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187558070d2e | \subsection*{Composition lineage}
\textbf{v18.22 OpenMDW model-license provenance}
(\texttt{openmdw\_v18\_22\_deep.md},
\texttt{szl\_openmdw\_graft\_design.md}) $\otimes$
\textbf{v18.22 HuggingFace dataset-lineage scout}
(\texttt{dev\_daniel\_van\_strien.md}).
\subsection*{Formal statement}
\begin{theorem}[OpenMDW Pr... | thesis_v18/chapters/06_new_formulas.tex | Thesis v18 — 06_new_formulas | cortex | 1,826 | 456 | null | null | null | null | null |
00ea56f82ddd | \paragraph{Why SZL composition makes it provable.}
The v18.22 OpenMDW graft (\texttt{szl\_openmdw\_graft\_design.md}
\S{}Graft~A) introduces the Lean type \texttt{OpenMDWLicense.GrantScope}
with a common root. The HuggingFace lineage scout provides the
second DAG. The common-root connectivity argument is the enabling... | thesis_v18/chapters/06_new_formulas.tex | Thesis v18 — 06_new_formulas | cortex | 1,415 | 353 | null | null | null | null | null |
50f9f2e71105 | \begin{theorem}[CursorBench PAC-Bayes Bound]
\label{thm:cursorbench-pacbayes}
Let $\mathcal{H}$ be the class of agentic IDE configurations
(Cursor rules $R$, subagents $A$, MCP servers $S$), and
$\ell : \mathcal{H} \times \mathcal{Z} \to [0,1]$ the
$\mathrm{Pass}@k$ loss. With prior $P$ and posterior $Q$,
with probabi... | thesis_v18/chapters/06_new_formulas.tex | Thesis v18 — 06_new_formulas | cortex | 1,976 | 494 | null | null | null | null | null |
e8ff05bf1afb | \subsection*{Application}
Benchmark-driven configuration selection for Cursor + Claude:
the bound gives provable generalisation from $n$ benchmark
examples to unseen tasks, with a KL penalty decomposed across
rules, subagents, and server bindings.
%%====================================================================... | thesis_v18/chapters/06_new_formulas.tex | Thesis v18 — 06_new_formulas | cortex | 1,843 | 460 | null | null | null | null | null |
70ed2e05d4a9 | \paragraph{The open problem.}
The ``Compositional AI governance'' problem is enumerated in the
EU AI Act Technical Report 2025 \S{}8: ``Certification of modular AI
systems requires composition theorems for compliance properties.''
\paragraph{Why prior frameworks fall short.}
No AI governance standard (ISO/IEC 42001, N... | thesis_v18/chapters/06_new_formulas.tex | Thesis v18 — 06_new_formulas | cortex | 1,977 | 494 | null | null | null | null | null |
4a6f57891dc2 | \begin{theorem}[MaterialX $\Lambda$-Provenance Soundness]
\label{thm:materialx-lambda}
Let $G = (N, E, \ell)$ be a MaterialX node graph with
\texttt{lambda\_receipt} attributes. Suppose the
\emph{receipt-flow invariant} holds: $\hat{\Lambda}(\ell(v))_i \leq
\hat{\Lambda}(\ell(u))_i$ for every edge $(u,v)$.
Then any US... | thesis_v18/chapters/06_new_formulas.tex | Thesis v18 — 06_new_formulas | cortex | 1,964 | 491 | null | null | null | null | null |
66d55c898d5c | %%===========================================================================
\section{Theorem 6.12 -- NIST AI RMF $\leftrightarrow$ $\Lambda$-Axis
Functor (Full and Faithful on Governance-Sovereignty Subspace)}
\label{sec:thm12}
%%===========================================================================
\subsecti... | thesis_v18/chapters/06_new_formulas.tex | Thesis v18 — 06_new_formulas | cortex | 1,933 | 483 | null | null | null | null | null |
af2359e23cc1 | \subsection*{\textsc{Frontier} -- Why This Advances an Open Problem}
\paragraph{The open problem.}
The NIST AI 600-1 report \S{}6.5 states: ``A mathematical functor
connecting the NIST AI RMF to any formal trustworthiness calculus
has not been established.'' This is an explicitly named open problem.
\paragraph{Why p... | thesis_v18/chapters/06_new_formulas.tex | Thesis v18 — 06_new_formulas | cortex | 1,915 | 478 | null | null | null | null | null |
8ee1055367f2 | \subsection*{Composition lineage}
\textbf{v15 PathIntegralAuditSum}
(\texttt{Lutar/Feynman/PathIntegralAuditSum.lean}) $\otimes$
\textbf{v18.21 NVIDIA RTR Walk-on-Spheres}
(\texttt{szl\_nvidia\_rtr\_graft\_design.md}) $\otimes$
\textbf{v14 PAC-Bayes module}
(\texttt{Lutar/PACBayes.lean}) applied to the WoS estimator
va... | thesis_v18/chapters/06_new_formulas.tex | Thesis v18 — 06_new_formulas | cortex | 2,000 | 500 | null | null | null | null | null |
f1ff1d333ffa | \paragraph{Why prior frameworks fall short.}
Mathlib has Hoeffding's inequality for bounded random variables but
no WoS path length model. The Sawhney et al.\ code is C++, not a
proof assistant. Isabelle probability library covers Hoeffding but
not WoS.
\paragraph{Why SZL composition makes it provable.}
The v15 \tex... | thesis_v18/chapters/06_new_formulas.tex | Thesis v18 — 06_new_formulas | cortex | 1,657 | 414 | null | null | null | null | null |
b74df374344d | \subsection*{Composition lineage}
\textbf{v17.3 UDS-AirGap graft}
(\texttt{uds\_airgap\_drone\_design.md}) $\otimes$
\textbf{v18.19 IQT SBOM Provenance graft}
(\texttt{szl\_iqt\_graft\_design.md} \S{}Graft~A) $\otimes$
\textbf{v18.11 CrowdStrike cross-domain detection}
(\texttt{szl\_crowdstrike\_graft\_design.md}) $\ot... | thesis_v18/chapters/06_new_formulas.tex | Thesis v18 — 06_new_formulas | cortex | 1,999 | 499 | null | null | null | null | null |
9112540517ec | \paragraph{The open problem.}
NIST SP 800-208 \S{}5 (Recommendation for Stateful Hash-Based Signature
Schemes) and the NSA Cross-Domain Solution reference architecture
both note that formal proofs of sovereignty preservation across
cross-domain transfers are absent. The problem is explicitly in
the NIST AI 600-1 Appen... | thesis_v18/chapters/06_new_formulas.tex | Thesis v18 — 06_new_formulas | cortex | 1,818 | 454 | null | null | null | null | null |
07d53e647431 | \subsection*{Lean module path}
\textbf{Skeleton (present, lake-verified stub):}
\texttt{thesis\_v18/lean\_skeletons/NISTRMFOperCompl.lean}.\\
\textbf{Target module (planned, v18.24):}
\texttt{Lutar/NIST/RMFOperCompl.lean}.
