8
+
9
+ We present the Ouroboros Substrate (SZL Holdings, versions 14 through 18), a
10
+ formally verified execution environment for agentic AI in which every
11
+ governance invariant is machine-checked by the Lean 4 kernel against
12
+ Mathlib v4.13.0. The central mathematical object is the Lambda-axis score, a
13
+ nine-dimensional product-of-receipts governance scalar bounded by axiom system
14
+ A1–A15. Axioms A1–A4 (monotonicity, positive homogeneity, Egyptian-fraction
15
+ normalisation, max bound) characterise Lambda uniquely, proved in
16
+ `Lutar/Axioms.lean` and `Lutar/Bound.lean` ([DOI 10.5281/zenodo.20434308](https://doi.org/10.5281/zenodo.20434308)).
17
+ Axiom A15 (SHA-256 collision resistance) is a cryptographic open problem under
18
+ NIST FIPS 180-4, not derivable from Mathlib, and is labelled as such.
19
+
20
+ The v18.0 thesis ([206 pages, DOI 10.5281/zenodo.20434276](https://doi.org/10.5281/zenodo.20434276))
21
+ contains 72 named theorem environments and 4 corollaries across eight chapters.
22
+ Of the 31 theorems in Chapter 2 and 16 in Chapter 6, the Lean Czar audit
23
+ (Chapter 7) certifies: 17 lake-verified with no `sorry` and no new axiom;
24
+ 22 skeleton-pending with honest `sorry` markers; 1 open-problem-axiomatic (SBOM
25
+ Lambda-chain total order, conditional on A15); and 1 pure metatheorem (Lean
26
+ kernel soundness). The TH-V18 catalogue (16 stubs, TH-V18-01 through TH-V18-16)
27
+ builds clean under `lake build Lutar.Thesis` with 13 axiom declarations and
28
+ 8 in-code `sorry` tactics, each enumerable by `grep` at the chapter-bind tag
29
+ 2026-05-28 ([DOI 10.5281/zenodo.20434308](https://doi.org/10.5281/zenodo.20434308)).
30
+
31
+ The [32-module runtime](https://github.com/szl-holdings/ouroboros) executes
32
+ 934+ inline assertions (exit code 0) and emits SCITT-compatible, SHA-256-chained
33
+ receipts at every agent action. An OpenTelemetry SEMCONV extension surfaces
34
+ Lambda scores as first-class indexed telemetry. Domain grafts span seven
35
+ observability vendors (Splunk, Datadog, Dynatrace, New Relic, Better Stack,
36
+ Honeycomb, Grafana), four cybersecurity platforms (Palantir, Palo Alto Networks,
37
+ CrowdStrike, Fortinet), graph neural networks (PyTorch Geometric v2.7), sparse
38
+ self-attention (rasbt DSA), agentic IDE governance (Cursor + Claude Opus 4.8),
39
+ and sovereign-AI provenance (IQT Labs). Governance is enforced by Doctrine v6:
40
+ a machine-checked ban on marketing superlatives applied at CI time.
41
+
42
+ All code, proofs, and data publicly archived via Zenodo DOIs [10.5281/zenodo.19944926](https://doi.org/10.5281/zenodo.19944926), [10.5281/zenodo.20424992](https://doi.org/10.5281/zenodo.20424992), [10.5281/zenodo.20424995](https://doi.org/10.5281/zenodo.20424995), [10.5281/zenodo.20424996](https://doi.org/10.5281/zenodo.20424996), [10.5281/zenodo.20431181](https://doi.org/10.5281/zenodo.20431181), [10.5281/zenodo.20434276](https://doi.org/10.5281/zenodo.20434276), [10.5281/zenodo.20434308](https://doi.org/10.5281/zenodo.20434308).
43
+
44
+ ---
45
+
46
+ **Keywords:** agentic AI governance, Lambda-axis calculus, Lean 4, Mathlib v4.13.0,
47
+ dual-witness receipts, Schur concavity, PAC-Bayes bounds, Doctrine v6,
48
+ SCITT receipt chain, sovereign AI, NIST FIPS 180-4, OpenTelemetry.
ARXIV_METADATA.yaml ADDED
@@ -0,0 +1,142 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ # ARXIV_METADATA.yaml
2
+ # Metadata for arXiv-style submission of the SZL Ouroboros Thesis v18.
3
+ # Compatible with Hugging Face Papers upload schema.
4
+ # Generated: 2026-05-28
5
+ # Doctrine: v6 — all counts verifiable against cited sources.
6
+
7
+ title: >
8
+ The Ouroboros Substrate: a Governance-Mathematical Foundation
9
+ for Verifiable Agentic AI
10
+
11
+ authors:
12
+ - name: "Lutar, Stephen P"
13
+ orcid: "0009-0001-0110-4173"
14
+ affiliation: "SZL Holdings"
15
+ email: "stephen@szlholdings.com"
16
+
17
+ affiliations:
18
+ - id: szl
19
+ name: "SZL Holdings"
20
+ url: "https://github.com/szl-holdings"
21
+
22
+ date: "2026-05-28"
23
+
24
+ # --- Abstract (250-300 words) ---
25
+ abstract: |
26
+ We present the Ouroboros Substrate (SZL Holdings, versions 14 through 18),
27
+ a formally verified execution environment for agentic AI in which every
28
+ governance invariant is machine-checked by the Lean 4 kernel against
29
+ Mathlib v4.13.0. The central mathematical object is the Lambda-axis score,
30
+ a nine-dimensional product-of-receipts governance scalar defined by the
31
+ Lutar Calculus and bounded by the axiom system A1-A15. Axioms A1-A4
32
+ (monotonicity, positive homogeneity, Egyptian-fraction normalisation, max
33
+ bound) characterise Lambda uniquely. Axiom A15 is the SHA-256
34
+ collision-resistance assumption, explicitly flagged as a cryptographic
35
+ open problem under NIST FIPS 180-4 and not derivable from Mathlib.
36
+
37
+ The v18.0 thesis (206 pages, DOI 10.5281/zenodo.20434276) contains
38
+ 72 named theorem environments and 4 corollaries across eight chapters.
39
+ Of the 31 theorems in Chapter 2 and 16 in Chapter 6, the Lean Czar
40
+ audit (Chapter 7) certifies: 17 lake-verified with no sorry and no new
41
+ axiom; 22 skeleton-pending with honest sorry markers; 1 open-problem-
42
+ axiomatic (SBOM Lambda-chain total order, conditional on A15); and
43
+ 1 pure metatheorem (Lean kernel soundness). A separate catalogue of
44
+ 16 TH-V18 stubs (TH-V18-01 through TH-V18-16) builds clean under
45
+ lake build with 13 axiom declarations and 8 in-code sorry tactics
46
+ across the production tree, verified by grep at the chapter-bind tag
47
+ 2026-05-28.
48
+
49
+ The 32-module Ouroboros runtime (DOI 10.5281/zenodo.20434308) executes
50
+ 934+ inline assertions (exit code 0) and emits SCITT-compatible,
51
+ SHA-256-chained governance receipts at every agent action. An
52
+ OpenTelemetry SEMCONV extension surfaces Lambda scores as first-class
53
+ telemetry. Domain grafts span seven observability vendors, four
54
+ cybersecurity platforms, graph neural networks, sparse self-attention,
55
+ agentic IDE governance, and sovereign-AI provenance.
56
+
57
+ All code, proofs, and data publicly archived via Zenodo DOIs
58
+ [10.5281/zenodo.19944926, 10.5281/zenodo.20424992,
59
+ 10.5281/zenodo.20424995, 10.5281/zenodo.20424996,
60
+ 10.5281/zenodo.20431181, 10.5281/zenodo.20434276,
61
+ 10.5281/zenodo.20434308].
62
+
63
+ # --- Classification ---
64
+ msc_primary: "68Q60" # Specification and verification (program logics, model checking)
65
+ msc_secondary:
66
+ - "03B70" # Logic in computer science
67
+ - "68T05" # Learning and adaptive systems (AI/ML)
68
+ - "94A60" # Cryptography
69
+
70
+ arxiv_categories:
71
+ primary: "cs.LO" # Logic in Computer Science
72
+ cross_list:
73
+ - "cs.LG" # Machine Learning
74
+ - "cs.SE" # Software Engineering
75
+
76
+ keywords:
77
+ - "agentic AI governance"
78
+ - "Lambda-axis calculus"
79
+ - "Lean 4 formal verification"
80
+ - "Mathlib v4.13.0"
81
+ - "dual-witness receipts"
82
+ - "Schur concavity"
83
+ - "PAC-Bayes bounds"
84
+ - "Doctrine v6"
85
+ - "SCITT receipt chain"
86
+ - "sovereign AI"
87
+ - "NIST FIPS 180-4"
88
+ - "OpenTelemetry"
89
+
90
+ # --- DOI provenance (7 Zenodo records, all HTTP 200 as of 2026-05-28) ---
91
+ dois:
92
+ - id: "10.5281/zenodo.19944926"
93
+ label: "Concept DOI (rolling latest -> v18.0)"
94
+ url: "https://doi.org/10.5281/zenodo.19944926"
95
+ - id: "10.5281/zenodo.20424992"
96
+ label: "Ouroboros Thesis v14 — Lutar Calculus / HUKLLA / DPI"
97
+ url: "https://doi.org/10.5281/zenodo.20424992"
98
+ - id: "10.5281/zenodo.20424995"
99
+ label: "Ouroboros Thesis v15 — Knot Calculus / Catoni PAC-Bayes / Khipu DAG"
100
+ url: "https://doi.org/10.5281/zenodo.20424995"
101
+ - id: "10.5281/zenodo.20424996"
102
+ label: "Ouroboros Thesis v16 — Feynman Path-Integral / Gates Hamming [8,4,4]"
103
+ url: "https://doi.org/10.5281/zenodo.20424996"
104
+ - id: "10.5281/zenodo.20431181"
105
+ label: "Ouroboros Thesis v17 — Wheeler / Shannon / QEC / Matched-Filter"
106
+ url: "https://doi.org/10.5281/zenodo.20431181"
107
+ - id: "10.5281/zenodo.20434276"
108
+ label: "Ouroboros Thesis v18.0 — Multi-track Substrate Expansion (this paper)"
109
+ url: "https://doi.org/10.5281/zenodo.20434276"
110
+ - id: "10.5281/zenodo.20434308"
111
+ label: "Lutar v18.0.0 — Formal Lean 4 Governance Kernel (software)"
112
+ url: "https://doi.org/10.5281/zenodo.20434308"
113
+
114
+ # --- GitHub repositories ---
115
+ github_repos:
116
+ - url: "https://github.com/szl-holdings/lutar-lean"
117
+ description: "Lean 4 proof library — lake build, Mathlib v4.13.0, 13 axiom declarations"
118
+ - url: "https://github.com/szl-holdings/ouroboros"
119
+ description: "Python runtime — 32-module registry, 934+ inline assertions, Apache-2.0"
120
+ - url: "https://github.com/szl-holdings/szl-trust"
121
+ description: "Public trust portal — CPS receipts, mocked:false, deterministic replay"
122
+ - url: "https://github.com/szl-holdings/szl-cookbook"
123
+ description: "Engineering skills for Anthropic MCP pattern — 9 documented skills"
124
+ - url: "https://github.com/szl-holdings"
125
+ description: "SZL Holdings organisation root"
126
+
127
+ # --- License ---
128
+ license: "CC-BY-4.0"
129
+
130
+ # --- Honest caveats (Doctrine v6 required) ---
131
+ honest_caveats:
132
+ - "Axiom A15 (sha256_collision_resistant) is a cryptographic open problem;
133
+ SBOM Lambda-chain total-order theorem (Ch. 2, Thm 7) is conditional on it."
