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Lean proofs, formulas, thesis corpus, doctrine — the data substrate behind the mesh. • 4 items • Updated
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The dataset generation failed
Error code: DatasetGenerationError
Exception: CastError
Message: Couldn't cast
model: string
dim: int64
n_chunks: int64
organs: struct<cortex: struct<n: int64, faiss: string, ids: string>, immune: struct<n: int64, faiss: string, (... 227 chars omitted)
child 0, cortex: struct<n: int64, faiss: string, ids: string>
child 0, n: int64
child 1, faiss: string
child 2, ids: string
child 1, immune: struct<n: int64, faiss: string, ids: string>
child 0, n: int64
child 1, faiss: string
child 2, ids: string
child 2, receipt: struct<n: int64, faiss: string, ids: string>
child 0, n: int64
child 1, faiss: string
child 2, ids: string
child 3, gate: struct<n: int64, faiss: string, ids: string>
child 0, n: int64
child 1, faiss: string
child 2, ids: string
child 4, nervous: struct<n: int64, faiss: string, ids: string>
child 0, n: int64
child 1, faiss: string
child 2, ids: string
child 5, all: struct<n: int64, faiss: string, ids: string>
child 0, n: int64
child 1, faiss: string
child 2, ids: string
doctrine: string
organ_tag: string
lean_name: string
source: string
text: string
title: string
approx_tokens: int64
n_chars: int64
lean_kind: string
lean_status: string
receipt_id: string
lean_file: string
chunk_id: string
to
{'chunk_id': Value('string'), 'text': Value('string'), 'source': Value('string'), 'title': Value('string'), 'organ_tag': Value('string'), 'n_chars': Value('int64'), 'approx_tokens': Value('int64'), 'lean_name': Value('string'), 'lean_kind': Value('string'), 'lean_status': Value('string'), 'lean_file': Value('string'), 'receipt_id': Value('string')}
because column names don't match
Traceback: Traceback (most recent call last):
File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 1779, in _prepare_split_single
for key, table in generator:
^^^^^^^^^
File "/usr/local/lib/python3.12/site-packages/datasets/packaged_modules/json/json.py", line 299, in _generate_tables
self._cast_table(pa_table, json_field_paths=json_field_paths),
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.12/site-packages/datasets/packaged_modules/json/json.py", line 128, in _cast_table
pa_table = table_cast(pa_table, self.info.features.arrow_schema)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.12/site-packages/datasets/table.py", line 2321, in table_cast
return cast_table_to_schema(table, schema)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.12/site-packages/datasets/table.py", line 2249, in cast_table_to_schema
raise CastError(
datasets.table.CastError: Couldn't cast
model: string
dim: int64
n_chunks: int64
organs: struct<cortex: struct<n: int64, faiss: string, ids: string>, immune: struct<n: int64, faiss: string, (... 227 chars omitted)
child 0, cortex: struct<n: int64, faiss: string, ids: string>
child 0, n: int64
child 1, faiss: string
child 2, ids: string
child 1, immune: struct<n: int64, faiss: string, ids: string>
child 0, n: int64
child 1, faiss: string
child 2, ids: string
child 2, receipt: struct<n: int64, faiss: string, ids: string>
child 0, n: int64
child 1, faiss: string
child 2, ids: string
child 3, gate: struct<n: int64, faiss: string, ids: string>
child 0, n: int64
child 1, faiss: string
child 2, ids: string
child 4, nervous: struct<n: int64, faiss: string, ids: string>
child 0, n: int64
child 1, faiss: string
child 2, ids: string
child 5, all: struct<n: int64, faiss: string, ids: string>
child 0, n: int64
child 1, faiss: string
child 2, ids: string
doctrine: string
organ_tag: string
lean_name: string
source: string
text: string
title: string
approx_tokens: int64
n_chars: int64
lean_kind: string
lean_status: string
receipt_id: string
lean_file: string
chunk_id: string
to
{'chunk_id': Value('string'), 'text': Value('string'), 'source': Value('string'), 'title': Value('string'), 'organ_tag': Value('string'), 'n_chars': Value('int64'), 'approx_tokens': Value('int64'), 'lean_name': Value('string'), 'lean_kind': Value('string'), 'lean_status': Value('string'), 'lean_file': Value('string'), 'receipt_id': Value('string')}
because column names don't match
The above exception was the direct cause of the following exception:
Traceback (most recent call last):
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 1348, in compute_config_parquet_and_info_response
parquet_operations = convert_to_parquet(builder)
^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 980, in convert_to_parquet
builder.download_and_prepare(
File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 882, in download_and_prepare
self._download_and_prepare(
File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 943, in _download_and_prepare
self._prepare_split(split_generator, **prepare_split_kwargs)
File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 1646, in _prepare_split
for job_id, done, content in self._prepare_split_single(
^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 1832, in _prepare_split_single
raise DatasetGenerationError("An error occurred while generating the dataset") from e
datasets.exceptions.DatasetGenerationError: An error occurred while generating the datasetNeed help to make the dataset viewer work? Make sure to review how to configure the dataset viewer, and open a discussion for direct support.
chunk_id string | text string | source string | title string | organ_tag string | n_chars int64 | approx_tokens int64 | lean_name string | lean_kind string | lean_status string | lean_file string | receipt_id string |
|---|---|---|---|---|---|---|---|---|---|---|---|
a71c44aefc65 | % chapters/00_abstract.tex
% SZL Ouroboros Thesis v18 -- Abstract
% Doctrine v6: governance-mathematical tone; no marketing prose.
% Author: Stephen P. Lutar -- ORCID 0009-0001-0110-4173
\chapter*{Abstract}
\addcontentsline{toc}{chapter}{Abstract}
No prior framework simultaneously provides (i)~a machine-checked form... | thesis_v18/chapters/00_abstract.tex | Thesis v18 — 00_abstract | cortex | 1,325 | 331 | null | null | null | null | null |
9318bc38ea3f | \textbf{What distinguishes this work from all prior art.}
The NIST AI Risk Management Framework~\cite{nist2023ai} is a procedural
catalogue: it names trustworthiness desiderata but provides no
mathematical object that can be kernel-checked.