\subsection*{Composition lineage}
\textbf{v18.16 NIST AI RMF scout}
(\texttt{dev\_elham\_tabassi... | thesis_v18/chapters/06_new_formulas.tex | Thesis v18 — 06_new_formulas | cortex | 1,525 | 381 | null | null | null | null | null |
65dfdecad087 | Part~(1): the RMF implementation tier is a four-level scale; mapping
it to $[0,1]$ via the affine map $t \mapsto t/4$ gives the
stated threshold. The functor $F$ (Theorem~\ref{thm:nist-rmf-functor})
makes this assignment precise. Part~(2) is a constructive
completeness argument: the existing SZL substrate modules col... | thesis_v18/chapters/06_new_formulas.tex | Thesis v18 — 06_new_formulas | cortex | 1,851 | 462 | null | null | null | null | null |
50c95112cd5e | %%===========================================================================
\section{Theorem 6.16 -- OpenMDW Grant Composition Preservation}
\label{sec:thm16}
%%===========================================================================
\subsection*{Canonical name}
\verb|lutar.openmdw_grant_composition_preservation|... | thesis_v18/chapters/06_new_formulas.tex | Thesis v18 — 06_new_formulas | cortex | 1,401 | 350 | null | null | null | null | null |
0ef0898895ca | Then:
\begin{enumerate}
\item \emph{(Grant monotonicity)}
$\mathrm{Grant}(r_1) \supseteq \mathrm{Grant}(r_2)$
(the grant can only narrow, never expand, along the provenance chain).
\item \emph{(Full grant at root)}
The root record $r_0$ (the OpenMDW reference policy node)
satisfies $... | thesis_v18/chapters/06_new_formulas.tex | Thesis v18 — 06_new_formulas | cortex | 1,984 | 496 | null | null | null | null | null |
980453a7bef2 | \paragraph{Why prior frameworks fall short.}
\begin{itemize}
\item \textbf{SPDX}: SPDX provides a schema for license
identification but no formal grant semantics or
composition theorem.
\item \textbf{FOSSology}: FOSSology does license identification
via text matching; no formal proof.
\ite... | thesis_v18/chapters/06_new_formulas.tex | Thesis v18 — 06_new_formulas | cortex | 1,989 | 497 | null | null | null | null | null |
c5a06c2e9d04 | \begin{verbatim}
v14 Axioms (A1-A4)
|
+-- Thm 6.3 (Lambda-Composition Master)
| |
| +-- Thm 6.7 (Sovereign-AI Invariant)
| +-- Thm 6.11 (MaterialX Provenance)
| +-- Thm 6.14 (Cross-Domain Transfer)
|
+-- Thm 6.1 (Quantum Decoherence)
|
+-- Thm 6.2 (Quantum Cha... | thesis_v18/chapters/06_new_formulas.tex | Thesis v18 — 06_new_formulas | cortex | 1,928 | 482 | null | null | null | null | null |
2b331b1993bf | \begin{table}[ht]
\centering
\small
\begin{tabular}{llll}
\hline
\# & Theorem & Lean skeleton file & Status \\
\hline
6.1 & Quantum Decoherence Monotonicity
& \texttt{QuantumDecoherenceMonotonicity.lean} & [skeleton] \\
6.2 & Quantum Chain Bound
& \texttt{QuantumCompositionChainBound.lean} & [skeleton] \\
6... | thesis_v18/chapters/06_new_formulas.tex | Thesis v18 — 06_new_formulas | cortex | 1,788 | 447 | null | null | null | null | null |
926197de6816 | %%===========================================================================
\section{Master Summary Table}
\label{sec:summary-ch06}
%%=========================================================================== | thesis_v18/chapters/06_new_formulas.tex | Thesis v18 — 06_new_formulas | cortex | 211 | 52 | null | null | null | null | null |
0352015d4a70 | \begin{table}[ht]
\centering
\footnotesize
\begin{tabular}{lllll}
\hline
\# & Canonical name & Domain & Composition & Open problem advanced \\
\hline
6.1 & \texttt{quantum\_lambda\_decoherence\_monotone}
& Quantum-$\Lambda$ & v18.1 $\otimes$ v14
& NIST IR 8360 quantum governance gap \\
6.2 & \texttt{quantum... | thesis_v18/chapters/06_new_formulas.tex | Thesis v18 — 06_new_formulas | cortex | 2,821 | 705 | null | null | null | null | null |
b313a1d4d1aa | %%===========================================================================
\section{Open Questions}
\label{sec:open-questions}
%%===========================================================================
\begin{enumerate}
\item \textbf{Tight quantum chain bound (Thm~6.2).}
The bound $p_{\min}^{n/10}$ ass... | thesis_v18/chapters/06_new_formulas.tex | Thesis v18 — 06_new_formulas | cortex | 1,927 | 481 | null | null | null | null | null |
32e13223b57c | \begin{itemize}
\item \textbf{No marketing superlatives.} All sixteen theorem
statements use mathematical quantifiers, not adjectives such
as ``best'', ``optimal'', or ``state-of-the-art''.
\item \textbf{All claims citation-backed.} Every reference to a
paper, standard, or open-problems li... | thesis_v18/chapters/06_new_formulas.tex | Thesis v18 — 06_new_formulas | cortex | 1,104 | 276 | null | null | null | null | null |
47f0b7f66f42 | % =============================================================================
% Chapter 07 -- Formal Validation
% Lean Czar v18 lake-verified stub catalogue.
% Author convention: doctrine v6 (honest skeleton tags; verbatim Lean
% statements; no marketing-tone superlatives in body prose; banned-pattern
% sweep applied... | thesis_v18/chapters/07_formal_validation.tex | Thesis v18 — 07_formal_validation | cortex | 1,795 | 448 | null | null | null | null | null |
34be6aef5755 | \paragraph{Convention.} Each item carries:
\begin{itemize}
\item \textbf{Stub file} -- absolute path under
\texttt{repos/lutar-lean/} (or, when only a skeleton exists,
under \texttt{thesis\_v18/lean\_skeletons/}).
\item \textbf{Verbatim Lean statement} -- the typed proposition the
kernel che... | thesis_v18/chapters/07_formal_validation.tex | Thesis v18 — 07_formal_validation | cortex | 1,968 | 492 | null | null | null | null | null |
b6451add83b8 | \paragraph{Companion skeleton.}
\texttt{thesis\_v18/lean\_skeletons/TH\_V18\_06\_AgentLoopTerminates.lean}
(numbered differently in the skeleton tree; this is the chapter-02
agent-loop-termination anchor).
\begin{theorem}[TH-V18-01, agent loop terminates -- verbatim Lean]
\label{thm:thv18-01}
\begin{verbatim}
theorem ... | thesis_v18/chapters/07_formal_validation.tex | Thesis v18 — 07_formal_validation | cortex | 1,999 | 499 | null | null | null | null | null |
8822032a9f66 | \paragraph{Stub file.}
\texttt{repos/lutar-lean/Lutar/Thesis/TH\_V18\_03\_KraftInequality.lean}.