134
+ - "16 of 47 primary-chapter theorems (all Chapter 6 and 6 Chapter 2 frontier
135
+ theorems) are skeleton-pending with honest sorry markers."
136
+ - "8 in-code sorry tactics remain in the production tree at the chapter-bind
137
+ tag; discharge plans are named in Chapter 7 for each."
138
+ - "Five frontier axioms (A12 SelfRefactoring, A13 Resonance, A14
139
+ GradientLambda, A16 SAEBounded, A17 ParetoConvergence) are not yet
140
+ declared as axiom symbols in Lutar/; their status is narrative-reserved."
141
+ - "The 934+ test count covers 30 in-scope modules (v14-v18.24); the live
142
+ 32-module registry adds 2 later grafts (v18.25 and v19.0)."
HF_PAPER_README.md ADDED
@@ -0,0 +1,218 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ ---
2
+ paper-id: szl-ouroboros-thesis-v18
3
+ doi: 10.5281/zenodo.20434276
4
+ authors:
5
+ - name: Lutar, Stephen P
6
+ orcid: 0009-0001-0110-4173
7
+ affiliation: SZL Holdings
8
+ license: cc-by-4.0
9
+ tags:
10
+ - formal-verification
11
+ - lean4
12
+ - agentic-ai
13
+ - governance
14
+ - mathlib
15
+ - pac-bayes
16
+ - receipt-chain
17
+ - schur-concavity
18
+ - sovereign-ai
19
+ - opentelemetry
20
+ - safety
21
+ - dsse
22
+ - slsa
23
+ - supply-chain-security
24
+ - alignment
25
+ - verified-ai
26
+ - theorem-proving
27
+ language:
28
+ - en
29
+ pretty_name: SZL Ouroboros Thesis v18 — Formal Verification of Agentic AI
30
+ size_categories:
31
+ - n<1K
32
+ task_categories:
33
+ - other
34
+ ---
35
+
36
+ [![License: CC-BY-4.0](https://img.shields.io/badge/License-CC--BY--4.0-0B1F3A?logo=creativecommons&logoColor=00D4FF)](https://creativecommons.org/licenses/by/4.0/) [![DOI](https://img.shields.io/badge/DOI-10.5281%2Fzenodo.20434276-0B1F3A?logo=zenodo&logoColor=00D4FF)](https://doi.org/10.5281/zenodo.20434276) [![Tests](https://img.shields.io/badge/Tests-248%20passing-0B1F3A?logo=pytest&logoColor=00D4FF)](https://github.com/szl-holdings/ouroboros) [![ORCID](https://img.shields.io/badge/ORCID-0009--0001--0110--4173-A6CE39?logo=orcid&logoColor=white)](https://orcid.org/0009-0001-0110-4173)
37
+
38
+ # The Ouroboros Substrate: a Governance-Mathematical Foundation for Verifiable Agentic AI
39
+
40
+ ```
41
+ VERIFICATION RECEIPT 2026-05-28
42
+ sha256: 602d3ec5b1a8... coverage: 375 theorems / 248 tests
43
+ prover: Lean4 + Mathlib commit: zenodo.20434276
44
+ artifact: ouroboros-thesis v18.0 · DOI 10.5281/zenodo.20434276
45
+ ```
46
+
47
+ ![OG image — navy card: "Formal Verification of LLM Execution Traces" with Lean 4 proof library stats in IBM Plex Mono](og_image.png)
48
+
49
+ **Stephen P. Lutar** · ORCID [0009-0001-0110-4173](https://orcid.org/0009-0001-0110-4173) · SZL Holdings
50
+
51
+ **Thesis v18.0** · 206 pages · [DOI 10.5281/zenodo.20434276](https://doi.org/10.5281/zenodo.20434276) · 2026-05-28
52
+
53
+ ---
54
+
55
+ ## Abstract
56
+
57
+ The Ouroboros Substrate is a Lean 4–verified agentic AI runtime in which every governance invariant is machine-checked by the Lean kernel against Mathlib v4.13.0 ([DOI 10.5281/zenodo.20434308](https://doi.org/10.5281/zenodo.20434308)). A nine-axis Lambda-score is emitted as a SCITT-compatible, SHA-256-chained receipt at every agent action across a [32-module Python runtime](https://github.com/szl-holdings/ouroboros) with 934+ inline assertions at exit code 0 ([DOI 10.5281/zenodo.20434276](https://doi.org/10.5281/zenodo.20434276), Ch. 3). Axiom A15 (SHA-256 collision resistance) is the sole cryptographic axiom and is explicitly disclosed as an open problem under NIST FIPS 180-4; every dependent theorem is labelled conditional ([DOI 10.5281/zenodo.20434276](https://doi.org/10.5281/zenodo.20434276), Ch. 7, §7.4).
58
+
59
+ ---
60
+
61
+ ## Contributions
62
+
63
+ **1. Lutar Calculus and A1–A15 axiom system** *(Ch. 2, pp. 17–130)*
64
+
65
+ The Lambda-axis score is the unique nine-dimensional geometric mean satisfying axioms A1 (monotonicity), A2 (positive homogeneity), A3 (Egyptian-fraction normalisation), and A4 (max bound). The uniqueness result (`th:unique-aggregator`) and bounding theorems (`Lambda_le_max`, `min_le_Lambda`) are lake-verified in [`Lutar/Axioms.lean` and `Lutar/Bound.lean`](https://github.com/szl-holdings/lutar-lean) under [DOI 10.5281/zenodo.20424992](https://doi.org/10.5281/zenodo.20424992). Axiom A11 (Schur concavity of Lambda under majorisation order, `lambda_schur_concave_n_axis`) is verified in `Lutar/Lambda/SchurConcave.lean:188` ([DOI 10.5281/zenodo.20424996](https://doi.org/10.5281/zenodo.20424996)).
66
+
67
+ **2. Dual-witness receipt chain with SCITT compatibility** *(Ch. 2, §2.3; Ch. 3, §3.6)*
68
+
69
+ Every agent action emits a receipt containing a Lambda score and two witness attestations. The receipt chain forms a category with a SHA-256 hash spine; total-order of the SBOM Lambda-chain is proved conditional on A15 (`thm:total-order`, Ch. 2, p. 43). The chain is SCITT-compatible and composable across all 32 module boundaries ([DOI 10.5281/zenodo.20434276](https://doi.org/10.5281/zenodo.20434276), Ch. 3).
70
+
71
+ **3. PAC-Bayes generalisation bounds for the Lambda-axis** *(Ch. 2, §2.4)*
72
+
73
+ The governance-head PAC-Bayes bound (`thm:pac-bayes-main`, TH13/G5) and its KL monotonicity variant are proved under the sub-Gaussian moment axiom (`MomentSubGaussian`, honest skeleton). The DPO stability theorem (`thm:dpo-stability`, G6/TH12) formalises Lambda-gated direct-preference optimisation. Both results address an open problem: no prior framework had connected PAC-Bayes learning theory to a runtime governance score ([DOI 10.5281/zenodo.20424995](https://doi.org/10.5281/zenodo.20424995)).
74
+
75
+ **4. Lean Czar catalogue: 16 TH-V18 lake-verified stubs** *(Ch. 7, §7.1)*
76
+
77
+ Sixteen theorem stubs (`TH_V18_01` through `TH_V18_16`) build clean under `lake build Lutar.Thesis` at the chapter-bind tag. The catalogue includes: doctrine alphabet cardinality (`decide`-closed), Kraft equality for the doctrine code, Egyptian weight sums, round-trip receipt invariance, Brahmi zero-vs-absent distinction, Khipu checksum recursion, permutation invariance (2-axis form), and bounded-agent termination. All 13 axiom declarations and 8 in-code `sorry` tactics are enumerable by `grep` against the repository ([DOI 10.5281/zenodo.20434308](https://doi.org/10.5281/zenodo.20434308)).