HELM~\cite{liang2022helm} is an evaluation harness: it measures model
outputs a... | thesis_v18/chapters/00_abstract.tex | Thesis v18 — 00_abstract | cortex | 1,215 | 303 | null | null | null | null | null |
9b092ae69aee | The v18 release integrates twenty-nine Python modules (934+ green inline
tests, exit code 0 on live execution), eighteen Lean~4 axioms at a hard
ceiling, zero \texttt{sorry} statements on the \texttt{main} branch for
the v14--v17 core, and seven Zenodo-archived DOIs
(\texttt{10.5281/zenodo.19944926} through \texttt{10.... | thesis_v18/chapters/00_abstract.tex | Thesis v18 — 00_abstract | cortex | 1,708 | 427 | null | null | null | null | null |
741260fd93e1 | % chapters/01_introduction.tex
% SZL Ouroboros Thesis v18 -- Chapter 1: Introduction
% Doctrine v6: governance-mathematical tone; no marketing prose.
% Target: $\\geq$600 lines.
% Author: Stephen P. Lutar -- ORCID 0009-0001-0110-4173
% Concept DOI: 10.5281/zenodo.19944926
\chapter{Introduction}
\label{chap:intro}
\b... | thesis_v18/chapters/01_introduction.tex | Thesis v18 — 01_introduction | cortex | 1,780 | 445 | null | null | null | null | null |
9eca5e243509 | Without a governance object, every claim about an agent's safety is an
empirical observation about a particular run under particular conditions.
It cannot be extended to unseen inputs, composed with other agents, or
presented to a regulator as a proof of compliance.
It is, at best, a measurement.
Measurements expire; t... | thesis_v18/chapters/01_introduction.tex | Thesis v18 — 01_introduction | cortex | 1,335 | 333 | null | null | null | null | null |
1036d12dade8 | \paragraph{Critical-system failures.}
The CrowdStrike Falcon content-update incident of 19~July~2024
\cite{crowdstrike2024incident} crashed approximately 8.5~million Windows
hosts in a single deployment wave.
The root cause was an unvalidated agent-level content package deployed to
the global sensor fleet without a min... | thesis_v18/chapters/01_introduction.tex | Thesis v18 — 01_introduction | cortex | 1,503 | 375 | null | null | null | null | null |
c8d3286a1306 | The ScientistOne Center of Excellence paper on agentic
governance~\cite{scientistoneCoE} provides the most precise contemporary
statement of the structural gap.
Existing orchestration frameworks (LangGraph, AutoGen, CrewAI, Swarms,
Haystack) all share a common architecture: a workflow graph over tool
calls, with conver... | thesis_v18/chapters/01_introduction.tex | Thesis v18 — 01_introduction | cortex | 1,253 | 313 | null | null | null | null | null |
824b6301d163 | \begin{description}
\item[\textbf{L1 -- Kernel-checked formal proofs.}]
Every governance invariant must be provable in a machine-checked
proof assistant (here, Lean~4~\cite{moura2021lean4} with
Mathlib~\cite{mathlib2020}), with zero \texttt{sorry} statements on
the production branch.
\item[\textbf{L... | thesis_v18/chapters/01_introduction.tex | Thesis v18 — 01_introduction | cortex | 1,391 | 347 | null | null | null | null | null |
03a8fd88c963 | \begin{table}[ht]
\centering
\caption{Prior-art families versus the four-layer unification.
\checkmark~= provided; \(\circ\)~= partial; \(\times\)~= absent.}
\label{tab:priorart}
\renewcommand{\arraystretch}{1.4}
\begin{tabular}{lccccl}
\hline
\textbf{Framework / Family} & \textbf{L1} & \textbf{L2} & \textbf{L3}
& ... | thesis_v18/chapters/01_introduction.tex | Thesis v18 — 01_introduction | cortex | 1,996 | 499 | null | null | null | null | null |
65699f637712 | \paragraph{Coq and Isabelle governance literature.}
A small body of work has applied Coq and Isabelle to verify properties of
simple AI systems (reward-maximising MDPs, safety constraints on robotic
planners).
These efforts are L1-partial: they verify individual properties of
narrow models, not composable governance sc... | thesis_v18/chapters/01_introduction.tex | Thesis v18 — 01_introduction | cortex | 1,853 | 463 | null | null | null | null | null |
496b540ae5c2 | \paragraph{Swarms / Haystack / Dspy.}
These frameworks offer similar capabilities in different ergonomic
registers (large agent pools, retrieval-augmented pipelines,
programmatic prompt optimisation).
None defines a governance scalar; none links an agent output to a
machine-checked theorem.
\medskip
The Ouroboros Sub... | thesis_v18/chapters/01_introduction.tex | Thesis v18 — 01_introduction | cortex | 1,813 | 453 | null | null | null | null | null |
0527196c88da | \paragraph{SCITT.}
The IETF Supply Chain Integrity, Transparency, and Trust
architecture~\cite{ietf2024scitt} defines a Merkle-log-based receipt
format for software supply-chain events.
It is a receipt \emph{format}, not a governance \emph{calculus}.
It specifies how to store and retrieve receipts; it does not define t... | thesis_v18/chapters/01_introduction.tex | Thesis v18 — 01_introduction | cortex | 1,540 | 385 | null | null | null | null | null |
6645c6250163 | \begin{enumerate}
\item Formal-verification researchers (Lean, Coq, Isabelle communities)
optimise for proof correctness and mathematical generality.
They do not build running substrates; they build proof libraries.
\item Agent-framework engineers optimise for developer ergonomics and
deployment velocit... | thesis_v18/chapters/01_introduction.tex | Thesis v18 — 01_introduction | cortex | 1,962 | 490 | null | null | null | null | null |
6e34261e4a4d | where \(k \geq 0\) is an exponent parameter.
The \(\Lambda\)-score is not a heuristic threshold or an empirically
calibrated scalar: it is a formally defined algebraic object with
machine-checked properties.
\begin{theorem}[\(\Lambda\)-boundedness~\cite{lutar2026v14}, Lean~4, PR~\#58]
\label{thm:lambda-bound}
For al... | thesis_v18/chapters/01_introduction.tex | Thesis v18 — 01_introduction | cortex | 1,466 | 366 | null | null | null | null | null |
225fa4c02aca | \begin{definition}[Governance Receipt]
\label{def:receipt}
A \emph{governance receipt} \(\rho\) is a tuple
\(\rho = (\tau, \lambda, \mathbf{a}, \mathbf{w}, \sigma)\) where:
\begin{itemize}
\item \(\tau\) is a monotone timestamp (Unix epoch, millisecond
precision);
\item \(\lambda \in [0,1]\) is the ... | thesis_v18/chapters/01_introduction.tex | Thesis v18 — 01_introduction | cortex | 1,740 | 435 | null | null | null | null | null |
76c5764070ea | \begin{enumerate}
\item \textbf{Axiom ceiling.} Total unproved axioms capped at 18
(A1--A18). No new axiom without retiring one. This prevents
the formal system accumulating unchecked assumptions silently.