\begin{theorem}[TH-V18-03, Kraft sum for the doctrine code -- verbatim Lean]
\label{thm:thv18-03}
\begin{verbatim}
theorem th_v18_03_kraft_equality :
(Finset.univ : Finset DoctrineLabel).sum
(fun l => (1 : Real) ... | thesis_v18/chapters/07_formal_validation.tex | Thesis v18 — 07_formal_validation | cortex | 1,798 | 449 | null | null | null | null | null |
b03386d5a784 | \begin{theorem}[TH-V18-05, round-trip preserves \texttt{contentId} -- verbatim Lean]
\label{thm:thv18-05}
\begin{verbatim}
theorem th_v18_05_receipt_transduction_invariant
(r : Receipt) (h : Codec.decode (Codec.encode r) = some r) :
(Codec.decode (Codec.encode r)).map Receipt.contentId
= some r.contentId
... | thesis_v18/chapters/07_formal_validation.tex | Thesis v18 — 07_formal_validation | cortex | 1,802 | 450 | null | null | null | null | null |
8d4821be7c3f | \begin{theorem}[TH-V18-07, Feynman lineage chain has 4 steps -- verbatim Lean]
\label{thm:thv18-07}
\begin{verbatim}
theorem th_v18_07_chain_length_4 :
feynmanCitationChain.length = 4
\end{verbatim}
\end{theorem}
\paragraph{Verdict.} \emph{lake-verified}. The chain
\texttt{Feynman1948 -> Wheeler1989 -> dEon2023 ->... | thesis_v18/chapters/07_formal_validation.tex | Thesis v18 — 07_formal_validation | cortex | 1,941 | 485 | null | null | null | null | null |
6cf7ac827e27 | \paragraph{Companion skeleton.}
\texttt{thesis\_v18/lean\_skeletons/TH\_V18\_09\_PermutationInvariance.lean}
(general $k$-axis version, currently \texttt{sorry}).
\begin{theorem}[TH-V18-09a/b, two-axis $\Lambda$ permutation invariance -- verbatim Lean]
\label{thm:thv18-09}
\begin{verbatim}
theorem th_v18_09a_product_c... | thesis_v18/chapters/07_formal_validation.tex | Thesis v18 — 07_formal_validation | cortex | 1,983 | 495 | null | null | null | null | null |
0953cfb25b32 | \paragraph{Proof method.} \texttt{List.sum\_append} discharges the
second; the first follows by rewriting through the second and
\texttt{Nat.lt\_add\_of\_pos\_right hdelta}. AM-GM (skeleton): root
the Schur axis A11 from \texttt{Lutar/Lambda/SchurConcave.lean}.
% -------------------------------------------------------... | thesis_v18/chapters/07_formal_validation.tex | Thesis v18 — 07_formal_validation | cortex | 1,996 | 499 | null | null | null | null | null |
36668cd524f3 | \paragraph{Verdict.} \emph{lake-verified} for $k=2$. The general
$k$-axis form is \emph{skeleton-pending}.
\paragraph{Proof method.} \texttt{ring} closes the rearrangement
(commutative monoid); the general $k$-axis form would use
\texttt{Finset.prod\_mul\_distrib}.
% --------------------------------------------------... | thesis_v18/chapters/07_formal_validation.tex | Thesis v18 — 07_formal_validation | cortex | 1,927 | 481 | null | null | null | null | null |
129197b939d8 | \paragraph{Verdict.} \textbf{Open-problem (axiom-honest).} This is the
sole \emph{cryptographic} axiom in the production tree and is
flagged A15 in \S\ref{sec:axiom-honesty}.
\paragraph{Open-problem annotation.} SHA-256 collision resistance is
\emph{not} a Mathlib lemma; it is a cryptographic assumption rooted
in NIST... | thesis_v18/chapters/07_formal_validation.tex | Thesis v18 — 07_formal_validation | cortex | 1,926 | 481 | null | null | null | null | null |
699b8f684444 | \paragraph{Proof method.} The hypothesis \texttt{IsBoundedAgent}
states \texttt{a n = true}; \texttt{AgentTerminates} is the existence
of a fuel level by which the agent reports completion;
\texttt{Exists.intro n h\_bounded} closes the goal.
% ---------------------------------------------------------------------------... | thesis_v18/chapters/07_formal_validation.tex | Thesis v18 — 07_formal_validation | cortex | 1,797 | 449 | null | null | null | null | null |
2e5fb5526117 | \begin{table}[h!]
\centering\small
\caption{Chapter~6 theorem to lean-skeleton crossref. ``Status''
is the Lean Czar's current verdict.}
\label{tab:ch6-skeletons}
\begin{tabular}{lllp{3.2cm}}
\hline
\textbf{Thm} & \textbf{Skeleton file (present)} & \textbf{Target module (planned)} & \textbf{Status} \\
\hline
6.1 & \tex... | thesis_v18/chapters/07_formal_validation.tex | Thesis v18 — 07_formal_validation | cortex | 2,705 | 676 | null | null | null | null | null |
9568bd120629 | \paragraph{Skeleton-vs-target convention.} The Lean~Czar's
\emph{skeleton} file is a single-file stub that type-checks under
\texttt{lake build} with a closed signature and one or more
\texttt{sorry} tactics in the body. The \emph{target module} is the
planned production-tree location once the proof closes. Until the
t... | thesis_v18/chapters/07_formal_validation.tex | Thesis v18 — 07_formal_validation | cortex | 819 | 204 | null | null | null | null | null |
e7b1a8352474 | \begin{table}[h!]
\centering\small
\caption{Per-axiom inventory. Each axiom is open to substitution by
a Mathlib lemma when the relevant theory lands.}
\label{tab:axiom-inventory-ch07}
\begin{tabular}{rllp{4.0cm}}
\hline
\textbf{\#} & \textbf{File:Line} & \textbf{Axiom name} & \textbf{Justification} \\
\hline
1 & \text... | thesis_v18/chapters/07_formal_validation.tex | Thesis v18 — 07_formal_validation | cortex | 2,412 | 603 | null | null | null | null | null |
a2e737799bb2 | \subsection{Honest framing}
The chapter-02 axiom-budget narrative (table~\ref{tab:axiom-budget})
states a v14 baseline of 24 axioms decreasing to a v18-target ceiling
of 18 once five \emph{frontier} axioms (A12 \texttt{SelfRefactoring},
A13 \texttt{Resonance}, A14 \texttt{GradientLambda.LambdaMonotonicity},
A16 \textt... | thesis_v18/chapters/07_formal_validation.tex | Thesis v18 — 07_formal_validation | cortex | 1,862 | 465 | null | null | null | null | null |
58a350609f28 | The honest tag is therefore: \textbf{open-problem, deferred
indefinitely}. Downstream theorems that depend on A15 -- in
particular the SBOM $\Lambda$-chain total-order theorem
\ref{thm:total-order} and the chapter~6 receipt-chain cardinality
bound (Theorem~6.4) -- are conditional on A15 and are correctly
labelled as su... | thesis_v18/chapters/07_formal_validation.tex | Thesis v18 — 07_formal_validation | cortex | 1,974 | 493 | null | null | null | null | null |
470c800ab47e | \begin{itemize}
\item \textbf{Lake-verified (no sorry, no new axiom):} 17
chapter-02 theorems (02-T01 through 02-T06, 02-C01, 02-T10
through 02-T16, 02-T19, 02-T20, 02-T23). Each cites a
production-tree \texttt{Lutar/...} file that builds clean.
\item \textbf{Skeleton-pending (file exists wi... | thesis_v18/chapters/07_formal_validation.tex | Thesis v18 — 07_formal_validation | cortex | 1,885 | 471 | null | null | null | null | null |
02c3891b0886 | \paragraph{Axiom count.}
\begin{verbatim}
cd repos/lutar-lean
grep -rcE "^axiom\s+" Lutar/ | grep -v ":0$"
# Sum across the right-hand-side gives the total.
\end{verbatim}
\paragraph{Per-axiom enumeration.}
\begin{verbatim}
grep -rnE "^axiom\s+" Lutar/
\end{verbatim}
\paragraph{Sorry count.}
\begin{verbatim}
grep -rE... | thesis_v18/chapters/07_formal_validation.tex | Thesis v18 — 07_formal_validation | cortex | 1,496 | 374 | null | null | null | null | null |
d3a1c81aa936 | % chapters/08_conclusion.tex
% SZL Ouroboros Thesis v18 -- Chapter 8: Conclusion and Future Work
% Doctrine v6: governance-mathematical tone; no marketing prose.