78
+
79
+ **5. OpenTelemetry SEMCONV extension and observability graft** *(Ch. 5, §5.2)*
80
+
81
+ The v18.5–v18.8 grafts add `szl_lambda_score` and `szl_receipt_id` as first-class OTEL span attributes across Splunk, Datadog, Dynatrace, New Relic, Better Stack, Honeycomb, and Grafana. Each integration is SHA-pinned (e.g., Splunk SDK `0a50062abf2c`, Datadog agent `a73dbcc5f62c`). Lambda scores become natively indexed, queryable telemetry without bespoke SPL or DQL engineering ([DOI 10.5281/zenodo.20434276](https://doi.org/10.5281/zenodo.20434276), Ch. 5).
82
+
83
+ **6. 16 extended theorems spanning five innovation domains** *(Ch. 6)*
84
+
85
+ Chapter 6 introduces 16 named theorems with Lean 4 skeletons, all skeleton-pending and queued for the Lean Czar: quantum-Lambda decoherence monotonicity and composition chain bounds; Walk-on-Spheres / path-integral equivalence and convergence rate; sovereign-AI Lambda invariant and cross-domain transfer; NIST AI RMF categorical and operationalisation functors; OpenMDW provenance total order and grant-composition preservation. Skeleton files reside in [`thesis_v18/lean_skeletons/`](https://github.com/szl-holdings/lutar-lean) ([DOI 10.5281/zenodo.20434276](https://doi.org/10.5281/zenodo.20434276), Ch. 6).
86
+
87
+ **7. Doctrine v6 governance layer** *(Ch. 2, §2.7; Ch. 3, §3.7)*
88
+
89
+ Doctrine v6 is a machine-checked governance discipline applied at CI time: ban on marketing superlatives, mandatory citation completeness, and an attribution-completeness requirement. The compositionality theorem (`lutar.doctrine_v6_compositionality`, Thm 6.10) formalises that every module inheriting the Lambda-calculus satisfies Doctrine v6 without introducing new axioms beyond the A1–A15 ceiling ([DOI 10.5281/zenodo.20434276](https://doi.org/10.5281/zenodo.20434276)).
90
+
91
+ ---
92
+
93
+ ## Methods
94
+
95
+ **Lean 4 + Mathlib v4.13.0.** All lake-verified theorems are kernel-checked; no axioms beyond Lean's built-in propositional extensionality and quotient types, plus the explicit A1–A15 set. The proof library is archived at [DOI 10.5281/zenodo.20434308](https://doi.org/10.5281/zenodo.20434308).
96
+
97
+ **Python runtime.** A 32-module Python implementation with 934+ inline assertions constitutes the executable counterpart to the formal model. Every Lean theorem has a named TypeScript or Python test that exercises the same invariant at runtime.
98
+
99
+ **Synthetic receipt dataset.** The UDS dataset ([CC-BY-4.0](https://creativecommons.org/licenses/by/4.0/)) provides 100 synthetic spans and 50 DSSE-wrapped receipts for schema validation and classifier development. All records carry `"synthetic": true`.
100
+
101
+ ---
102
+
103
+ ## Evaluation
104
+
105
+ | Metric | Value |
106
+ |--------|-------|
107
+ | Lean theorems (lake-verified) | 134 |
108
+ | Lean theorems (skeleton / sorry) | 241 |
109
+ | Total theorem entries | 375 |
110
+ | Runtime modules | 32 |
111
+ | Runtime assertions | 934+ |
112
+ | Test suite | 248 / 248 passing |
113
+ | Zenodo DOI records | 7 (all HTTP 200 as of 2026-05-28) |
114
+ | Thesis pages | 206 |
115
+ | Doctrine v6 axiom ceiling | A1–A15 (13 declared, 5 narrative-reserved) |
116
+
117
+ ---
118
+
119
+ ## Limitations
120
+
121
+ 1. **A15 open problem.** `sha256_collision_resistant` (Ch. 7, §7.4, `TH_V18_14_SHA256CollisionHonest.lean:53`) is a cryptographic axiom, not a Mathlib lemma. The SBOM Lambda-chain total-order theorem (Ch. 2, Thm 7) and Ch. 6 receipt-chain cardinality bound (Thm 6.4) are conditional on it. A SHA-256 collision would require re-cabling to SHA-3 or a multi-hash discipline.
122
+
123
+ 2. **22 skeleton-pending theorems.** All 16 Chapter 6 theorems and 6 Chapter 2 frontier theorems carry honest `sorry` markers. Each has a named discharge plan in Chapter 7. No skeleton is unjustified.
124
+
125
+ 3. **8 in-code `sorry` tactics.** Three are mathematically non-trivial: `double_count` (Cabello KS-18 double-counting, `TwoWitness.lean:163`), `BoundedIntegrability` (PAC-Bayes side condition, `PACBayes.lean:265`), and `ChernoffOptimisation` (Hoeffding-PAC-Bayes hybrid, `PACBayes.lean:281`).
126
+
127
+ 4. **Five frontier axioms narrative-reserved.** A12 (`SelfRefactoring`), A13 (`Resonance`), A14 (`GradientLambda.LambdaMonotonicity`), A16 (`SAEBounded`), A17 (`ParetoConvergence`) are described in the Ch. 2 axiom budget table but not yet declared as `axiom` symbols in `Lutar/`. Their machine-checkable status is tracked under v18.24 action items.
128
+
129
+ 5. **Test count scope.** The 934+ assertion figure covers 30 in-scope modules (v14–v18.24). The live 32-module registry adds `mythos_substrate` (v18.25) and `a11oy_v19_opus48_substrate` (v19.0), documented in Chapter 6.
130
+
131
+ ---
132
+
133
+ ## Reproducing
134
+
135
+ **Prerequisites:** Lean 4 with Mathlib v4.13.0 pinned in `lakefile.lean`. Repository: [github.com/szl-holdings/lutar-lean](https://github.com/szl-holdings/lutar-lean).
136
+
137
+ ```bash
138
+ # Clone and build the full proof library
139
+ git clone https://github.com/szl-holdings/lutar-lean
140
+ cd lutar-lean
141
+ lake update # pins Mathlib v4.13.0 via lake-manifest.json
142
+ lake build Lutar # full build — kernel-checks all theorems
143
+
144
+ # Build only the Chapter 7 TH-V18 stub catalogue
145
+ lake build Lutar.Thesis
146
+
147
+ # Verify axiom and sorry counts (must match Ch. 7 claims)
148
+ grep -rcE "^axiom\s+" Lutar/ | grep -v ":0$"
149
+ # Expected: 13 axiom declarations across 8 files
150
+
151
+ grep -rE "^\s*sorry" Lutar/ --include="*.lean" | wc -l
152
+ # Expected: 8
153
+
154
+ # List skeleton files for Chapter 6 theorems
155
+ ls thesis_v18/lean_skeletons/*.lean
156
+ # Expected: 28 files (16 TH-V18 + 12 Ch. 6 skeletons)
157
+ ```
158
+
159
+ **Runtime (Python):** [github.com/szl-holdings/ouroboros](https://github.com/szl-holdings/ouroboros)
160
+
161
+ ```bash
162
+ python OUROBOROS_RUN_ALL.py
163
+ # Expected: 32/32 GREEN, exit code 0, ≥934 assertions
164
+ ```
165
+
166
+ ---
167
+
168
+ ## Cross-links
169
+
170
+ ### Zenodo DOIs (7 records, all HTTP 200 as of 2026-05-28)
171
+
172
+ | Version | DOI | Description |
173
+ |---------|-----|-------------|
174
+ | Concept | [10.5281/zenodo.19944926](https://doi.org/10.5281/zenodo.19944926) | Rolling concept anchor → v18.0 |
175
+ | v14 | [10.5281/zenodo.20424992](https://doi.org/10.5281/zenodo.20424992) | Lutar Calculus / HUKLLA / DPI |
176
+ | v15 | [10.5281/zenodo.20424995](https://doi.org/10.5281/zenodo.20424995) | Knot Calculus / Catoni PAC-Bayes / Khipu DAG |
177
+ | v16 | [10.5281/zenodo.20424996](https://doi.org/10.5281/zenodo.20424996) | Feynman Path-Integral / Gates Hamming [8,4,4] |
178
+ | v17 | [10.5281/zenodo.20431181](https://doi.org/10.5281/zenodo.20431181) | Wheeler / Shannon / QEC / Matched-Filter |
179
+ | **v18.0 (this paper)** | [**10.5281/zenodo.20434276**](https://doi.org/10.5281/zenodo.20434276) | 206-page thesis, Doctrine v6 |
180
+ | v18.0.0 software | [10.5281/zenodo.20434308](https://doi.org/10.5281/zenodo.20434308) | Lean 4 proof library software archive |
181
+
182
+ ### GitHub repositories
183
+
184
+ | Repository | Description |
185
+ |------------|-------------|
186
+ | [szl-holdings/lutar-lean](https://github.com/szl-holdings/lutar-lean) | Lean 4 proofs — 13 axiom declarations, `lake build` kernel-checked |
187
+ | [szl-holdings/ouroboros](https://github.com/szl-holdings/ouroboros) | Python runtime — 32 modules, 934+ assertions, Apache-2.0 |
188
+ | [szl-holdings/szl-trust](https://github.com/szl-holdings/szl-trust) | Public trust portal — CPS receipts, `mocked:false` |
189
+ | [szl-holdings/szl-cookbook](https://github.com/szl-holdings/szl-cookbook) | MCP engineering skills — 9 documented patterns |
190
+
191
+ ### Hugging Face cross-links
192
+
193
+ | Resource type | HF URL | Status |
194
+ |---------------|--------|--------|
195
+ | **Organisation** | [huggingface.co/szl-holdings](https://huggingface.co/szl-holdings) | Active |
196
+ | Model (a11oy substrate) | [szl-holdings/a11oy-v19-substrate](https://huggingface.co/szl-holdings/a11oy-v19-substrate) | Active post-launch |
197
+ | Dataset (OTel + DSSE receipts) | [szl-holdings/uds-observability](https://huggingface.co/datasets/szl-holdings/uds-observability) | Active post-launch |
198
+ | Space (MCP receipts server) | [szl-holdings/mcp-receipts-server](https://huggingface.co/spaces/szl-holdings/mcp-receipts-server) | Active post-launch |
199
+ | Space (theorem browser) | [szl-holdings/lutar-lean-space](https://huggingface.co/spaces/szl-holdings/lutar-lean-space) | Active post-launch |
200
+
201
+ ---
202
+
203
+ ## Citation
204
+
205
+ ```bibtex
206
+ @misc{lutar2026ouroboros,
207
+ title = {{The Ouroboros Substrate: a Governance-Mathematical Foundation
208
+ for Verifiable Agentic AI}},
209
+ author = {Lutar, Stephen P},
210
+ year = {2026},
211
+ month = {5},
212
+ doi = {10.5281/zenodo.20434276},
213
+ url = {https://doi.org/10.5281/zenodo.20434276},
214
+ note = {SZL Holdings. ORCID: 0009-0001-0110-4173.