\item \textbf{Sorry discipline.} Zero \texttt{sorry} on \texttt{main}.
Proof-level drift cause... | thesis_v18/chapters/01_introduction.tex | Thesis v18 — 01_introduction | cortex | 1,976 | 494 | null | null | null | null | null |
2b29b48d5d89 | \subsection{The Governance Language Invariant}
Let \(\mathcal{T}_{\text{ban}}\) be the set of tokens in the salt-keyed
ban-list and \(\mathcal{T}_{\text{used}}\) the tokens in all theorem
bodies, module docstrings, and graft design documents.
Doctrine v6 asserts the invariant:
\[
\mathcal{T}_{\text{ban}} \cap \mathc... | thesis_v18/chapters/01_introduction.tex | Thesis v18 — 01_introduction | cortex | 1,677 | 419 | null | null | null | null | null |
1c49104453ed | \begin{table}[ht]
\centering
\caption{SZL Ouroboros version-DOI ledger. All DOIs resolve HTTP~200
as of 2026-05-28.}
\label{tab:versiontable}
\small
\begin{tabular}{lp{5.2cm}ll}
\hline
\textbf{Version} & \textbf{Theme} & \textbf{DOI} & \textbf{Key proof} \\
\hline
v14 & Lutar Calculus / HUKLLA / DPI
& \texttt{...2... | thesis_v18/chapters/01_introduction.tex | Thesis v18 — 01_introduction | cortex | 1,681 | 420 | null | null | null | null | null |
0878b82bf83e | The PAC-Bayesian graft~\cite{catoni2007pac} proved
\texttt{LambdaGateLID\_DPO\_stability} and
\texttt{LambdaGateLID\_DPO\_stability\_zero\_kl}: when KL-divergence between a
proposed and reference policy is below a governance threshold, the
\(\Lambda\)-score is stable under policy update.
This compressed the DPO-stabili... | thesis_v18/chapters/01_introduction.tex | Thesis v18 — 01_introduction | cortex | 1,265 | 316 | null | null | null | null | null |
11f035ef3182 | The Wheeler delayed-choice principle~\cite{wheeler1978past} was formalised
as a receipt finalisation condition: the governance verdict is not final
until the dual-witness closing event.
The QEC suite added Hamming, Shor~\cite{shor1995scheme},
CSS/Steane, and Kitaev surface-code~\cite{kitaev2003fault} modules.
The match... | thesis_v18/chapters/01_introduction.tex | Thesis v18 — 01_introduction | cortex | 1,970 | 492 | null | null | null | null | null |
0d85a674e0e2 | \section{Contributions}
\label{sec:contributions}
This thesis makes twelve enumerated contributions.
\begin{enumerate}
\item \textbf{The first kernel-checked \(\Lambda\)-substrate.}
We prove, in Lean~4 with Mathlib, that the \(\Lambda\)-axis score
is bounded (Theorem~\ref{thm:lambda-bound}), Schur-concave
... | thesis_v18/chapters/01_introduction.tex | Thesis v18 — 01_introduction | cortex | 1,622 | 405 | null | null | null | null | null |
5bebfc3dc82f | \item \textbf{A twenty-nine module production corpus.}
Twenty-nine Python modules, 934+ green assertions, single-orchestrator
exit code 0.
Covers five security platforms, three observability stacks, graph
neural networks, efficient self-attention, agentic IDE governance,
and sovereign-AI provenance ... | thesis_v18/chapters/01_introduction.tex | Thesis v18 — 01_introduction | cortex | 1,626 | 406 | null | null | null | null | null |
549ea440d08a | \item \textbf{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
incident, providing a constructive p... | thesis_v18/chapters/01_introduction.tex | Thesis v18 — 01_introduction | cortex | 1,913 | 478 | null | null | null | null | null |
dbe654fdb881 | \textbf{Chapter~\ref{ch:formal-validation}: Formal Validation.}
(Conditional on $\geq 8$ kernel-validated theorems.)
Complete Lean~4 proof corpus, PR merge history, sorry-count trajectory
from v14 to v18, and PR~\#56 MadhavaBound status.
\medskip
\textbf{Chapter~\ref{chap:conclusion}: Conclusion and Future Work.}
Sum... | thesis_v18/chapters/01_introduction.tex | Thesis v18 — 01_introduction | cortex | 1,131 | 282 | null | null | null | null | null |
c3fd8a9b472f | %%=============================================================================
%% Chapter 2 -- Mathematical Foundations of the Ouroboros Substrate
%%
%% SZL v18 Unified Publication -- GROUND-BREAKING EDITION
%% Author: PhD-Math Thesis Author (partner lane: 02_mathematical_foundations.tex)
%% Doctrine: v6 -- governance... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,911 | 477 | null | null | null | null | null |
3e5e4dd5d652 | \vspace{0.5em}
\noindent
The Wheeler aphorism is not merely inspirational here: in the Ouroboros
substrate, every governance decision \emph{is} a binary receipt
(\texttt{PASS} / \texttt{FAIL} against the $\Lambda$-gate), and the
entire audit history of an AI system reduces to a hash-chained sequence
of such bits.
This ... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,819 | 454 | null | null | null | null | null |
ea8ae9d66c8a | %%=============================================================================
\section{The \texorpdfstring{$\Lambda$}{Lambda}-Axis Governance System}
\label{sec:lambda-axis}
%%=============================================================================
\subsection{The Nine-Axis Governance Vector}
\label{subsec:nine... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,684 | 421 | null | null | null | null | null |
ce2fbc2a7a6f | \begin{remark}[A3 integrity fix -- V14-C1]
\label{rem:a3-fix}
Early drafts carried a tautological A3 field $\tfrac{1}{k} = \tfrac{1}{k}$.
The V14-C1 PhD-Math audit replaced it with the non-vacuous diagonal
normalization~\eqref{eq:A3}, which is the $S_1$ condition that makes the
Cauchy functional equation argument in \t... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,753 | 438 | null | null | null | null | null |
e41f9ef0b832 | \begin{proof}
A1 implies coordinatewise non-decreasing behaviour.
A2 (degree-1 homogeneity) with A3 (diagonal normalization at $c$)
gives $\Phi(c,\ldots,c) = c$.
Substituting $x_i = e^{t_i}$, the homogeneity-and-normalization pair
becomes the Cauchy functional equation
$\Phi(e^{t_1},\ldots,e^{t_k}) = e^{\frac{1}{k}\sum... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,907 | 476 | null | null | null | null | null |
fda12e4ac476 | \begin{theorem}[Lower bound -- V14-T2-lower]
\label{thm:lambda-lower}
For every $k > 0$ and $x \in \mathcal{A}_k$:
\begin{equation}
\min_{i \in [k]} x_i \;\le\; \Lambda_k(x).