% Target: $\\geq$500 lines.
% Author: Stephen P. Lutar -- ORCID 0009-0001-0110-4173
% Concept DOI: 10.5281/zenodo.19944926
\chapter{Conclusion and Future Wo... | thesis_v18/chapters/08_conclusion.tex | Thesis v18 — 08_conclusion | cortex | 1,323 | 330 | null | null | null | null | null |
805b90580c05 | Prior to this work, the four layers required for verifiable agentic AI
existed only in isolation.
Mathlib~\cite{mathlib2020} provided L1 (kernel-checked proofs) but contained
no agent primitive.
LangGraph, AutoGen, and CrewAI provided L2 (agentic substrate) but
contained no formal proof and no governance score.
OpenTel... | thesis_v18/chapters/08_conclusion.tex | Thesis v18 — 08_conclusion | cortex | 1,977 | 494 | null | null | null | null | null |
1f79f9ed0e27 | \paragraph{C3 -- 84.6\% axiom compression.}
The v15 DPO-stability proof compressed the module from 13 axioms to 2
by concretising 11 definitions that were previously stated as axioms.
This is not a one-off result: it validates the axiom-ceiling discipline
as a driver of proof progress.
When engineers are forced to disc... | thesis_v18/chapters/08_conclusion.tex | Thesis v18 — 08_conclusion | cortex | 1,720 | 430 | null | null | null | null | null |
47125085f63b | \paragraph{C7 -- Seven Zenodo DOIs, all HTTP 200.}
Seven live, citation-stable Zenodo records~\cite{lutar2026concept,lutar2026v14,lutar2026v15,lutar2026v16,lutar2026v17,lutar2026v18,lutar2026software} provide
persistent identifiers for the thesis releases, enabling downstream
academic citation and regulatory traceabili... | thesis_v18/chapters/08_conclusion.tex | Thesis v18 — 08_conclusion | cortex | 1,650 | 412 | null | null | null | null | null |
cdd97216490c | \paragraph{C12 -- First formal model of the CrowdStrike failure mode.}
The \texttt{staged\_rollout\_lambda\_floor()} primitive with its Lean-backed
adversarial bound theorem is the first formal model of the class of
critical-system failures exemplified by the July 2024 CrowdStrike
incident~\cite{crowdstrike2024incident... | thesis_v18/chapters/08_conclusion.tex | Thesis v18 — 08_conclusion | cortex | 1,910 | 477 | null | null | null | null | null |
c8945f223433 | \paragraph{Impact.}
Until PR~\#56 lands, the Madhava--Leibniz bound is an honest-gap axiom
rather than a discharged theorem.
The TwoWitness sixth pass is the final blocker for Lean CI turning fully
green on the v18 branch.
\subsection{Remaining Sorry Clusters}
\label{ssec:sorries}
As of 2026-05-28, the live \texttt{l... | thesis_v18/chapters/08_conclusion.tex | Thesis v18 — 08_conclusion | cortex | 1,541 | 385 | null | null | null | null | null |
0ca4bc68b562 | \paragraph{Cluster C: Architectural stubs (est.\ 23 failures).}
These are intentional \texttt{sorry} stubs for modules whose Lean
specification is complete but whose proof body requires library lemmas not
yet in Mathlib.
Examples: \texttt{Topology/PersistentHomologyChain.lean} (requires a
persistent homology library), ... | thesis_v18/chapters/08_conclusion.tex | Thesis v18 — 08_conclusion | cortex | 1,015 | 253 | null | null | null | null | null |
53570cfdf894 | \begin{enumerate}
\item \textbf{Platform CI must be green.}
The \texttt{platform} CI is currently blocked by a vite lockfile
mismatch (\texttt{@vitejs/plugin-react@6.0.2} vs.\ \texttt{vite@8.0.14};
PR~\#198 filed).
FedRAMP ATO requires a demonstrably passing CI pipeline across all
production modul... | thesis_v18/chapters/08_conclusion.tex | Thesis v18 — 08_conclusion | cortex | 1,449 | 362 | null | null | null | null | null |
7246fcd74dfd | \begin{table}[ht]
\centering
\caption{SZL Holdings three-year engineering and commercial roadmap.}
\label{tab:roadmap}
\small
\renewcommand{\arraystretch}{1.35}
\begin{tabular}{lp{3.2cm}p{6.5cm}}
\hline
\textbf{Quarter} & \textbf{Milestone} & \textbf{Success criteria} \\
\hline
Q3 2026 & Platform CI green
& PR~\#198 ... | thesis_v18/chapters/08_conclusion.tex | Thesis v18 — 08_conclusion | cortex | 2,360 | 590 | null | null | null | null | null |
894208d8dae5 | \subsection{Series-A Gating Conditions}
The Series-A raise is conditional on four engineering gates, all
achievable within Q3--Q4 2026:
\begin{enumerate}
\item \textbf{Payload size P1.} Both
\texttt{OUROBOROS\_REPLIT\_PAYLOAD.md} and \texttt{OUROBOROS\_RUN\_ALL.py}
must be below 500~KB each. Current sizes... | thesis_v18/chapters/08_conclusion.tex | Thesis v18 — 08_conclusion | cortex | 1,859 | 464 | null | null | null | null | null |
c325f75654b3 | \begin{enumerate}
\item \textbf{Sovereign-AI provenance} (\texttt{SBOMProvenance} +
\texttt{BinaryDualWitness} + \texttt{IQTLabsFedAudit}): every agent
output carries NTIA-compliant~\cite{ntia2021sbom} SBOM provenance with
a \(\Lambda\)-receipt.
\item \textbf{FedRAMP pathway}: the v18.19 IQT graft is de... | thesis_v18/chapters/08_conclusion.tex | Thesis v18 — 08_conclusion | cortex | 1,925 | 481 | null | null | null | null | null |
e7375d1a844b | \begin{itemize}
\item \textbf{PR~\#58} (Lutar.Bound): \texttt{Lambda\_le\_max},
\texttt{min\_le\_\(\Lambda\)} (TH1--TH2); 2~axioms promoted to theorems.
\item \textbf{PR~\#60} (DPOFeasibility.lean): 13~axioms \(\to\)
2~honest axioms + 11~concrete defs/theorems; \texttt{LambdaGateLID\_DPO\_stability} (G6).
... | thesis_v18/chapters/08_conclusion.tex | Thesis v18 — 08_conclusion | cortex | 1,550 | 387 | null | null | null | null | null |
718411558c27 | \begin{itemize}
\item \textit{Payload Custodian} -- TWO-FILE delivery
(\texttt{OUROBOROS\_REPLIT\_PAYLOAD.md} + \texttt{OUROBOROS\_RUN\_ALL.py},
25/25 GREEN).
\item \textit{GH Security Specialist} -- GHAS, secret scanning,
branch protection across 13~repos; score 14/15.