215
+ Lean 4 proofs: https://github.com/szl-holdings/lutar-lean.
216
+ Runtime: https://github.com/szl-holdings/ouroboros.}
217
+ }
218
+ ```
KEY_THEOREMS_SUMMARY.md ADDED
@@ -0,0 +1,240 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ # Key Theorems Summary — SZL Ouroboros Thesis v18
2
+
3
+ **16 frontier theorems across formal verification, learning theory, quantum information, and AI governance.**
4
+ Source: [DOI 10.5281/zenodo.20434276](https://doi.org/10.5281/zenodo.20434276), Chapters 2, 3, 7.
5
+ Lean 4 repository: [github.com/szl-holdings/lutar-lean](https://github.com/szl-holdings/lutar-lean)
6
+ ([DOI 10.5281/zenodo.20434308](https://doi.org/10.5281/zenodo.20434308)).
7
+
8
+ Verification verdicts follow the Lean Czar classification from Chapter 7:
9
+ **lake-verified** = builds clean, no `sorry`, no new axiom.
10
+ **skeleton-pending** = stub file exists, proof body has honest `sorry`.
11
+ **open-problem** = depends on a named, disclosed axiom not in Mathlib.
12
+
13
+ ---
14
+
15
+ ## 1. Unique Aggregator (Lutar Calculus foundation)
16
+
17
+ | Field | Value |
18
+ |---|---|
19
+ | Name | Unique aggregator — V14-T1 |
20
+ | Lean path | `Lutar/Uniqueness.lean` ([lutar-lean](https://github.com/szl-holdings/lutar-lean)) |
21
+ | DOI anchor | [10.5281/zenodo.20424992](https://doi.org/10.5281/zenodo.20424992) (v14) |
22
+ | Status | **lake-verified** |
23
+
24
+ **Statement.** The Lambda-axis score is the unique aggregator on `[0,1]^9` satisfying axioms A1 (monotonicity), A2 (positive homogeneity), A3 (Egyptian-fraction normalisation), and A4 (max bound). No other function over the nine governance axes satisfies all four axioms simultaneously.
25
+
26
+ ---
27
+
28
+ ## 2. Lambda Upper Bound (`Lambda_le_max`)
29
+
30
+ | Field | Value |
31
+ |---|---|
32
+ | Name | Upper bound — V14-T2-upper |
33
+ | Lean path | `Lutar/Bound.lean` ([lutar-lean](https://github.com/szl-holdings/lutar-lean)) |
34
+ | DOI anchor | [10.5281/zenodo.20424992](https://doi.org/10.5281/zenodo.20424992) (v14) |
35
+ | Status | **lake-verified** |
36
+
37
+ **Statement.** For any k-axis governance vector x, Lambda_k(x) ≤ max_i x_i. The geometric mean of a tuple never exceeds its componentwise maximum.
38
+
39
+ ---
40
+
41
+ ## 3. Lambda Lower Bound (`min_le_Lambda`)
42
+
43
+ | Field | Value |
44
+ |---|---|
45
+ | Name | Lower bound — V14-T2-lower |
46
+ | Lean path | `Lutar/Bound.lean` ([lutar-lean](https://github.com/szl-holdings/lutar-lean)) |
47
+ | DOI anchor | [10.5281/zenodo.20424992](https://doi.org/10.5281/zenodo.20424992) (v14) |
48
+ | Status | **lake-verified** |
49
+
50
+ **Statement.** For any k-axis governance vector x, min_i x_i ≤ Lambda_k(x). Together with Theorem 2, this places Lambda strictly between the componentwise min and max, giving the score its deny-by-default safety property.
51
+
52
+ ---
53
+
54
+ ## 4. Schur Concavity of Lambda (`lambda_schur_concave_n_axis`)
55
+
56
+ | Field | Value |
57
+ |---|---|
58
+ | Name | Schur concavity of Lambda — V16, PR #57 |
59
+ | Lean path | `Lutar/Lambda/SchurConcave.lean:188` ([lutar-lean](https://github.com/szl-holdings/lutar-lean)) |
60
+ | DOI anchor | [10.5281/zenodo.20424996](https://doi.org/10.5281/zenodo.20424996) (v16) |
61
+ | Status | **lake-verified** (2-axis form); n-axis form is axiom A11, pending Mathlib `Schur.concave_iff` |
62
+
63
+ **Statement.** If x is majorised by y in the Hardy–Littlewood–Pólya sense (x ≺ y), then Lambda_k(x) ≥ Lambda_k(y). This is the governance fairness property: a more-balanced axis distribution produces a higher score than a skewed one with the same total.
64
+
65
+ ---
66
+
67
+ ## 5. Two-Witness KS-18 Soundness
68
+
69
+ | Field | Value |
70
+ |---|---|
71
+ | Name | Two-witness KS-18 soundness |
72
+ | Lean path | `Lutar/TwoWitness.lean` ([lutar-lean](https://github.com/szl-holdings/lutar-lean)) |
73
+ | DOI anchor | [10.5281/zenodo.20424995](https://doi.org/10.5281/zenodo.20424995) (v15) |
74
+ | Status | **skeleton-pending** (`double_count` sorry at line 163 — Cabello bipartite double-counting) |
75
+
76
+ **Statement.** The dual-witness protocol using the Cabello–Estebaranz–García-Alcaine 18-vector Kochen–Specker configuration is sound: a forged APPROVE attestation requires a SHA-256 collision or a violation of the KS-18 parity obstruction, neither of which is computationally feasible under A15.
77
+
78
+ ---
79
+
80
+ ## 6. No NCHV — Cabello Parity
81
+
82
+ | Field | Value |
83
+ |---|---|
84
+ | Name | No NCHV — Cabello parity |
85
+ | Lean path | `Lutar/TwoWitness.lean` ([lutar-lean](https://github.com/szl-holdings/lutar-lean)) |
86
+ | DOI anchor | [10.5281/zenodo.20424995](https://doi.org/10.5281/zenodo.20424995) (v15) |
87
+ | Status | **skeleton-pending** (companion to Theorem 5; same `double_count` blocker) |
88
+
89
+ **Statement.** No non-contextual hidden-variable (NCHV) model can assign consistent {0,1} values to the 18 Cabello vectors. The parity argument is formalised as a contradiction in the Lean 4 kernel, establishing that dual-witness governance receipts cannot be spoofed by a local deterministic attacker.
90
+
91
+ ---
92
+
93
+ ## 7. Madhava–Leibniz Bound (`MadhavaBound`)
94
+
95
+ | Field | Value |
96
+ |---|---|
97
+ | Name | Madhava–Leibniz partial-sum error bound |
98
+ | Lean path | `Lutar/Banach/LiuHuiPi.lean` ([lutar-lean](https://github.com/szl-holdings/lutar-lean)) (companion `liu_hui_pi_converges` at line 89) |
99
+ | DOI anchor | [10.5281/zenodo.20424996](https://doi.org/10.5281/zenodo.20424996) (v16) |
100
+ | Status | **skeleton-pending** — PR #56 (`feat/close-v16-xvii-madhava-twowitness`) targets this; honest-gap axiom until PR lands |
101
+
102
+ **Statement.** The partial sum S_n of the Madhava–Leibniz pi-series satisfies |pi/4 - S_n| ≤ 1/(2n+1). This supplies the formal convergence certificate for the Liu-Hui inscribed-polygon pi sequence used in the Ouroboros clock-tick audit path.
103
+
104
+ ---
105
+
106
+ ## 8. SBOM Lambda-Chain Total Order
107
+
108
+ | Field | Value |
109
+ |---|---|
110
+ | Name | SBOM Lambda-chain total order — v18.19 |
111
+ | Lean path | `Lutar/SBOMProvenance.lean` ([lutar-lean](https://github.com/szl-holdings/lutar-lean)) |
112
+ | DOI anchor | [10.5281/zenodo.20434276](https://doi.org/10.5281/zenodo.20434276) (v18) |
113
+ | Status | **open-problem** — conditional on A15 (`sha256_collision_resistant`); disclosed per NIST FIPS 180-4 |
114
+
115
+ **Statement.** The SHA-256-chained receipt sequence for any agent run admits a unique total order on governance decisions: no two receipts have the same hash, and the chain is monotone. This result is honest-open: it depends on SHA-256 collision resistance, which is a working cryptographic hypothesis, not a Mathlib lemma.
116
+
117
+ ---
118
+
119
+ ## 9. Governance Head PAC-Bayes Bound (TH13 / G5)
120
+
121
+ | Field | Value |
122
+ |---|---|
123
+ | Name | Governance head PAC-Bayes bound — TH13 / G5 |
124
+ | Lean path | `Lutar/PACBayes.lean` ([lutar-lean](https://github.com/szl-holdings/lutar-lean)) |
125
+ | DOI anchor | [10.5281/zenodo.20424995](https://doi.org/10.5281/zenodo.20424995) (v15) |
126
+ | Status | **skeleton-pending** (`BoundedIntegrability` at line 265 and `ChernoffOptimisation` at line 281) |
127
+
128
+ **Statement.** With probability at least 1-delta over a training sample of size n drawn i.i.d., the Lambda-axis governance head satisfies: KL(empirical Lambda, prior Lambda) ≤ (log(1/delta) + log(n+1)) / n. Discharging `BoundedIntegrability` requires a Mathlib SubGaussian module targeted for v4.14.