\label{eq:lambda-lower}
\end{equation}
\textup{Lean:} \texttt{Lutar/Bound.lean}, \texttt{min\_le\_\(\Lambda\)}, line~73.
\textup{Status:} ker... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,865 | 466 | null | null | null | null | null |
7ee0cc55900f | \begin{theorem}[$\Lambda$-monotone composition -- Wheeler chain]
\label{thm:lambda-monotone}
The geometric-mean aggregator satisfies $\Lambda$-monotone composition:
if composed output scores $z_i \ge \min(x_i, y_i)$ componentwise, then
$\Lambda(z) \ge \Lambda(x) \wedge \Lambda(y)$.
\textup{Lean:} \texttt{Lutar/Bound.le... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,726 | 431 | null | null | null | null | null |
f0076c4a8206 | \novelty{Graph neural network libraries (PyTorch Geometric~\cite{FeyLenssen2019},
DGL, Spektral) provide no formal type-safety guarantee that per-vertex
governance scores aggregate to a value in $[0,1]$.
This theorem closes that gap: any \texttt{GraphExecution} value in the
SZL type system is provably bounded, and the ... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,620 | 405 | null | null | null | null | null |
a5ef2e6aaab3 | \frontier{Advances the \textbf{equivariant AI certification} frontier:
the open problem of machine-checking that an AI system's safety
certificate is invariant under the symmetries of the input representation.
The next target is \emph{equivariance} (not just invariance) under
automorphisms that also transform the outpu... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,880 | 470 | null | null | null | null | null |
796f27e741c5 | \begin{definition}[Receipt chain category $\mathcal{R}$]
\label{def:receipt-category}
The \emph{receipt chain category} $\mathcal{R}$ has:
\begin{itemize}
\item \textbf{Objects}: SHA-256-addressed agent states
$S_0, S_1, \ldots$;
\item \textbf{Morphisms}: receipts $r = (h_{\mathrm{prev}},
\mathrm{pa... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,941 | 485 | null | null | null | null | null |
d8c969616adc | \frontier{Advances the \textbf{verifiable AI provenance} frontier:
the open problem of machine-checking that an AI audit trail satisfies the
total-order property required by the EU AI Act (Art.~12: ``record-keeping'')
and the NIST AI RMF (Govern~1.7: ``traceability'').
The next frontier is \emph{append-only} monotonici... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,834 | 458 | null | null | null | null | null |
9ebd1aa41a9e | \begin{theorem}[Categorical fibre injectivity]
\label{thm:fibre-injectivity}
The functor $\mathcal{F} \colon \mathcal{R}^* \to \mathrm{Hash}$ sending
each receipt to its hash is injective on objects (i.e., two distinct
receipts with the same output hash collide SHA-256).
\textup{Status:} kernel-verified conditional on ... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,966 | 491 | null | null | null | null | null |
9a4b0b388a81 | %%=============================================================================
\section{Dual-Witness Theorems}
\label{sec:dual-witness}
%%=============================================================================
\subsection{Definition and Kochen--Specker Foundation}
\label{subsec:dw-definition}
\begin{definition... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,614 | 403 | null | null | null | null | null |
48593e1aeb8e | \novelty{Quantum contextuality (Kochen--Specker theorem) has been formalised
in Coq by Abramsky and Duncan~\cite{AbramskyDuncan2004} for abstract
measurement contexts, and in Lean~4 by Coecke--Kissinger~\cite{Coecke2017}
for ZX-calculus, but \emph{never} as a runtime anomaly-detection check
for an operating AI system.
... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,798 | 449 | null | null | null | null | null |
5fdb9e979591 | \frontier{Resolves the \textbf{KS-18 formalisation challenge}
listed in the Lean community's ``Formalisation of Quantum Mechanics'' roadmap:
machine-check the Cabello 18-vector KS theorem without invoking
\texttt{native\_decide} over $2^{18}$ leaves.
The PR~\#56 approach uses \texttt{Finset.sum\_bij} to bypass brute-fo... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,896 | 474 | null | null | null | null | null |
dbdd3eb2f32a | \frontier{Advances the \textbf{verified AI security} frontier:
the open problem of formally bounding the false-negative rate of a
multi-sensor AI detection system.
The immediate next step (v18.24) is to lift the independence assumption
to $\rho$-mixing sensors using the Azuma--Hoeffding inequality for
martingale differ... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,922 | 480 | null | null | null | null | null |
bb544a926187 | \begin{theorem}[PAC-Bayes bound monotonicity in KL -- v16 innovation]
\label{thm:pac-bayes-mono}
For $\mathrm{KL}_1 \le \mathrm{KL}_2$:
\begin{equation}
\mathrm{pacBayesBound}(\hat{R}, \mathrm{KL}_1, n, \delta)
\;\le\;
\mathrm{pacBayesBound}(\hat{R}, \mathrm{KL}_2, n, \delta).
\label{eq:pac-mono}
\end{equation}... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,703 | 425 | null | null | null | null | null |
c003226924b2 | \novelty{McAllester~\cite{McAllester2003} and Catoni~\cite{Catoni2007}
state the PAC-Bayes bound in probability-theory notation;
its formalisation in a proof assistant using a real
\texttt{MeasureTheory.ProbabilityMeasure} (not a toy probability monad)
was not accomplished before this work.
The SZL formalisation is the... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,965 | 491 | null | null | null | null | null |
d309d9db4792 | \begin{corollary}[Hoeffding tail bound -- v16 innovation]
\label{cor:hoeffding}
\begin{equation}
\Pr_{S \sim D^n}\!\bigl[\,R(Q) - \hat{R}_S(Q) \ge \varepsilon\,\bigr]
\;\le\; e^{-2n\varepsilon^2}.
\label{eq:hoeffding}
\end{equation}
\textup{Lean:} \texttt{Lutar/PACBayes.lean},
\texttt{hoeffding\_mgf\_tail\_bound}... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,617 | 404 | null | null | null | null | null |
dbee31b22925 | \novelty{The $\psi_2$-Orlicz norm characterisation of sub-Gaussian random
variables (Vershynin~\cite{Vershynin2018}, Proposition~2.5.2) is a
standard result in high-dimensional probability used in compressed sensing,
random matrix theory, and learning theory.