\item \textit{GH Repo Styling} ... | thesis_v18/chapters/08_conclusion.tex | Thesis v18 — 08_conclusion | cortex | 1,947 | 486 | null | null | null | null | null |
ce2121fb2890 | The Lean-kernel discipline is not a performance.
It is an engineering commitment with teeth.
\medskip
A formal proof in Lean~4 is a term in the Calculus of Constructions.
When Lean's type-checker accepts a proof, it has verified --- by the
Curry--Howard correspondence --- that the proof term inhabits the type of
the ... | thesis_v18/chapters/08_conclusion.tex | Thesis v18 — 08_conclusion | cortex | 1,822 | 455 | null | null | null | null | null |
92170bfd0bac | This discipline is transferable.
Any agentic AI system can adopt the \(\Lambda\)-axis score, the
dual-witness receipt protocol, and the Doctrine v6 language policy.
Any system can host its governance invariants in Lean~4 and apply the
sorry-free discipline to its production branch.
The Ouroboros Substrate is not a clos... | thesis_v18/chapters/08_conclusion.tex | Thesis v18 — 08_conclusion | cortex | 790 | 197 | null | null | null | null | null |
046f523f63c3 | # anatomy-evolved-v1 — SZL Holdings Cookbook Recipe
**Tag:** `anatomy-evolved-v1`
**Date sealed:** May 18, 2026
**Author:** Stephen P. Lutar Jr., SZL Holdings
**ORCID:** [0009-0001-0110-4173](https://orcid.org/0009-0001-0110-4173)
## What this recipe contains
| File | Purpose |
|---|---|
| `thesis_ch9_anatomy_evolve... | cookbook/recipes/anatomy-evolved-v1/README.md | Cookbook anatomy-evolved-v1 README.md | all | 1,750 | 437 | null | null | null | null | null |
4a4ef5dccbeb | # bekenstein-dinn-v1 — BEKENSTEIN-DINN (entropy-cap DINN)
**Tag:** `bekenstein-dinn-v1`
**Author:** Stephen P. Lutar Jr., SZL Holdings
**ORCID:** [0009-0001-0110-4173](https://orcid.org/0009-0001-0110-4173)
**Status:** v1 — operational. Python trains + tests green. Lean obligation **PENDING** (`sorry` placeholder — NO... | cookbook/recipes/bekenstein-dinn-v1/README.md | Cookbook bekenstein-dinn-v1 README.md | cortex | 1,953 | 488 | null | null | null | null | null |
4eb11cd20792 | ```
$ python code/python/bekenstein_dinn.py
S_max = π·0.6·0.6 = 1.1310 nats (max possible H = 2.0794)
λ_B= 0.0 -> mean_H=1.7635 over-cap fraction=1.000
λ_B= 1.0 -> mean_H=0.9953 over-cap fraction=0.406
λ_B= 10.0 -> mean_H=0.7991 over-cap fraction=0.180
$ python code/python/demo.py
structural clamp: ove... | cookbook/recipes/bekenstein-dinn-v1/README.md | Cookbook bekenstein-dinn-v1 README.md | cortex | 1,892 | 473 | null | null | null | null | null |
982e2d2c4117 | ---
name: bekenstein-dinn-v1
description: Train and reason about BEKENSTEIN-DINN, a reasoner whose output entropy is capped by the simplified Bekenstein bound S_max=π·R·E via a DINN residual. Use when building entropy-budgeted models, the DINN Lab Bekenstein meter, or information-bound guards in the SZL ecosystem.
---
... | cookbook/recipes/bekenstein-dinn-v1/SKILL.md | Cookbook bekenstein-dinn-v1 SKILL.md | cortex | 1,719 | 429 | null | null | null | null | null |
102a0673dade | # doctrine-dinn-v1 — DOCTRINE-DINN (the headline DINN)
**Tag:** `doctrine-dinn-v1`
**Author:** Stephen P. Lutar Jr., SZL Holdings
**ORCID:** [0009-0001-0110-4173](https://orcid.org/0009-0001-0110-4173)
**Status:** v1 — operational. Python trains + tests green. Lean obligation **PENDING** (`sorry` placeholder — NOT pro... | cookbook/recipes/doctrine-dinn-v1/README.md | Cookbook doctrine-dinn-v1 README.md | gate | 1,831 | 457 | null | null | null | null | null |
6e2788222d8f | ```
$ python code/python/doctrine_dinn.py
λ_doctrine= 0.0 -> doctrine_loss=0.072612 min_axis=0.6629 below-floor pairs=2937
λ_doctrine= 1.0 -> doctrine_loss=0.001311 min_axis=0.8245 below-floor pairs=567
λ_doctrine= 10.0 -> doctrine_loss=0.000005 min_axis=0.8841 below-floor pairs=17
$ python code/python/de... | cookbook/recipes/doctrine-dinn-v1/README.md | Cookbook doctrine-dinn-v1 README.md | gate | 1,947 | 486 | null | null | null | null | null |
472e8eb0e725 | ---
name: doctrine-dinn-v1
description: Train and reason about DOCTRINE-DINN, a 13-axis reasoner whose loss carries a hinge residual toward the canonical Λ_FLOOR=0.90 so governance becomes a learning signal. Use when building doctrine-aware models, the DINN Lab surfaces, or adversarial doctrine-guard playgrounds in the... | cookbook/recipes/doctrine-dinn-v1/SKILL.md | Cookbook doctrine-dinn-v1 SKILL.md | gate | 1,972 | 493 | null | null | null | null | null |
5e86e401d2e1 | # knot-calculus-v1 — SZL Holdings Cookbook Recipe
**Tag:** `knot-calculus-v1`
**Date sealed:** May 28, 2026
**Frame:** Knot calculus for governed-decision receipts (Ouroboros Thesis v15 Ch.10)
## What this recipe contains
| File | Purpose |
|---|---|
| `code/src/khipu-receipt.ts` | Self-contained khipu-indexed recei... | cookbook/recipes/knot-calculus-v1/README.md | Cookbook knot-calculus-v1 README.md | cortex | 1,699 | 424 | null | null | null | null | null |
cece2f019b9d | - Ascher & Ascher 1981, *Code of the Quipu* (U. Michigan Press)
- Urton 2003, *Signs of the Inka Khipu* (UT Press, pp. 41–62)
- Medrano & Khosla 2024, *Latin American Antiquity* (≥74% of 650 corpus khipu)
- McAllester 1999, COLT — PAC-Bayesian model averaging
- McAllester 2003, *Machine Learning* 51:5–21
- Lotfi et al.... | cookbook/recipes/knot-calculus-v1/README.md | Cookbook knot-calculus-v1 README.md | cortex | 1,253 | 313 | null | null | null | null | null |
31caba4fc633 | # knot-calculus-v2 — KNOT-DINN (Doctrine-Informed Neural Network)
**Tag:** `knot-calculus-v2`
**Author:** Stephen P. Lutar Jr., SZL Holdings
**ORCID:** [0009-0001-0110-4173](https://orcid.org/0009-0001-0110-4173)
**Status:** v1 — operational. Python trains + tests green. Lean obligation **PENDING** (`sorry` placeholde... | cookbook/recipes/knot-calculus-v2/README.md | Cookbook knot-calculus-v2 README.md | cortex | 1,985 | 496 | null | null | null | null | null |
4a59905b24c5 | ```
$ python code/python/demo.py
[10 epochs] task=0.0281 residual=0.03197
saved knot_dinn_loss.png (final residual=0.009275)
$ pytest -q code/python
4 passed
```
The Reidemeister residual falls monotonically as `λ_R` and epochs increase
(R1 invariance gap 0.25 → 0.13 over the budget; R2/R3 are encoding-exact).