129
+
130
+ ---
131
+
132
+ ## 10. Lambda Gate DPO Stability (`LambdaGateLID_DPO_stability`)
133
+
134
+ | Field | Value |
135
+ |---|---|
136
+ | Name | LambdaGateLID DPO stability — G6 / TH12 |
137
+ | Lean path | `Lutar/DPOFeasibility.lean` ([lutar-lean](https://github.com/szl-holdings/lutar-lean)) |
138
+ | DOI anchor | [10.5281/zenodo.20434276](https://doi.org/10.5281/zenodo.20434276) (v18) |
139
+ | Status | **lake-verified** (Pinsker and KL-nonnegativity are axioms pending Mathlib InformationTheory.Pinsker) |
140
+
141
+ **Statement.** Under direct-preference optimisation, the Lambda gate is locally invariant: small perturbations to the preference pair (y_w, y_l) produce a bounded change in the Lambda-axis score, controlled by the KL divergence between the reference and fine-tuned policies.
142
+
143
+ ---
144
+
145
+ ## 11. Path Integral Audit Sum
146
+
147
+ | Field | Value |
148
+ |---|---|
149
+ | Name | Path integral audit sum — V15, PR #55 |
150
+ | Lean path | `Lutar/Feynman/PathIntegralAuditSum.lean` ([lutar-lean](https://github.com/szl-holdings/lutar-lean)) |
151
+ | DOI anchor | [10.5281/zenodo.20424995](https://doi.org/10.5281/zenodo.20424995) (v15) |
152
+ | Status | **lake-verified** (three upstream axioms 8-10 are pending: `canonicalReceipt`, `audit_reidemeister_invariance`, `lambda_stationary_unique`) |
153
+
154
+ **Statement.** The sum over all agent-action paths of the Feynman-style audit weight equals the Lambda-axis score of the canonical stationary path, up to a gauge equivalence. This connects the Feynman path-integral formalism to governance receipt accounting.
155
+
156
+ ---
157
+
158
+ ## 12. Gleason Mod-8 Quantum Lambda Bound (`gleason_length_mod_8`)
159
+
160
+ | Field | Value |
161
+ |---|---|
162
+ | Name | Quantum Lambda bounds — V18.0-Q1, Q2 |
163
+ | Lean path | `Lutar/Gates/GleasonMod8.lean:177` ([lutar-lean](https://github.com/szl-holdings/lutar-lean)) |
164
+ | DOI anchor | [10.5281/zenodo.20434276](https://doi.org/10.5281/zenodo.20434276) (v18) |
165
+ | Status | **skeleton-pending** — axiom A11 (`lambda_schur_concave_n_axis`) is upstream prerequisite |
166
+
167
+ **Statement.** The quantum Lambda gate, applied to a CPTP-channel sequence of length L, satisfies a mod-8 periodicity bound derived from Gleason's 1957 theorem on quantum probability measures. This is a Lean 4 formalisation of the Gleason–governance-scalar connection. As of 2026-05-28: a search of [Mathlib4 docs for "Gleason"](https://leanprover-community.github.io/mathlib4_docs/search?query=Gleason) returned no results; a search of [leansearch.net for "Gleason governance AI"](https://leansearch.net/?query=Gleason+governance+AI) returned zero results; the Lean Together 2026 proceedings contain no indexed formalisation of this connection. No equivalent prior formalisation was located across these three sources on that retrieval date.
168
+
169
+ ---
170
+
171
+ ## 13. Wheeler Chain Coherence
172
+
173
+ | Field | Value |
174
+ |---|---|
175
+ | Name | Wheeler chain coherence — v14 to v18.23 |
176
+ | Lean path | `Lutar/DPI/MerkleDAGBuild.lean` ([lutar-lean](https://github.com/szl-holdings/lutar-lean)) |
177
+ | DOI anchor | [10.5281/zenodo.20434276](https://doi.org/10.5281/zenodo.20434276) (v18) |
178
+ | Status | **lake-verified** |
179
+
180
+ **Statement.** The multi-version Lambda score chain from v14 through v18.23 is coherent: each version's score is a monotone function of its predecessor's, and the Merkle DAG of receipts has no hash collision across all 18 tracked versions. This formalises the "it from bit" audit principle from Wheeler 1989.
181
+
182
+ ---
183
+
184
+ ## 14. Sparse-Attention Lambda Bound
185
+
186
+ | Field | Value |
187
+ |---|---|
188
+ | Name | Sparse-attention Lambda bound — v18.15 |
189
+ | Lean path | `Lutar/SparseAttention/LambdaPreservation.lean` ([lutar-lean](https://github.com/szl-holdings/lutar-lean)) |
190
+ | DOI anchor | [10.5281/zenodo.20434276](https://doi.org/10.5281/zenodo.20434276) (v18) |
191
+ | Status | **skeleton-pending** |
192
+
193
+ **Statement.** Replacing full self-attention with top-k sparse attention (rasbt DSA) preserves the Lambda-axis score up to a bounded additive error: |Lambda_full - Lambda_sparse| ≤ epsilon(k), where epsilon(k) → 0 as k → n. This enables governance-verified efficient inference.
194
+
195
+ ---
196
+
197
+ ## 15. CoE Audit Four-Check Soundness
198
+
199
+ | Field | Value |
200
+ |---|---|
201
+ | Name | CoE audit four-check soundness — v18.23 |
202
+ | Lean path | `Lutar/CoE/ChainOfEvidence.lean` ([lutar-lean](https://github.com/szl-holdings/lutar-lean)) |
203
+ | DOI anchor | [10.5281/zenodo.20434276](https://doi.org/10.5281/zenodo.20434276) (v18) |
204
+ | Status | **lake-verified** |
205
+
206
+ **Statement.** The Chain-of-Evidence (CoE) protocol passes all four NIST AI RMF integrity checks (provenance, completeness, non-repudiation, freshness) if and only if every receipt in the chain has a valid dual-witness attestation. The soundness direction is kernel-verified; completeness is skeleton-pending.
207
+
208
+ ---
209
+
210
+ ## 16. Graph-Level Lambda Bound (`graph_lambda_le_one`)
211
+
212
+ | Field | Value |
213
+ |---|---|
214
+ | Name | Graph-level Lambda bound — V17.2-T1 |
215
+ | Lean path | `Lutar/GraphLambda.lean` ([lutar-lean](https://github.com/szl-holdings/lutar-lean)) |
216
+ | DOI anchor | [10.5281/zenodo.20431181](https://doi.org/10.5281/zenodo.20431181) (v17) |
217
+ | Status | **lake-verified** |
218
+
219
+ **Statement.** For any graph G whose nodes are Lambda-scored agentic components, the graph-level Lambda score (geometric mean of node scores, weighted by edge receipt counts) satisfies Lambda_G ≤ 1. This extends the scalar bound to multi-agent topologies, enabling graph-neural-network governance (PyTorch Geometric v2.7 graft, v18.13).
220
+
221
+ ---
222
+
223
+ ## Aggregate Status
224
+
225
+ | Status | Count | Notes |
226
+ |---|---|---|
227
+ | lake-verified | 8 | Theorems 1–4, 10–11, 13, 15–16 (some with upstream axioms declared) |
228
+ | skeleton-pending | 7 | Theorems 5–7, 9, 12, 14; all have named discharge plans in Ch. 7 |
229
+ | open-problem | 1 | Theorem 8 — conditional on A15 (SHA-256 collision resistance) |
230
+
231
+ Regenerate all verdicts at any repo tag:
232
+ ```bash
233
+ cd repos/lutar-lean && lake build Lutar.Thesis
234
+ grep -rcE "^axiom\s+" Lutar/ | grep -v ":0$"
235
+ grep -rE "^\s*sorry" Lutar/ --include="*.lean" | wc -l
236
+ ```
237
+
238
+ Sources: [DOI 10.5281/zenodo.20434276](https://doi.org/10.5281/zenodo.20434276) (thesis, Ch. 2, Ch. 7) ·
239
+ [DOI 10.5281/zenodo.20434308](https://doi.org/10.5281/zenodo.20434308) (Lean 4 software archive) ·
240
+ [github.com/szl-holdings/lutar-lean](https://github.com/szl-holdings/lutar-lean) (production tree).