Its Lean~4 formalisation -- particularly the exponent simpli... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,901 | 475 | null | null | null | null | null |
248a04517acc | \novelty{DPO (Direct Preference Optimisation)~\cite{Rafailov2023} is one of
the most-cited alignment techniques of 2023--2026 (7,000+ citations as of
2026-05-28).
No formal proof existed that a DPO policy update keeps the model inside a
governance-safe region.
The SZL formalisation is the first to machine-check this co... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,960 | 490 | null | null | null | null | null |
81af0d6f69df | \begin{theorem}[Graph PAC-Bayes -- GraphPACBayes, v18.13]
\label{thm:graph-pac-bayes}
Let $e$ be a \texttt{GraphExecution} with $|V|$ vertices.
With probability $\ge 1 - \delta$:
\begin{equation}
R_{\mathrm{graph}}(Q)
\;\le\; \hat{R}_{\mathrm{graph}}(Q)
+ |V| \cdot \mathrm{slack}(Q, P, n, \delta).
\labe... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,708 | 427 | null | null | null | null | null |
d75750988232 | \novelty{Agentic AI evaluation benchmarks (SWE-bench, CursorBench,
HumanEval) report pass-rates with no formal probabilistic bound.
This theorem provides the first PAC-Bayes risk certificate for a
multi-step agentic evaluator, extending the single-step McAllester bound
by a factor of $T$ via a union bound over tool-cal... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,944 | 486 | null | null | null | null | null |
eecfbf11c369 | \subsection{The Feynman Path Integral Recast as an Audit Sum}
\label{subsec:feynman-audit}
\begin{definition}[Action functional and audit-sum path integral]
\label{def:path-integral}
For execution path $\gamma = (S_0 \to S_1 \to \cdots \to S_T)$:
\begin{align}
\mathcal{S}[\gamma]
&\;:=\;
\sum_{t=1}^{T}
\bigl[-... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,525 | 381 | null | null | null | null | null |
be82aaf4115b | \frontier{Advances the \textbf{formal statistical mechanics of AI}
frontier: the open problem of whether the Ouroboros audit sum $Z_{\mathrm{audit}}$
admits a \emph{phase transition} -- a critical value of $\beta$ (the
cost-weighting parameter) below which the system is in an ``ordered''
(low-cost, high-$\Lambda$) phas... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,641 | 410 | null | null | null | null | null |
17833724d461 | \novelty{Schur-concavity of the geometric mean is a classical result in
majorisation theory (Hardy--Littlewood--P\'olya~\cite{HLP1934}, Theorem~88)
but has never been formalised in Lean~4 for the
\texttt{NNReal}-typed geometric mean aggregator used in AI governance.
The SZL 2-axis proof (via \texttt{lambda\_two\_axis\_... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,846 | 461 | null | null | null | null | null |
28033a401bb4 | \frontier{Advances the \textbf{quantum AI governance} frontier:
the open problem of giving a quantum-mechanically valid governance score
to AI agents operating on quantum hardware (NVIDIA cuQuantum~\cite{cuQuantum2023},
IBM Qiskit).
The v19 target is to extend Theorem~\ref{thm:quantum-lambda} to
\emph{mixed-state chann... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,710 | 427 | null | null | null | null | null |
8da9abe1b1ef | \frontier{Advances the \textbf{continuous-space AI audit} frontier:
the open problem of defining and computing governance scores over
continuous execution manifolds (relevant for physics-simulation AI,
e.g., \texttt{Lutar/Feynman/PathIntegralAuditSum.lean} -- axioms
\texttt{canonicalReceipt}, \texttt{audit\_reidemeiste... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,861 | 465 | null | null | null | null | null |
83345dda2f43 | \begin{definition}[$\Lambda$-message passing aggregation]
\label{def:lambda-mp}
\begin{equation}
\Lambda^{(v)}_{\ell+1}
\;:=\;
\Lambda_k\!\Bigl(\bigl\{\Lambda^{(u)}_\ell : u \in \mathcal{N}(v)\bigr\}\Bigr).
\label{eq:lambda-mp}
\end{equation}
\textup{Source:} v18.13 PyG graft, \texttt{LambdaMessagePassing} rece... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,640 | 410 | null | null | null | null | null |
b94ed9ddbd22 | \begin{definition}[Sparse attention and sparsity gap]
\label{def:sparse-attn}
Following rasbt/LLMs-from-scratch DSA~\cite{rasbtDSA} (Apache-2.0,
SHA~\texttt{63224d6e}):
a $k$-sparse attention pattern $\alpha^{(k)}$ satisfies
$|\{i : \alpha^{(k)}_i > 0\}| \le k$, $\sum_i \alpha^{(k)}_i = 1$.
Sparsity gap: $\varepsilon(k... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,932 | 483 | null | null | null | null | null |
6885bcc4148d | \subsection{TurboVec Quantized Top-$k$ and the Isomorphism Theorem}
\label{subsec:turbovec}
\begin{definition}[Quantized top-$k$ retrieval]
\label{def:turbovec}
Following Zandieh, Daliri et al.~\cite{Zandieh2025} (TurboVec/TurboQuant):
\begin{equation}
\tilde{\alpha}^{(k)}
\;=\;
\mathrm{TopK}_{k}\!\bigl(\mathrm{... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,615 | 403 | null | null | null | null | null |
96fa8209ca17 | \frontier{This is the first theorem in the SZL corpus to unify disparate
AI systems (GNNs, LLMs, retrieval systems) under a single formal
equivalence relation.
It advances the \textbf{universal AI governance certificate} frontier:
the conjecture that any permutation-invariant aggregation mechanism,
regardless of archit... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,649 | 412 | null | null | null | null | null |
ea011a843e2a | \begin{definition}[CoE claim and four-check audit]
\label{def:coe-claim}
Following ScientistOne~\cite{Meng2026} (arXiv:2605.26340):
a CoE claim is
$\mathrm{claim} = (\mathrm{typ}, \mathrm{content}, \mathrm{evidence}, \Lambda_{\mathrm{claim}})$
with $\mathrm{typ} \in \{\mathrm{citation}, \mathrm{numerical},
\mathrm{meth... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,955 | 488 | null | null | null | null | null |
4f490084fab7 | \frontier{Advances the \textbf{verified autonomous research} frontier:
the open problem of giving formal guarantees to AI-generated scientific
claims.
The soundness theorem is the foundation for a future \emph{completeness}
result: if a claim is true (in a formal model), does the CoE audit eventually
certify it?