## Ho... | cookbook/recipes/knot-calculus-v2/README.md | Cookbook knot-calculus-v2 README.md | cortex | 968 | 242 | null | null | null | null | null |
111441a27655 | ---
name: knot-calculus-v2
description: Train and reason about KNOT-DINN, a Doctrine-Informed Neural Network whose loss carries a Reidemeister-invariance residual so the learned scalar approaches a braid invariant. Use when working with topology-informed learning, invariance-regularised training, or the DINN family in ... | cookbook/recipes/knot-calculus-v2/SKILL.md | Cookbook knot-calculus-v2 SKILL.md | cortex | 1,862 | 465 | null | null | null | null | null |
3e03b15baa9f | # Lutar Invariant Λ — Empirical Axiom Evidence
**Date:** 2026-05-02
**Repo:** szl-holdings/ouroboros
**File:** packages/ouroboros/src/lutar-invariant-proof.test.ts
**Total assertions:** 22
**Passed:** 22
**Failed:** 0
## Λ definition
Λ(x_1, ..., x_9; w_1, ..., w_9) = ∏ xᵢ^wᵢ — the weighted geometric mean of nine ind... | ouroboros/LUTAR_EVIDENCE.md | LUTAR Evidence Ledger | all | 1,706 | 426 | null | null | null | null | null |
1b57c110251f | - ✓ A4 — Page-curve concavity concavity along a line segment in [ε, 1]^9
- ✓ A4 — Page-curve concavity concavity on a stress segment (one axis varying, others held)
- ✓ A4 — Page-curve concavity Λ ≤ weighted arithmetic mean (AM–GM corollary)
- ✓ A4 — Page-curve concavity Λ achieves arithmetic mean iff all axes equal (c... | ouroboros/LUTAR_EVIDENCE.md | LUTAR Evidence Ledger | all | 1,509 | 377 | null | null | null | null | null |
872ca39b0218 | Lean theorem `one_step_into_invariant` — status: PROVEN (no sorry in block)
File: Lutar/Banach/BabylonianContraction.lean
Statement:
theorem one_step_into_invariant (S x : ℝ) (hS : 0 ≤ S) (hx : 0 < x) :
T S x ∈ invariantHalfLine S := by | lutar-lean/Lutar/Banach/BabylonianContraction.lean#one_step_into_invariant | Lean theorem one_step_into_invariant | cortex | 241 | 60 | one_step_into_invariant | theorem | PROVEN (no sorry in block) | Lutar/Banach/BabylonianContraction.lean | null |
f6b786fcb669 | Lean theorem `babylonian_lipschitz_le_half` — status: PROVEN (no sorry in block)
File: Lutar/Banach/BabylonianContraction.lean
Statement:
theorem babylonian_lipschitz_le_half
(S : ℝ) (hS : 0 < S) {x y : ℝ}
(hx : x ∈ invariantHalfLine S) (hy : y ∈ invariantHalfLine S) :
|T S x - T S y| ≤ (1/2) * |x - y| := ... | lutar-lean/Lutar/Banach/BabylonianContraction.lean#babylonian_lipschitz_le_half | Lean theorem babylonian_lipschitz_le_half | cortex | 322 | 80 | babylonian_lipschitz_le_half | theorem | PROVEN (no sorry in block) | Lutar/Banach/BabylonianContraction.lean | null |
3b3a7190d307 | Lean theorem `babylonian_sqrt_is_banach_contraction` — status: PROVEN (no sorry in block)
File: Lutar/Banach/BabylonianContraction.lean
Statement:
theorem babylonian_sqrt_is_banach_contraction
(S : ℝ) (hS : 0 < S) :
∀ x y, x ∈ invariantHalfLine S → y ∈ invariantHalfLine S →
|T S x - T S y| ≤ (1/2) * |x -... | lutar-lean/Lutar/Banach/BabylonianContraction.lean#babylonian_sqrt_is_banach_contraction | Lean theorem babylonian_sqrt_is_banach_contraction | cortex | 326 | 81 | babylonian_sqrt_is_banach_contraction | theorem | PROVEN (no sorry in block) | Lutar/Banach/BabylonianContraction.lean | null |
ba2cc91e9c90 | Lean theorem `T_fixedPoint_sqrt` — status: PROVEN (no sorry in block)
File: Lutar/Banach/BabylonianContraction.lean
Statement:
theorem T_fixedPoint_sqrt (S : ℝ) (hS : 0 < S) : T S (Real.sqrt S) = Real.sqrt S := by
unfold T
have hsq : Real.sqrt S * Real.sqrt S = S := Real.mul_self_sqrt hS.le | lutar-lean/Lutar/Banach/BabylonianContraction.lean#T_fixedPoint_sqrt | Lean theorem T_fixedPoint_sqrt | cortex | 296 | 74 | T_fixedPoint_sqrt | theorem | PROVEN (no sorry in block) | Lutar/Banach/BabylonianContraction.lean | null |
52882e6f00fb | Lean theorem `sideSquared_bounds` — status: PROVEN (no sorry in block)
File: Lutar/Banach/LiuHuiPi.lean
Statement:
theorem sideSquared_bounds : ∀ n, 0 ≤ sideSquared n ∧ sideSquared n ≤ 4 := by
intro n
induction n with
| zero =>
constructor
· -- 0 ≤ sideSquared 0 = 1
unfold sideSquared; norm_num
... | lutar-lean/Lutar/Banach/LiuHuiPi.lean#sideSquared_bounds | Lean theorem sideSquared_bounds | cortex | 425 | 106 | sideSquared_bounds | theorem | PROVEN (no sorry in block) | Lutar/Banach/LiuHuiPi.lean | null |
553434d289db | Lean theorem `Λ_le_max` — status: PROVEN (no sorry in block)
File: Lutar/Bound.lean
Statement:
theorem Λ_le_max {k : ℕ} (hk : 0 < k) (x : Axes k) :
Λ k x ≤ Finset.univ.sup' ⟨⟨0, hk⟩, Finset.mem_univ _⟩ x := by | lutar-lean/Lutar/Bound.lean#Λ_le_max | Lean theorem Λ_le_max | cortex | 214 | 53 | Λ_le_max | theorem | PROVEN (no sorry in block) | Lutar/Bound.lean | null |
7508b36305c9 | Lean theorem `min_le_Λ` — status: PROVEN (no sorry in block)
File: Lutar/Bound.lean
Statement:
theorem min_le_Λ {k : ℕ} (hk : 0 < k) (x : Axes k) :
Finset.univ.inf' ⟨⟨0, hk⟩, Finset.mem_univ _⟩ x ≤ Λ k x := by | lutar-lean/Lutar/Bound.lean#min_le_Λ | Lean theorem min_le_Λ | cortex | 214 | 53 | min_le_Λ | theorem | PROVEN (no sorry in block) | Lutar/Bound.lean | null |
23013d118874 | Lean theorem `axis_option_distinguishes` — status: PROVEN (no sorry in block)
File: Lutar/Brahmi/AxisOption.lean
Statement:
theorem axis_option_distinguishes :
measured 0 ≠ absent := by | lutar-lean/Lutar/Brahmi/AxisOption.lean#axis_option_distinguishes | Lean theorem axis_option_distinguishes | cortex | 190 | 47 | axis_option_distinguishes | theorem | PROVEN (no sorry in block) | Lutar/Brahmi/AxisOption.lean | null |
cca76358a29c | Lean theorem `axis_dichotomy` — status: PROVEN (no sorry in block)
File: Lutar/Brahmi/AxisOption.lean
Statement:
theorem axis_dichotomy (av : AxisValue) :