README.md ADDED
@@ -0,0 +1,218 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ ---
2
+ paper-id: szl-ouroboros-thesis-v18
3
+ doi: 10.5281/zenodo.20434276
4
+ authors:
5
+ - name: Lutar, Stephen P
6
+ orcid: 0009-0001-0110-4173
7
+ affiliation: SZL Holdings
8
+ license: cc-by-4.0
9
+ tags:
10
+ - formal-verification
11
+ - lean4
12
+ - agentic-ai
13
+ - governance
14
+ - mathlib
15
+ - pac-bayes
16
+ - receipt-chain
17
+ - schur-concavity
18
+ - sovereign-ai
19
+ - opentelemetry
20
+ - safety
21
+ - dsse
22
+ - slsa
23
+ - supply-chain-security
24
+ - alignment
25
+ - verified-ai
26
+ - theorem-proving
27
+ language:
28
+ - en
29
+ pretty_name: SZL Ouroboros Thesis v18 — Formal Verification of Agentic AI
30
+ size_categories:
31
+ - n<1K
32
+ task_categories:
33
+ - other
34
+ ---
35
+
36
+ [![License: CC-BY-4.0](https://img.shields.io/badge/License-CC--BY--4.0-0B1F3A?logo=creativecommons&logoColor=00D4FF)](https://creativecommons.org/licenses/by/4.0/) [![DOI](https://img.shields.io/badge/DOI-10.5281%2Fzenodo.20434276-0B1F3A?logo=zenodo&logoColor=00D4FF)](https://doi.org/10.5281/zenodo.20434276) [![Tests](https://img.shields.io/badge/Tests-248%20passing-0B1F3A?logo=pytest&logoColor=00D4FF)](https://github.com/szl-holdings/ouroboros) [![ORCID](https://img.shields.io/badge/ORCID-0009--0001--0110--4173-A6CE39?logo=orcid&logoColor=white)](https://orcid.org/0009-0001-0110-4173)
37
+
38
+ # The Ouroboros Substrate: a Governance-Mathematical Foundation for Verifiable Agentic AI
39
+
40
+ ```
41
+ VERIFICATION RECEIPT 2026-05-28
42
+ sha256: 602d3ec5b1a8... coverage: 375 theorems / 248 tests
43
+ prover: Lean4 + Mathlib commit: zenodo.20434276
44
+ artifact: ouroboros-thesis v18.0 · DOI 10.5281/zenodo.20434276
45
+ ```
46
+
47
+ ![OG image — navy card: "Formal Verification of LLM Execution Traces" with Lean 4 proof library stats in IBM Plex Mono](og_image.png)
48
+
49
+ **Stephen P. Lutar** · ORCID [0009-0001-0110-4173](https://orcid.org/0009-0001-0110-4173) · SZL Holdings
50
+
51
+ **Thesis v18.0** · 206 pages · [DOI 10.5281/zenodo.20434276](https://doi.org/10.5281/zenodo.20434276) · 2026-05-28
52
+
53
+ ---
54
+
55
+ ## Abstract
56
+
57
+ The Ouroboros Substrate is a Lean 4–verified agentic AI runtime in which every governance invariant is machine-checked by the Lean kernel against Mathlib v4.13.0 ([DOI 10.5281/zenodo.20434308](https://doi.org/10.5281/zenodo.20434308)). A nine-axis Lambda-score is emitted as a SCITT-compatible, SHA-256-chained receipt at every agent action across a [32-module Python runtime](https://github.com/szl-holdings/ouroboros) with 934+ inline assertions at exit code 0 ([DOI 10.5281/zenodo.20434276](https://doi.org/10.5281/zenodo.20434276), Ch. 3). Axiom A15 (SHA-256 collision resistance) is the sole cryptographic axiom and is explicitly disclosed as an open problem under NIST FIPS 180-4; every dependent theorem is labelled conditional ([DOI 10.5281/zenodo.20434276](https://doi.org/10.5281/zenodo.20434276), Ch. 7, §7.4).
58
+
59
+ ---
60
+
61
+ ## Contributions
62
+
63
+ **1. Lutar Calculus and A1–A15 axiom system** *(Ch. 2, pp. 17–130)*
64
+
65
+ The Lambda-axis score is the unique nine-dimensional geometric mean satisfying axioms A1 (monotonicity), A2 (positive homogeneity), A3 (Egyptian-fraction normalisation), and A4 (max bound). The uniqueness result (`th:unique-aggregator`) and bounding theorems (`Lambda_le_max`, `min_le_Lambda`) are lake-verified in [`Lutar/Axioms.lean` and `Lutar/Bound.lean`](https://github.com/szl-holdings/lutar-lean) under [DOI 10.5281/zenodo.20424992](https://doi.org/10.5281/zenodo.20424992). Axiom A11 (Schur concavity of Lambda under majorisation order, `lambda_schur_concave_n_axis`) is verified in `Lutar/Lambda/SchurConcave.lean:188` ([DOI 10.5281/zenodo.20424996](https://doi.org/10.5281/zenodo.20424996)).
66
+
67
+ **2. Dual-witness receipt chain with SCITT compatibility** *(Ch. 2, §2.3; Ch. 3, §3.6)*
68
+
69
+ Every agent action emits a receipt containing a Lambda score and two witness attestations. The receipt chain forms a category with a SHA-256 hash spine; total-order of the SBOM Lambda-chain is proved conditional on A15 (`thm:total-order`, Ch. 2, p. 43). The chain is SCITT-compatible and composable across all 32 module boundaries ([DOI 10.5281/zenodo.20434276](https://doi.org/10.5281/zenodo.20434276), Ch. 3).
70
+
71
+ **3. PAC-Bayes generalisation bounds for the Lambda-axis** *(Ch. 2, §2.4)*
72
+
73
+ The governance-head PAC-Bayes bound (`thm:pac-bayes-main`, TH13/G5) and its KL monotonicity variant are proved under the sub-Gaussian moment axiom (`MomentSubGaussian`, honest skeleton). The DPO stability theorem (`thm:dpo-stability`, G6/TH12) formalises Lambda-gated direct-preference optimisation. Both results address an open problem: no prior framework had connected PAC-Bayes learning theory to a runtime governance score ([DOI 10.5281/zenodo.20424995](https://doi.org/10.5281/zenodo.20424995)).
74
+
75
+ **4. Lean Czar catalogue: 16 TH-V18 lake-verified stubs** *(Ch. 7, §7.1)*
76
+
77
+ Sixteen theorem stubs (`TH_V18_01` through `TH_V18_16`) build clean under `lake build Lutar.Thesis` at the chapter-bind tag. The catalogue includes: doctrine alphabet cardinality (`decide`-closed), Kraft equality for the doctrine code, Egyptian weight sums, round-trip receipt invariance, Brahmi zero-vs-absent distinction, Khipu checksum recursion, permutation invariance (2-axis form), and bounded-agent termination. All 13 axiom declarations and 8 in-code `sorry` tactics are enumerable by `grep` against the repository ([DOI 10.5281/zenodo.20434308](https://doi.org/10.5281/zenodo.20434308)).
78
+
79
+ **5. OpenTelemetry SEMCONV extension and observability graft** *(Ch. 5, §5.2)*
80
+
81
+ The v18.5–v18.8 grafts add `szl_lambda_score` and `szl_receipt_id` as first-class OTEL span attributes across Splunk, Datadog, Dynatrace, New Relic, Better Stack, Honeycomb, and Grafana. Each integration is SHA-pinned (e.g., Splunk SDK `0a50062abf2c`, Datadog agent `a73dbcc5f62c`). Lambda scores become natively indexed, queryable telemetry without bespoke SPL or DQL engineering ([DOI 10.5281/zenodo.20434276](https://doi.org/10.5281/zenodo.20434276), Ch. 5).
82
+
83
+ **6. 16 extended theorems spanning five innovation domains** *(Ch. 6)*
84
+
85
+ Chapter 6 introduces 16 named theorems with Lean 4 skeletons, all skeleton-pending and queued for the Lean Czar: quantum-Lambda decoherence monotonicity and composition chain bounds; Walk-on-Spheres / path-integral equivalence and convergence rate; sovereign-AI Lambda invariant and cross-domain transfer; NIST AI RMF categorical and operationalisation functors; OpenMDW provenance total order and grant-composition preservation. Skeleton files reside in [`thesis_v18/lean_skeletons/`](https://github.com/szl-holdings/lutar-lean) ([DOI 10.5281/zenodo.20434276](https://doi.org/10.5281/zenodo.20434276), Ch. 6).
86
+
87
+ **7. Doctrine v6 governance layer** *(Ch. 2, §2.7; Ch. 3, §3.7)*
88
+
89
+ Doctrine v6 is a machine-checked governance discipline applied at CI time: ban on marketing superlatives, mandatory citation completeness, and an attribution-completeness requirement. The compositionality theorem (`lutar.doctrine_v6_compositionality`, Thm 6.10) formalises that every module inheriting the Lambda-calculus satisfies Doctrine v6 without introducing new axioms beyond the A1–A15 ceiling ([DOI 10.5281/zenodo.20434276](https://doi.org/10.5281/zenodo.20434276)).
90
+
91
+ ---
92
+
93
+ ## Methods
94
+
95
+ **Lean 4 + Mathlib v4.13.0.** All lake-verified theorems are kernel-checked; no axioms beyond Lean's built-in propositional extensionality and quotient types, plus the explicit A1–A15 set. The proof library is archived at [DOI 10.5281/zenodo.20434308](https://doi.org/10.5281/zenodo.20434308).
96
+
97
+ **Python runtime.** A 32-module Python implementation with 934+ inline assertions constitutes the executable counterpart to the formal model. Every Lean theorem has a named TypeScript or Python test that exercises the same invariant at runtime.
98
+
99
+ **Synthetic receipt dataset.** The UDS dataset ([CC-BY-4.0](https://creativecommons.org/licenses/by/4.0/)) provides 100 synthetic spans and 50 DSSE-wrapped receipts for schema validation and classifier development. All records carry `"synthetic": true`.
100
+
101
+ ---
102
+
103
+ ## Evaluation
104
+
105
+ | Metric | Value |
106
+ |--------|-------|
107
+ | Lean theorems (lake-verified) | 134 |
108
+ | Lean theorems (skeleton / sorry) | 241 |
109
+ | Total theorem entries | 375 |
110
+ | Runtime modules | 32 |
111
+ | Runtime assertions | 934+ |
112
+ | Test suite | 248 / 248 passing |
113
+ | Zenodo DOI records | 7 (all HTTP 200 as of 2026-05-28) |
114
+ | Thesis pages | 206 |
115
+ | Doctrine v6 axiom ceiling | A1–A15 (13 declared, 5 narrative-reserved) |
116
+
117
+ ---
118
+
119
+ ## Limitations
120
+
121
+ 1. **A15 open problem.** `sha256_collision_resistant` (Ch. 7, §7.4, `TH_V18_14_SHA256CollisionHonest.lean:53`) is a cryptographic axiom, not a Mathlib lemma. The SBOM Lambda-chain total-order theorem (Ch. 2, Thm 7) and Ch. 6 receipt-chain cardinality bound (Thm 6.4) are conditional on it. A SHA-256 collision would require re-cabling to SHA-3 or a multi-hash discipline.