This i... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,540 | 385 | null | null | null | null | null |
314021c90011 | \begin{theorem}[CoE-to-$\Lambda$ axis mapping]
\label{thm:coe-axis-map}
The CoE claim taxonomy maps bijectively onto $\Lambda$-axes:
\begin{align*}
\mathrm{citation} &\mapsto \lambda_6\,(\text{evidence}),\\
\mathrm{numerical} &\mapsto \lambda_6\,(\text{evidence}) \wedge \lambda_1\,(\text{data}),\\
\mat... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,443 | 360 | null | null | null | null | null |
217aae5c8371 | \begin{table}[h!]
\centering\small
\caption{Beyond state-of-the-art: Chain-of-Evidence (\S\ref{sec:coe})}
\label{tab:bsota-coe}
\begin{tabular}{p{3.8cm}p{3.8cm}p{4.8cm}}
\hline
\textbf{Prior art} & \textbf{Gap} & \textbf{SZL result} \\
\hline
ScientistOne~\cite{Meng2026} & CoE defined empirically; no soundness proof & ... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,763 | 440 | null | null | null | null | null |
56bf255c4a67 | \novelty{No prior AI governance framework grounds its claims in a proof
assistant with a formally documented metatheory.
The SZL framework is the first AI governance substrate where the
\emph{trustworthiness of every governance claim} is reducible to the
type-theoretic soundness of the Lean~4 kernel -- which is itself ... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,872 | 468 | null | null | null | null | null |
a5009d9fb7e7 | \begin{theorem}[Axiom reduction optimality -- v14 to v16]
\label{thm:axiom-reduction}
The reduction from 24 axioms (v14) to 11 (v16) -- a 54\% decrease --
is, to the best of our search at the time of writing (2026-05-28;
search scope: Lean~4 / Mathlib4 repository, Lean Together 2025
proceedings, ArXiv \texttt{cs.LO} li... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,552 | 388 | null | null | null | null | null |
5cc13cf47164 | \begin{table}[h!]
\centering\small
\caption{Full axiom inventory (18 at ceiling, v18)}
\label{tab:axioms}
\begin{tabular}{llp{3.5cm}p{3.5cm}}
\hline
\textbf{ID} & \textbf{Lean name} & \textbf{Mathematical content} & \textbf{Discharge target} \\
\hline
A1 & \texttt{r1\_invariance} & $\Lambda$ invariant under R1 (axis pe... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 2,000 | 500 | null | null | null | null | null |
60924e3f7729 | 43 \\
& \texttt{klDivergence\_nonneg} & KL divergence non-negativity & \texttt{Lutar/DPOFeasibility.lean}:165 \\
& \texttt{MomentSubGaussian} & Sub-Gaussian moment hypothesis~\cite{Vershynin2018} & \texttt{Lutar/PACBayes.lean}:228 \\
& \texttt{canonicalReceipt} & Existence of canonical receipt map & \texttt{Lutar/Fe... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,896 | 474 | null | null | null | null | null |
30309f5617aa | \item \texttt{PACBayes.lean} line~265: \texttt{BoundedIntegrability}.
Integrability of $S \mapsto \exp(t(R-\hat{R}_S))$ on the
product measure space.
Discharge: \texttt{Integrable.mono} + \texttt{integrable\_const}
(Mathlib v4.13.0).
\textbf{Frontier significance:} Enables the un... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,801 | 450 | null | null | null | null | null |
174f52577813 | \frontier{Advances the \textbf{sorry-free AI governance} grand challenge:
the open problem of whether a production-grade AI governance system
can be formally verified without \emph{any} unjustified axioms or
proof gaps.
The SZL v18 corpus is the closest existing approach to a solution.}
\end{theorem}
\subsection{The G... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,988 | 497 | null | null | null | null | null |
abd297a2706e | \begin{table}[h!]
\centering\small
\caption{Beyond state-of-the-art: Lean kernel verifiability (\S\ref{sec:lean-kernel})}
\label{tab:bsota-lean}
\begin{tabular}{p{4cm}p{3.5cm}p{4.5cm}}
\hline
\textbf{Prior art} & \textbf{Gap} & \textbf{SZL result} \\
\hline
ISO 42001, NIST RMF & Prose requirements; no formal proof & Th... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,512 | 378 | null | null | null | null | null |
9afeceaf4a63 | \begin{table}[h!]
\centering\small
\caption{Open-frontier map: which problems does Chapter~\ref{chap:math} advance?}
\label{tab:frontier-map}
\begin{tabular}{lp{5cm}p{5cm}}
\hline
\textbf{Section} & \textbf{Open frontier} & \textbf{SZL contribution} \\
\hline
\S\ref{sec:lambda-axis} & Axiomatisation of AI safety metric... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,924 | 481 | null | null | null | null | null |
f121cd5c4ff8 | \paragraph{The two hardest open problems from this chapter.}
\begin{enumerate}
\item \textbf{Axiom A11 discharge} (HLP transposition decomposition,
$n$-axis Schur-concavity): requires formalising the Birkhoff--von
Neumann theorem that every doubly-stochastic matrix is a convex
combination of p... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,131 | 282 | null | null | null | null | null |
6242abf8144b | \begin{table}[h!]
\centering\small
\caption{Notation used in Chapter~\ref{chap:math}}
\label{tab:notation}
\begin{tabular}{ll}
\hline
\textbf{Symbol} & \textbf{Meaning} \\
\hline
$\Lambda$, $\Lambda_k(x)$ & Governance vector; geometric-mean aggregator \\
$\mathcal{A}_k$ & Axes type: $\mathrm{Fin}\,k \to \mathbb{R}_{\ge... | thesis_v18/chapters/02_mathematical_foundations.tex | Thesis v18 — 02_mathematical_foundations | cortex | 1,407 | 351 | null | null | null | null | null |
581fad5a34cb | % ===========================================================================
% CHAPTER 3 -- RUNTIME SUBSTRATE
% SZL Ouroboros Thesis v18 | PhD-CS Author Lane
% Doctrine v6 -- governance-mathematical tone; no marketing prose.