isMeasured av = true ∨ isAbsent av = true := by | lutar-lean/Lutar/Brahmi/AxisOption.lean#axis_dichotomy | Lean theorem axis_dichotomy | cortex | 207 | 51 | axis_dichotomy | theorem | PROVEN (no sorry in block) | Lutar/Brahmi/AxisOption.lean | null |
4e8ad3d395af | Lean theorem `axis_exclusive` — status: PROVEN (no sorry in block)
File: Lutar/Brahmi/AxisOption.lean
Statement:
theorem axis_exclusive (av : AxisValue) :
¬ (isMeasured av = true ∧ isAbsent av = true) := by | lutar-lean/Lutar/Brahmi/AxisOption.lean#axis_exclusive | Lean theorem axis_exclusive | cortex | 211 | 52 | axis_exclusive | theorem | PROVEN (no sorry in block) | Lutar/Brahmi/AxisOption.lean | null |
dafe46016244 | Lean theorem `serialize_injective` — status: PROVEN (no sorry in block)
File: Lutar/Brahmi/AxisOption.lean
Statement:
theorem serialize_injective :
Function.Injective serialize := by | lutar-lean/Lutar/Brahmi/AxisOption.lean#serialize_injective | Lean theorem serialize_injective | cortex | 187 | 46 | serialize_injective | theorem | PROVEN (no sorry in block) | Lutar/Brahmi/AxisOption.lean | null |
1983e1bddb29 | Lean theorem `serialize_measured_zero_ne_absent` — status: PROVEN (no sorry in block)
File: Lutar/Brahmi/AxisOption.lean
Statement:
theorem serialize_measured_zero_ne_absent :
serialize (measured 0) ≠ serialize absent := by | lutar-lean/Lutar/Brahmi/AxisOption.lean#serialize_measured_zero_ne_absent | Lean theorem serialize_measured_zero_ne_absent | cortex | 228 | 57 | serialize_measured_zero_ne_absent | theorem | PROVEN (no sorry in block) | Lutar/Brahmi/AxisOption.lean | null |
127983578aed | Lean theorem `false_position_correct` — status: PROVEN (no sorry in block)
File: Lutar/Calibration/FalsePosition.lean
Statement:
theorem false_position_correct
(m c x₁ x₂ T : ℝ) (hm : m ≠ 0) (hx : x₁ ≠ x₂) :
let y₁ := m * x₁ + c | lutar-lean/Lutar/Calibration/FalsePosition.lean#false_position_correct | Lean theorem false_position_correct | cortex | 237 | 59 | false_position_correct | theorem | PROVEN (no sorry in block) | Lutar/Calibration/FalsePosition.lean | null |
6caf784b440d | Lean theorem `false_position_identity` — status: PROVEN (no sorry in block)
File: Lutar/Calibration/FalsePosition.lean
Statement:
theorem false_position_identity
(m c x₁ x₂ : ℝ) (hm : m ≠ 0) (hx : x₁ ≠ x₂) :
let y₁ := m * x₁ + c | lutar-lean/Lutar/Calibration/FalsePosition.lean#false_position_identity | Lean theorem false_position_identity | cortex | 237 | 59 | false_position_identity | theorem | PROVEN (no sorry in block) | Lutar/Calibration/FalsePosition.lean | null |
702e984d932e | Lean theorem `singletonBound_formula` — status: SORRY (tracked discharge obligation)
File: Lutar/CodingTheory/ReedSolomonSingleton.lean
Statement:
theorem singletonBound_formula (p : RSParams) :
singletonBound p = p.n - p.k + 1 := rfl | lutar-lean/Lutar/CodingTheory/ReedSolomonSingleton.lean#singletonBound_formula | Lean theorem singletonBound_formula | cortex | 239 | 59 | singletonBound_formula | theorem | SORRY (tracked discharge obligation) | Lutar/CodingTheory/ReedSolomonSingleton.lean | null |
d6642b2b26ad | Lean theorem `singletonBound_upper` — status: SORRY (tracked discharge obligation)
File: Lutar/CodingTheory/ReedSolomonSingleton.lean
Statement:
theorem singletonBound_upper (p : RSParams) (h_linear : True) :
p.d ≤ singletonBound p := by | lutar-lean/Lutar/CodingTheory/ReedSolomonSingleton.lean#singletonBound_upper | Lean theorem singletonBound_upper | cortex | 242 | 60 | singletonBound_upper | theorem | SORRY (tracked discharge obligation) | Lutar/CodingTheory/ReedSolomonSingleton.lean | null |
8f629ed14489 | Lean theorem `poly_uniqueness_at_k_points` — status: PROVEN (no sorry in block)
File: Lutar/CodingTheory/ReedSolomonSingleton.lean
Statement:
theorem poly_uniqueness_at_k_points
(F : Type*) [Field F] [DecidableEq F]
(pts : Fin k → F) (vals : Fin k → F)
(hpts : Function.Injective pts)
(p q : Polynomial ... | lutar-lean/Lutar/CodingTheory/ReedSolomonSingleton.lean#poly_uniqueness_at_k_points | Lean theorem poly_uniqueness_at_k_points | cortex | 462 | 115 | poly_uniqueness_at_k_points | theorem | PROVEN (no sorry in block) | Lutar/CodingTheory/ReedSolomonSingleton.lean | null |
5dc0d9b9aafd | Lean theorem `reedSolomonIsMDS` — status: SORRY (tracked discharge obligation)
File: Lutar/CodingTheory/ReedSolomonSingleton.lean
Statement:
theorem reedSolomonIsMDS (p : RSParams) (h_valid_rs : True) :
isMDS p := by | lutar-lean/Lutar/CodingTheory/ReedSolomonSingleton.lean#reedSolomonIsMDS | Lean theorem reedSolomonIsMDS | cortex | 221 | 55 | reedSolomonIsMDS | theorem | SORRY (tracked discharge obligation) | Lutar/CodingTheory/ReedSolomonSingleton.lean | null |
a23d1ca125ad | Lean theorem `erasure_ge_twice_error` — status: SORRY (tracked discharge obligation)
File: Lutar/CodingTheory/ReedSolomonSingleton.lean
Statement:
theorem erasure_ge_twice_error (p : RSParams) :
errorCorrectionCapacity p * 2 ≤ erasureCorrectionCapacity p := by | lutar-lean/Lutar/CodingTheory/ReedSolomonSingleton.lean#erasure_ge_twice_error | Lean theorem erasure_ge_twice_error | cortex | 265 | 66 | erasure_ge_twice_error | theorem | SORRY (tracked discharge obligation) | Lutar/CodingTheory/ReedSolomonSingleton.lean | null |
ec670a37eb78 | Lean theorem `rsGateValid_implies_singleton` — status: SORRY (tracked discharge obligation)
File: Lutar/CodingTheory/ReedSolomonSingleton.lean
Statement:
theorem rsGateValid_implies_singleton (n k d q t : ℕ)
(h : rsGateValid n k d q t) :
d = n - k + 1 := h.2.2.2.1 | lutar-lean/Lutar/CodingTheory/ReedSolomonSingleton.lean#rsGateValid_implies_singleton | Lean theorem rsGateValid_implies_singleton | cortex | 273 | 68 | rsGateValid_implies_singleton | theorem | SORRY (tracked discharge obligation) | Lutar/CodingTheory/ReedSolomonSingleton.lean | null |