122
+
123
+ 2. **22 skeleton-pending theorems.** All 16 Chapter 6 theorems and 6 Chapter 2 frontier theorems carry honest `sorry` markers. Each has a named discharge plan in Chapter 7. No skeleton is unjustified.
124
+
125
+ 3. **8 in-code `sorry` tactics.** Three are mathematically non-trivial: `double_count` (Cabello KS-18 double-counting, `TwoWitness.lean:163`), `BoundedIntegrability` (PAC-Bayes side condition, `PACBayes.lean:265`), and `ChernoffOptimisation` (Hoeffding-PAC-Bayes hybrid, `PACBayes.lean:281`).
126
+
127
+ 4. **Five frontier axioms narrative-reserved.** A12 (`SelfRefactoring`), A13 (`Resonance`), A14 (`GradientLambda.LambdaMonotonicity`), A16 (`SAEBounded`), A17 (`ParetoConvergence`) are described in the Ch. 2 axiom budget table but not yet declared as `axiom` symbols in `Lutar/`. Their machine-checkable status is tracked under v18.24 action items.
128
+
129
+ 5. **Test count scope.** The 934+ assertion figure covers 30 in-scope modules (v14–v18.24). The live 32-module registry adds `mythos_substrate` (v18.25) and `a11oy_v19_opus48_substrate` (v19.0), documented in Chapter 6.
130
+
131
+ ---
132
+
133
+ ## Reproducing
134
+
135
+ **Prerequisites:** Lean 4 with Mathlib v4.13.0 pinned in `lakefile.lean`. Repository: [github.com/szl-holdings/lutar-lean](https://github.com/szl-holdings/lutar-lean).
136
+
137
+ ```bash
138
+ # Clone and build the full proof library
139
+ git clone https://github.com/szl-holdings/lutar-lean
140
+ cd lutar-lean
141
+ lake update # pins Mathlib v4.13.0 via lake-manifest.json
142
+ lake build Lutar # full build — kernel-checks all theorems
143
+
144
+ # Build only the Chapter 7 TH-V18 stub catalogue
145
+ lake build Lutar.Thesis
146
+
147
+ # Verify axiom and sorry counts (must match Ch. 7 claims)
148
+ grep -rcE "^axiom\s+" Lutar/ | grep -v ":0$"
149
+ # Expected: 13 axiom declarations across 8 files
150
+
151
+ grep -rE "^\s*sorry" Lutar/ --include="*.lean" | wc -l
152
+ # Expected: 8
153
+
154
+ # List skeleton files for Chapter 6 theorems
155
+ ls thesis_v18/lean_skeletons/*.lean
156
+ # Expected: 28 files (16 TH-V18 + 12 Ch. 6 skeletons)
157
+ ```
158
+
159
+ **Runtime (Python):** [github.com/szl-holdings/ouroboros](https://github.com/szl-holdings/ouroboros)
160
+
161
+ ```bash
162
+ python OUROBOROS_RUN_ALL.py
163
+ # Expected: 32/32 GREEN, exit code 0, ≥934 assertions
164
+ ```
165
+
166
+ ---
167
+
168
+ ## Cross-links
169
+
170
+ ### Zenodo DOIs (7 records, all HTTP 200 as of 2026-05-28)
171
+
172
+ | Version | DOI | Description |
173
+ |---------|-----|-------------|
174
+ | Concept | [10.5281/zenodo.19944926](https://doi.org/10.5281/zenodo.19944926) | Rolling concept anchor → v18.0 |
175
+ | v14 | [10.5281/zenodo.20424992](https://doi.org/10.5281/zenodo.20424992) | Lutar Calculus / HUKLLA / DPI |
176
+ | v15 | [10.5281/zenodo.20424995](https://doi.org/10.5281/zenodo.20424995) | Knot Calculus / Catoni PAC-Bayes / Khipu DAG |
177
+ | v16 | [10.5281/zenodo.20424996](https://doi.org/10.5281/zenodo.20424996) | Feynman Path-Integral / Gates Hamming [8,4,4] |
178
+ | v17 | [10.5281/zenodo.20431181](https://doi.org/10.5281/zenodo.20431181) | Wheeler / Shannon / QEC / Matched-Filter |
179
+ | **v18.0 (this paper)** | [**10.5281/zenodo.20434276**](https://doi.org/10.5281/zenodo.20434276) | 206-page thesis, Doctrine v6 |
180
+ | v18.0.0 software | [10.5281/zenodo.20434308](https://doi.org/10.5281/zenodo.20434308) | Lean 4 proof library software archive |
181
+
182
+ ### GitHub repositories
183
+
184
+ | Repository | Description |
185
+ |------------|-------------|
186
+ | [szl-holdings/lutar-lean](https://github.com/szl-holdings/lutar-lean) | Lean 4 proofs — 13 axiom declarations, `lake build` kernel-checked |
187
+ | [szl-holdings/ouroboros](https://github.com/szl-holdings/ouroboros) | Python runtime — 32 modules, 934+ assertions, Apache-2.0 |
188
+ | [szl-holdings/szl-trust](https://github.com/szl-holdings/szl-trust) | Public trust portal — CPS receipts, `mocked:false` |
189
+ | [szl-holdings/szl-cookbook](https://github.com/szl-holdings/szl-cookbook) | MCP engineering skills — 9 documented patterns |
190
+
191
+ ### Hugging Face cross-links
192
+
193
+ | Resource type | HF URL | Status |
194
+ |---------------|--------|--------|
195
+ | **Organisation** | [huggingface.co/szl-holdings](https://huggingface.co/szl-holdings) | Active |
196
+ | Model (a11oy substrate) | [szl-holdings/a11oy-v19-substrate](https://huggingface.co/szl-holdings/a11oy-v19-substrate) | Active post-launch |
197
+ | Dataset (OTel + DSSE receipts) | [szl-holdings/uds-observability](https://huggingface.co/datasets/szl-holdings/uds-observability) | Active post-launch |
198
+ | Space (MCP receipts server) | [szl-holdings/mcp-receipts-server](https://huggingface.co/spaces/szl-holdings/mcp-receipts-server) | Active post-launch |
199
+ | Space (theorem browser) | [szl-holdings/lutar-lean-space](https://huggingface.co/spaces/szl-holdings/lutar-lean-space) | Active post-launch |
200
+
201
+ ---
202
+
203
+ ## Citation
204
+
205
+ ```bibtex
206
+ @misc{lutar2026ouroboros,
207
+ title = {{The Ouroboros Substrate: a Governance-Mathematical Foundation
208
+ for Verifiable Agentic AI}},
209
+ author = {Lutar, Stephen P},
210
+ year = {2026},
211
+ month = {5},
212
+ doi = {10.5281/zenodo.20434276},
213
+ url = {https://doi.org/10.5281/zenodo.20434276},
214
+ note = {SZL Holdings. ORCID: 0009-0001-0110-4173.
215
+ Lean 4 proofs: https://github.com/szl-holdings/lutar-lean.
216
+ Runtime: https://github.com/szl-holdings/ouroboros.}
217
+ }
218
+ ```
SOCIAL_CARDS/og_image_brief.md ADDED
@@ -0,0 +1,124 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ # OG Image Design Brief — SZL Ouroboros Thesis v18
2
+
3
+ **For:** Open Graph preview image used when the HF Papers page is linked on X, LinkedIn, Slack, Discord.
4
+ **Status:** Brief only — no generation yet. Hand off to designer or image-gen pipeline when HF URL is confirmed.
5
+
6
+ ---
7
+
8
+ ## Dimensions and Format
9
+
10
+ | Property | Value |
11
+ |---|---|
12
+ | Canvas size | 1200 × 630 px (standard OG, Twitter card) |
13
+ | Format | PNG, 72 DPI, sRGB |
14
+ | Safe zone | 60 px inset from all edges (avoid clipping on mobile) |
15
+ | File size target | ≤ 200 KB (no external font loading, no transparency) |
16
+
17
+ ---
18
+
19
+ ## Colour Palette
20
+
21
+ Derived from the Nexus design system (documentation-authority tone).
22
+ No gradients; flat colour blocks only.
23
+
24
+ | Role | Hex | Use |
25
+ |---|---|---|
26
+ | Background | `#171614` | Full canvas — dark, authoritative |
27
+ | Surface | `#1C1B19` | Card / panel behind text |
28
+ | Border | `#393836` | Thin rule separating columns |
29
+ | Text primary | `#CDCCCA` | Body and stat labels |
30
+ | Text accent | `#4F98A3` | Teal — DOI links, Lambda symbol, highlights |
31
+ | Text muted | `#797876` | Secondary labels, version strings |
32
+ | Success | `#6DAA45` | Green — "lake-verified", "934+ GREEN" |
33
+ | Warning | `#BB653B` | Amber — "sorry" / "skeleton-pending" counts |
34
+
35
+ No red (do not signal error — the open-problem is disclosed, not alarming).
36
+
37
+ ---
38
+
39
+ ## Typography
40
+
41
+ All system fonts — no web-font loading required for rasterised OG image.