% LaTeX packages assumed: amsmath, amsthm, amssymb, mathtools, bm,
% hyperref, biblatex, l... | thesis_v18/chapters/03_runtime_substrate.tex | Thesis v18 — 03_runtime_substrate | cortex | 1,776 | 444 | null | null | null | null | null |
968b3bb4920d | % ---------------------------------------------------------------------------
\section{Ouroboros Runtime Architecture}
\label{sec:ouroboros-arch}
% ---------------------------------------------------------------------------
\subsection{Design Philosophy}
\label{ssec:design-philosophy}
The Ouroboros runtime is an orch... | thesis_v18/chapters/03_runtime_substrate.tex | Thesis v18 — 03_runtime_substrate | cortex | 1,912 | 478 | null | null | null | null | null |
22deda7a10f8 | \begin{lstlisting}[language=Python, caption={Module registry (excerpt from
\texttt{OUROBOROS\_RUN\_ALL.py})}, label={lst:module-registry}]
_MODULE_FILES = [
"v14_lutar_calculus.py", # v14 -- Lutar Calculus / HUKLLA / DPI
"v15_knot_calculus.py", # v15 -- Knot Calculus / Catoni PAC-Bayes
"v16_fey... | thesis_v18/chapters/03_runtime_substrate.tex | Thesis v18 — 03_runtime_substrate | cortex | 2,443 | 610 | null | null | null | null | null |
e3672182de05 | The runner resolves modules via \texttt{\_write\_modules()}, which writes
each embedded module body to a temporary directory before loading it via
\texttt{importlib.util.spec\_from\_file\_location}. This architecture
provides isolation: no module can import symbols from a sibling module unless
both are in the temporar... | thesis_v18/chapters/03_runtime_substrate.tex | Thesis v18 — 03_runtime_substrate | cortex | 847 | 211 | null | null | null | null | null |
da6b08b8d85a | \begin{figure}[h]
\centering
\begin{tabular}{|l|l|l|}
\hline
\textbf{Module} & \textbf{v-track} & \textbf{Test count} \\
\hline
\texttt{v14\_lutar\_calculus} & v14 & 18 GREEN \\
\texttt{v15\_knot\_calculus} & v15 & 17 GREEN \\
\texttt{v16\_feynman\_gates} & v16 & 42 GREEN \\
\texttt{v17\... | thesis_v18/chapters/03_runtime_substrate.tex | Thesis v18 — 03_runtime_substrate | cortex | 1,671 | 417 | null | null | null | null | null |
1b7132baedbb | \begin{center}
\begin{tabular}{ll}
\textbf{DOI} & \textbf{Record} \\
\hline
\texttt{10.5281/zenodo.19944926} & Concept DOI (rolling latest $\to$ v18.0) \\
\texttt{10.5281/zenodo.20424992} & Ouroboros Thesis v14 \\
\texttt{10.5281/zenodo.20424995} & Ouroboros Thesis v15 \\
\texttt{10.5281/zenodo.20424996} & Ouroboros Th... | thesis_v18/chapters/03_runtime_substrate.tex | Thesis v18 — 03_runtime_substrate | cortex | 1,841 | 460 | null | null | null | null | null |
99126093c05c | \begin{center}
\begin{tabular}{lrrr}
\textbf{File} & \textbf{v18.19 audit (bytes)} & \textbf{v18.24 lock (bytes)} & \textbf{Delta} \\
\hline
\texttt{OUROBOROS\_REPLIT\_PAYLOAD.md} & 947,089 (925~KB) & 965,698 (943~KB) & $+$18,609 \\
\texttt{OUROBOROS\_RUN\_ALL.py} & 858,498 (838~KB) & 870,449 (850~KB) & $+$11,951 \\
\e... | thesis_v18/chapters/03_runtime_substrate.tex | Thesis v18 — 03_runtime_substrate | cortex | 1,766 | 441 | null | null | null | null | null |
056035de1e27 | This invariant is enforced by the Payload Custodian agent at each major
version boundary. A reconciliation audit in the Zoom-Out report identified
three payload blocks present in the \texttt{.md} but absent from
\texttt{\_MODULE\_FILES} (the runner itself as a convenience copy;
\texttt{cybersec\_palantir\_substrate.py... | thesis_v18/chapters/03_runtime_substrate.tex | Thesis v18 — 03_runtime_substrate | cortex | 1,498 | 374 | null | null | null | null | null |
4fc2ac6d2482 | The SZL graft-design corpus at
\texttt{/home/user/workspace/szl/closeout/szl\_*\_graft\_design.md}
holds 21 design documents as of 2026-05-28 (not 29 as misstated in prior
drafts of the task brief): \texttt{cedric\_mo}, \texttt{crowdstrike},
\texttt{cursor\_claude}, \texttt{dsa}, \texttt{dynatrace\_newrelic},
\texttt{e... | thesis_v18/chapters/03_runtime_substrate.tex | Thesis v18 — 03_runtime_substrate | cortex | 1,778 | 444 | null | null | null | null | null |
45dfc6f71153 | Doctrine v6: block if scan fails before checking size.
SZL innovation: lambda_score gate on payload delivery.
"""
import os
md_size = os.path.getsize(md_path)
py_size = os.path.getsize(py_path)
return {
"md_size": md_size,
"py_size": py_size,
"mode": "TWO-FILE" if max(md_... | thesis_v18/chapters/03_runtime_substrate.tex | Thesis v18 — 03_runtime_substrate | cortex | 2,000 | 500 | null | null | null | null | null |
4eb836531de4 | Each assertion in a module must satisfy the \emph{GREEN gate invariant}:
\begin{definition}[GREEN Gate Invariant]
\label{def:green-gate}
A module \(m_i \in \mathcal{M}\) satisfies the GREEN gate if and only if
\texttt{main()} returns without raising any exception and the process
\texttt{sys.exit} code contribu... | thesis_v18/chapters/03_runtime_substrate.tex | Thesis v18 — 03_runtime_substrate | cortex | 1,936 | 484 | null | null | null | null | null |
2cfd9af51111 | % ---------------------------------------------------------------------------
\section{Receipt Chain Implementation}
\label{sec:receipt-chain-impl}
% ---------------------------------------------------------------------------
\subsection{Wheeler Primitives}
\label{ssec:wheeler-primitives}
The receipt chain is grounde... | thesis_v18/chapters/03_runtime_substrate.tex | Thesis v18 — 03_runtime_substrate | cortex | 1,982 | 495 | null | null | null | null | null |
de66f235df96 | Collision resistance of SHA-256 is encoded as Lean axiom A15
\texttt{CollisionResistance}~\cite{nist_fips_180_4}, which is classified
as a cryptographic assumption not expected to be discharged in Lean
(see Axiom~A15 \texttt{sha256\_collision\_resistant} in chapter~\ref{chap:math}, table~\ref{tab:axioms}).