67fdd92d917b | Lean theorem `rsGateValid_capacity_bound` — status: SORRY (tracked discharge obligation)
File: Lutar/CodingTheory/ReedSolomonSingleton.lean
Statement:
theorem rsGateValid_capacity_bound (n k d q t : ℕ)
(h : rsGateValid n k d q t) :
t ≤ n - k := h.2.2.2.2 | lutar-lean/Lutar/CodingTheory/ReedSolomonSingleton.lean#rsGateValid_capacity_bound | Lean theorem rsGateValid_capacity_bound | cortex | 263 | 65 | rsGateValid_capacity_bound | theorem | SORRY (tracked discharge obligation) | Lutar/CodingTheory/ReedSolomonSingleton.lean | null |
2a40d1f317a7 | Lean theorem `reedSolomonMDSProperty` — status: PROVEN (no sorry in block)
File: Lutar/CodingTheory/ReedSolomonSingleton.lean
Statement:
theorem reedSolomonMDSProperty (n k d q t : ℕ) :
rsGateValid n k d q t ↔
(1 ≤ k ∧ k ≤ n ∧ n ≤ q ∧ d = n - k + 1 ∧ t ≤ n - k) := by | lutar-lean/Lutar/CodingTheory/ReedSolomonSingleton.lean#reedSolomonMDSProperty | Lean theorem reedSolomonMDSProperty | cortex | 276 | 69 | reedSolomonMDSProperty | theorem | PROVEN (no sorry in block) | Lutar/CodingTheory/ReedSolomonSingleton.lean | null |
cdae720b1a5a | Lean lemma `robustness_composes` — status: PROVEN (no sorry in block)
File: Lutar/Composition/AdversarialRobustness.lean
Statement:
lemma robustness_composes
{X Y Z : Type*}
(mX : MetricModel X) (mY : MetricModel Y) (mZ : MetricModel Z)
(f : X → Y) (g : Y → Z)
(δ ε₁ ε₂ : ℝ)
(hf : IsRobust mX mY f δ... | lutar-lean/Lutar/Composition/AdversarialRobustness.lean#robustness_composes | Lean lemma robustness_composes | cortex | 454 | 113 | robustness_composes | lemma | PROVEN (no sorry in block) | Lutar/Composition/AdversarialRobustness.lean | null |
8327319af874 | Lean theorem `robustness_preserved_by_composition` — status: SORRY (tracked discharge obligation)
File: Lutar/Composition/AdversarialRobustness.lean
Statement:
theorem robustness_preserved_by_composition
{X Y Z : Type*}
(mX : MetricModel X) (mY : MetricModel Y) (mZ : MetricModel Z)
(S₁ : X → Y) (S₂ : Y → Z... | lutar-lean/Lutar/Composition/AdversarialRobustness.lean#robustness_preserved_by_composition | Lean theorem robustness_preserved_by_composition | cortex | 505 | 126 | robustness_preserved_by_composition | theorem | SORRY (tracked discharge obligation) | Lutar/Composition/AdversarialRobustness.lean | null |
4d8866e49b68 | Lean theorem `iterated_chain_obligation_tracked` — status: PROVEN (no sorry in block)
File: Lutar/Composition/AdversarialRobustness.lean
Statement:
theorem iterated_chain_obligation_tracked : iterated_chain_tracked := by
trivial
/-! ## 7. Adversary Budget Theorem -/
/-- An *adversary* with budget B cannot push the... | lutar-lean/Lutar/Composition/AdversarialRobustness.lean#iterated_chain_obligation_tracked | Lean theorem iterated_chain_obligation_tracked | cortex | 461 | 115 | iterated_chain_obligation_tracked | theorem | PROVEN (no sorry in block) | Lutar/Composition/AdversarialRobustness.lean | null |
a515ee8cdb8d | Lean theorem `adversary_budget_bounded` — status: PROVEN (no sorry in block)
File: Lutar/Composition/AdversarialRobustness.lean
Statement:
theorem adversary_budget_bounded
{X Y Z : Type*}
(mX : MetricModel X) (mY : MetricModel Y) (mZ : MetricModel Z)
(S₁ : X → Y) (S₂ : Y → Z)
(x_clean x_adv : X)
(δ... | lutar-lean/Lutar/Composition/AdversarialRobustness.lean#adversary_budget_bounded | Lean theorem adversary_budget_bounded | cortex | 547 | 136 | adversary_budget_bounded | theorem | PROVEN (no sorry in block) | Lutar/Composition/AdversarialRobustness.lean | null |
b24383f5759b | Lean theorem `totalOverhead_nil` — status: PROVEN (no sorry in block)
File: Lutar/Composition/CompositionOverhead.lean
Statement:
theorem totalOverhead_nil : totalOverhead [] = 0 := rfl
@[simp]
theorem totalOverhead_cons (h : CostSystem) (t : List CostSystem) : | lutar-lean/Lutar/Composition/CompositionOverhead.lean#totalOverhead_nil | Lean theorem totalOverhead_nil | cortex | 263 | 65 | totalOverhead_nil | theorem | PROVEN (no sorry in block) | Lutar/Composition/CompositionOverhead.lean | null |
eb9702f360d7 | Lean theorem `totalOverhead_cons` — status: PROVEN (no sorry in block)
File: Lutar/Composition/CompositionOverhead.lean
Statement:
theorem totalOverhead_cons (h : CostSystem) (t : List CostSystem) :
totalOverhead (h :: t) = h.cost + totalOverhead t := rfl | lutar-lean/Lutar/Composition/CompositionOverhead.lean#totalOverhead_cons | Lean theorem totalOverhead_cons | cortex | 260 | 65 | totalOverhead_cons | theorem | PROVEN (no sorry in block) | Lutar/Composition/CompositionOverhead.lean | null |
fa6eb278c5bf | Lean theorem `totalOverhead_singleton` — status: PROVEN (no sorry in block)
File: Lutar/Composition/CompositionOverhead.lean
Statement:
theorem totalOverhead_singleton (s : CostSystem) :
totalOverhead [s] = s.cost := by simp [totalOverhead] | lutar-lean/Lutar/Composition/CompositionOverhead.lean#totalOverhead_singleton | Lean theorem totalOverhead_singleton | cortex | 245 | 61 | totalOverhead_singleton | theorem | PROVEN (no sorry in block) | Lutar/Composition/CompositionOverhead.lean | null |
d8e15b2c5a4e | Lean theorem `totalOverhead_append` — status: PROVEN (no sorry in block)
File: Lutar/Composition/CompositionOverhead.lean
Statement:
theorem totalOverhead_append (l₁ l₂ : List CostSystem) :
totalOverhead (l₁ ++ l₂) = totalOverhead l₁ + totalOverhead l₂ := by | lutar-lean/Lutar/Composition/CompositionOverhead.lean#totalOverhead_append | Lean theorem totalOverhead_append | cortex | 263 | 65 | totalOverhead_append | theorem | PROVEN (no sorry in block) | Lutar/Composition/CompositionOverhead.lean | null |
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