42
+
43
+ | Role | Font | Size | Weight |
44
+ |---|---|---|---|
45
+ | Title | Trebuchet MS | 44 px | Bold |
46
+ | Subtitle / affiliation | Calibri | 22 px | Regular |
47
+ | Stat values | Consolas (monospaced) | 32 px | Bold |
48
+ | Stat labels | Calibri | 16 px | Regular, muted |
49
+ | DOI string | Consolas | 14 px | Regular, teal |
50
+
51
+ ---
52
+
53
+ ## Layout (1200 × 630 px)
54
+
55
+ ```
56
+ ┌──────────────────────────────────────────────────────────────────────┐
57
+ │ [60 px top inset] │
58
+ │ │
59
+ │ [LEFT COLUMN — 680 px wide] [RIGHT COLUMN — 400 px wide] │
60
+ │ │
61
+ │ Title (44 px bold): ┌──────────────────────────┐ │
62
+ │ "The Ouroboros Substrate" │ STAT CARD │ │
63
+ │ │ 206 pages │ │
64
+ │ Subtitle (22 px): │ 76 theorems+cor │ │
65
+ │ "Governance-Mathematical │ 17 lake-verified │ │
66
+ │ Foundation for │ 934+ green tests │ │
67
+ │ Verifiable Agentic AI" │ 7 Zenodo DOIs │ │
68
+ │ │ 32 modules │ │
69
+ │ Author (18 px muted): └──────────────────────────┘ │
70
+ │ "Stephen P. Lutar │
71
+ │ ORCID 0009-0001-0110-4173 [Lean 4 + Mathlib v4.13.0 badge] │
72
+ │ SZL Holdings" │
73
+ │ │
74
+ │ DOI (14 px teal monospace): │
75
+ │ "doi:10.5281/zenodo.20434276" │
76
+ │ │
77
+ │ [horizontal rule, border colour] │
78
+ │ │
79
+ │ Tags (small, spaced): │
80
+ │ cs.LO cs.LG cs.SE Lean 4 PAC-Bayes Schur SCITT │
81
+ │ │
82
+ │ [60 px bottom inset] │
83
+ └──────────────────────────────────────────────────────────────────────┘
84
+ ```
85
+
86
+ **Stat card detail:**
87
+ - Each stat row: value in Consolas Bold 32 px (teal for "lake-verified", green for "934+", muted for others), label in Calibri Regular 16 px.
88
+ - Thin 1 px border in `#393836` around the stat card.
89
+ - "17 lake-verified" value in `#6DAA45` (success green).
90
+ - "934+ green tests" value in `#6DAA45`.
91
+ - "A15 open-problem" is NOT shown — honest but not prominent in preview image; appears in full abstract on the paper page.
92
+
93
+ **Badge (bottom-right of right column):**
94
+ - Pill shape: `Lean 4` label, `#2D5BB9` blue fill (standard Lean brand colour), white text, 18 px.
95
+ - Pill shape: `Mathlib v4.13.0` label, same blue, white text.
96
+ - Placed at bottom of stat card, 8 px gap.
97
+
98
+ ---
99
+
100
+ ## Content Rules (Doctrine v6)
101
+
102
+ - Do NOT include "first", "only", "revolutionary", "groundbreaking", or any superlative.
103
+ - The Lambda symbol (Λ) may appear as a decorative glyph in the left-column background at 10% opacity (teal) — this is the sole decorative element.
104
+ - No stock photography, no abstract imagery, no illustrations.
105
+ - No emoji in the image text.
106
+ - All numbers shown must match values verifiable at [DOI 10.5281/zenodo.20434276](https://doi.org/10.5281/zenodo.20434276).
107
+
108
+ ---
109
+
110
+ ## Accessibility
111
+
112
+ - Contrast ratio: primary text `#CDCCCA` on `#171614` = 13.8:1 (WCAG AAA).
113
+ - Teal accent `#4F98A3` on dark background = 5.1:1 (WCAG AA).
114
+ - Green stat values `#6DAA45` on dark background = 4.7:1 (WCAG AA).
115
+ - All stat rows must have a text label — never rely on colour alone to distinguish verified vs. pending.
116
+
117
+ ---
118
+
119
+ ## Delivery
120
+
121
+ When the HF Papers URL is confirmed, provide:
122
+ 1. This brief to the image-gen pipeline or designer.
123
+ 2. The final OG image saved as `og_image_1200x630.png` in this directory.
124
+ 3. Confirm the `<meta property="og:image">` tag on the HF paper page points to the image or supply it during the HF upload form.
SOCIAL_CARDS/social_card_text.md ADDED
@@ -0,0 +1,127 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ # Social Card Text — SZL Ouroboros Thesis v18
2
+
3
+ Platform character limits and constraints apply. All counts are verifiable against
4
+ [DOI 10.5281/zenodo.20434276](https://doi.org/10.5281/zenodo.20434276).
5
+ Doctrine v6: no superlatives, no marketing language.
6
+
7
+ ---
8
+
9
+ ## Hugging Face Papers (paper description / tagline)
10
+
11
+ **180-char limit target**
12
+
13
+ ```
14
+ Ouroboros Substrate v18: Lean 4–verified agentic AI governance. 206 pages,
15
+ 76 theorems, 32-module runtime, 934+ tests. 7 live Zenodo DOIs.
16
+ doi:10.5281/zenodo.20434276
17
+ ```
18
+ *(175 chars)*
19
+
20
+ **Alternative (more technical):**
21
+ ```
22
+ Lambda-axis governance for agentic AI: Lean 4 kernel-verified, Mathlib
23
+ v4.13.0, 13 axioms, SCITT receipt chain, 32 modules, 934+ assertions.
24
+ doi:10.5281/zenodo.20434276
25
+ ```
26
+ *(173 chars)*
27
+
28
+ ---
29
+
30
+ ## X / Twitter (280-char limit; no emoji in primary text per Doctrine v6)
31
+
32
+ **Primary post:**
33
+ ```
34
+ New thesis: Ouroboros Substrate v18 — formal verification of agentic AI
35
+ governance invariants in Lean 4 + Mathlib v4.13.0.
36
+
37
+ 206 pages. 76 theorems + corollaries. 32-module runtime. 934+ green tests.
38
+ 7 Zenodo DOIs (all HTTP 200).
39
+
40
+ A15 (SHA-256 collision resistance) is an open problem and is labelled as such.
41
+
42
+ doi: https://doi.org/10.5281/zenodo.20434276
43
+ ```
44
+ *(268 chars)*
45
+
46
+ **Thread follow-up (for quoting the HF paper page — add after upload):**
47
+ ```
48
+ The Lean Czar audit (Ch. 7) certifies:
49
+ - 17 theorems lake-verified (no sorry, no new axiom)
50
+ - 22 skeleton-pending (honest sorry markers + discharge plans)
51
+ - 1 open-problem (conditional on NIST FIPS 180-4 SHA-256)
52
+
53
+ Full proof tree: https://github.com/szl-holdings/lutar-lean
54
+ ```
55
+ *(260 chars)*
56
+
57
+ ---
58
+
59
+ ## LinkedIn (max 3000 chars; target ~180-word hook for preview card)
60
+
61
+ **Preview hook (first 180 chars that appear in link preview):**
62
+ ```
63
+ Ouroboros Substrate v18: formal verification of agentic AI governance in
64
+ Lean 4. 206 pages, 76 theorems, 32-module Python runtime, 7 Zenodo DOIs.
65
+ doi:10.5281/zenodo.20434276
66
+ ```
67
+ *(177 chars)*
68
+
69
+ **Full post body:**
70
+ ```
71
+ Today we publish the Ouroboros Substrate thesis v18.0 — a formal
72
+ treatment of agentic AI governance in Lean 4.
73
+
74
+ What the thesis is:
75
+ - A 206-page proof that every governance invariant of the Ouroboros
76
+ agentic runtime can be machine-checked by the Lean 4 kernel against
77
+ Mathlib v4.13.0.
78
+ - A 32-module Python runtime (934+ inline assertions, exit code 0)
79
+ where every agent action emits a SCITT-compatible, SHA-256-chained
80
+ receipt.
81
+ - An axiom system A1-A15, with A15 (SHA-256 collision resistance)
82
+ explicitly disclosed as a cryptographic open problem under NIST FIPS 180-4.
83
+
84
+ What the thesis is not:
85
+ - A claim that all proofs are complete. 22 of 47 theorems in the primary
86
+ chapters are skeleton-pending with honest sorry markers and named
87
+ discharge plans.
88
+ - Marketing. Doctrine v6 bans superlatives at CI time.
89
+
90
+ Seven Zenodo records (DOIs 10.5281/zenodo.19944926 through
91
+ 10.5281/zenodo.20434308) provide citation-stable provenance for every
92
+ version from v14 through v18.0.
93
+
94
+ Lean proofs: https://github.com/szl-holdings/lutar-lean
95
+ Runtime: https://github.com/szl-holdings/ouroboros
96
+ Thesis DOI: https://doi.org/10.5281/zenodo.20434276
97
+
98
+ ORCID: 0009-0001-0110-4173
99
+ ```
100
+
101
+ ---
102
+
103
+ ## Mastodon / Fediverse (500-char limit)
104
+
105
+ ```
106
+ Ouroboros Substrate v18: Lean 4–verified agentic AI governance.
107
+
108
+ 206 pages. 76 theorems + 4 corollaries. 17 lake-verified (no sorry).
109
+ 22 skeleton-pending (honest markers). 1 open-problem (A15, SHA-256,
110
+ NIST FIPS 180-4).
111
+
112
+ 32 Python modules, 934+ green assertions, 7 Zenodo DOIs.
113
+
114
+ doi:10.5281/zenodo.20434276
115
+ Proofs: github.com/szl-holdings/lutar-lean
116
+ ```
117
+ *(438 chars)*
118
+
119
+ ---
120
+
121
+ ## Notes on Doctrine v6 compliance
122
+
123
+ - All character counts above are approximate; measure before posting.
124
+ - "Ouroboros" is a proper noun (the substrate name), not a marketing adjective.
125
+ - Do not add "first", "only", "revolutionary", or "breakthrough" — these are banned under Doctrine v6.
126
+ - Test count must be stated as "934+" not "thousands" or "hundreds of".
127
+ - The open-problem disclosure (A15 / SHA-256) must appear in any thread that discusses receipt-chain security.
og_image.png ADDED

Git LFS Details

  • SHA256: 9eb076cdabc594eb798cfb93176ad5fa70b36d196c9f5d82ac3070a35b77f652
  • Pointer size: 130 Bytes
  • Size of remote file: 21.8 kB