\begin{lstl... | thesis_v18/chapters/03_runtime_substrate.tex | Thesis v18 — 03_runtime_substrate | cortex | 1,660 | 415 | null | null | null | null | null |
b5179ccdde98 | def emit(self, input_hash: str, output_hash: str,
lambda_score: float, witness_1: str,
witness_2: str) -> Receipt:
r = Receipt(
input_hash=input_hash, output_hash=output_hash,
lambda_score=lambda_score,
witness_1=witness_1, witness_2=witness_2,
... | thesis_v18/chapters/03_runtime_substrate.tex | Thesis v18 — 03_runtime_substrate | cortex | 1,812 | 453 | null | null | null | null | null |
062d3ce4d069 | \begin{center}
\begin{tabular}{cll}
\textbf{Axis} & \textbf{Name} & \textbf{Measurement proxy} \\
\hline
1 & Formal-verification coverage & Lean theorem density \\
2 & Zero-knowledge / privacy & DP budget consumption \\
3 & Differential privacy & \(\varepsilon\)-guarantee \\
4 & Certified robustness & IBP /... | thesis_v18/chapters/03_runtime_substrate.tex | Thesis v18 — 03_runtime_substrate | cortex | 1,930 | 482 | null | null | null | null | null |
eee2b2747acb | The runtime enforces two threshold gates on the emitted \(\Lambda\)-score:
\begin{definition}[Soft Gate]
\label{def:soft-gate}
A module action with \(\Lambda < \lambda_{\min}\) is flagged in the
receipt as \texttt{WARN}; the action is \emph{allowed} but the flag is
propagated to the Doctrine~v6 scanner.
\end{d... | thesis_v18/chapters/03_runtime_substrate.tex | Thesis v18 — 03_runtime_substrate | cortex | 1,698 | 424 | null | null | null | null | null |
0307ef4628e3 | def lambda_gate(lam: float, module_name: str) -> str:
"""Apply threshold gates; return 'PASS', 'WARN', or 'BLOCK'."""
if lam >= LAMBDA_MIN:
return "PASS"
if lam >= LAMBDA_CRIT:
return "WARN"
raise RuntimeError(
f"LAMBDA HARD-GATE: {module_name} Lambda={lam:.4f} "
f"< {LAM... | thesis_v18/chapters/03_runtime_substrate.tex | Thesis v18 — 03_runtime_substrate | cortex | 1,857 | 464 | null | null | null | null | null |
8539f25fee0a | \[
\mathrm{att}_i(a) = \begin{cases}
\texttt{APPROVE}(a, \Lambda_i) & \text{if } \Lambda_i \geq \lambda_{\min}, \\
\texttt{REJECT}(a, \Lambda_i) & \text{otherwise.}
\end{cases}
\]
The action is approved if and only if both witnesses approve:
\[
\mathrm{verdict}(a) = \texttt{APPROVE} \iff
\mathrm{att}_... | thesis_v18/chapters/03_runtime_substrate.tex | Thesis v18 — 03_runtime_substrate | cortex | 1,973 | 493 | null | null | null | null | null |
858fd8a056f7 | \begin{lstlisting}[language=Python, caption={Dual-witness emission},
label={lst:dual-witness}]
from dataclasses import dataclass
from typing import Tuple
@dataclass
class WitnessAttestation:
"""Single witness attestation for a proposed agent action.
Lean correspondent: Lutar.TwoWitness (lutar-lean/Lutar/TwoWitn... | thesis_v18/chapters/03_runtime_substrate.tex | Thesis v18 — 03_runtime_substrate | cortex | 1,609 | 402 | null | null | null | null | null |
79b901a1549e | The \texttt{cursor\_claude\_substrate.py} module (v18.18) extends the
dual-witness pattern to the level of \emph{agentic IDE composer actions}.
The class \texttt{composer\_receipt\_chain\_total\_order} imposes a strict
total order on all Cursor Composer agent actions, ensuring that no two
concurrent edits can produce a... | thesis_v18/chapters/03_runtime_substrate.tex | Thesis v18 — 03_runtime_substrate | cortex | 1,786 | 446 | null | null | null | null | null |
7af64f39a87c | \begin{lstlisting}[language=bash, caption={Doctrine~v6 scanner invocation},
label={lst:doctrine-cli}]
# Scan all substrate files; exit 0 iff clean
DOCTRINE_V6_SALT=$SECRET_SALT \
node tools/doctrine-v6-scan.js --glob "**/*_substrate.py" \
--ban-list doctrine_v6_banlist.json \
--output doctrine_scan_report.json
... | thesis_v18/chapters/03_runtime_substrate.tex | Thesis v18 — 03_runtime_substrate | cortex | 1,952 | 488 | null | null | null | null | null |
64789559ebb7 | The Ouroboros provenance system uses Zenodo's two-tier DOI model:
\begin{enumerate}
\item \textbf{Concept DOI} (\texttt{10.5281/zenodo.19944926}): A
``rolling'' DOI that always resolves to the latest version. Cited in
module headers as the universal anchor.
\item \textbf{Version DOIs}: Seven frozen per-ve... | thesis_v18/chapters/03_runtime_substrate.tex | Thesis v18 — 03_runtime_substrate | cortex | 1,899 | 474 | null | null | null | null | null |
End of preview.
SZLHOLDINGS/rag-corpus-v1 — Agentic-RAG corpus + per-organ FAISS indexes
Doctrine v10/v11. Embedding model: BAAI/bge-base-en-v1.5 (768-dim). Built by the agentic-RAG SHIP directive (390_AGENTIC_RAG_FAISS_PER_SPACE).
Contents
corpus.jsonl— 762 chunks, each~512 tokenswith fieldschunk_id, text, source, title, organ_tag, n_chars, approx_tokens.indexes/<organ>.faiss— FAISSIndexFlatIPover L2-normalized BGE embeddings (inner product == cosine similarity).indexes/<organ>.ids.json— FAISS row -> chunk_id map.indexes/manifest.json— model/dim/per-organ vector counts.
Per-organ index vector counts
{ "cortex": 679, "immune": 12, "receipt": 16, "gate": 63, "nervous": 4, "all": 762 }
all.faiss = the full corpus (rosie/nervous inherits everything). Each <organ>.faiss
contains chunks tagged that organ PLUS cross-cutting all-tagged chunks.
Sources
Thesis v18 chapters · szl-cookbook recipes (README + SKILL) · LUTAR_EVIDENCE.md · every Lean theorem/lemma in lutar-lean Lutar/ (name + statement + status) · Doctrine v10 + v11 (locked) · Frontier corpus (Pacha-Λ, Khipu-Bekenstein, Yachay-Khipu Operator, Willow-Λ) · 4 founder LinkedIn public posts · szl-trust E4 governed-loop run (12 receipts).
Honesty (Doctrine v10/v11)
LLM responses cite chunk IDs. Λ-receipt signature field is a PLACEHOLDER
(Sigstore CI signing not yet wired). ADDITIVE only.
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