From b305bdbcb1cc5b0abb428f6310772cc03d84e3c9 Mon Sep 17 00:00:00 2001 From: mrwulf Date: Fri, 17 Jul 2026 09:39:04 +0200 Subject: [PATCH] =?UTF-8?q?paper=20v0.3:=20the=20reinvention=20=E2=80=94?= =?UTF-8?q?=20accountable=20distribution=20of=20machine-checked=20evidence?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Executes the approved reinvention outline, using the round-11 GPT-5.6 draft as base material; the operator remains the author of record and this pass is the authorial fact-check + completion of that draft. New title: 'Accountable Distribution of Machine-Checked Correctness Evidence: A Transparency Model and the Lean Transparency Log' (16 pp). Old 19-page system report archived byte-identical as v0.2 (paper/ltl-v0.2.{tex,pdf}, served at /paper/v0.2; v0.1 unchanged). Every factual claim in the draft was verified against the estate before adoption: 222 inventoried constants + 61 reviewed cones (README:36), all four fidelity counts, the gap-14 lied-size witness reproduced empirically (deployed verify_consistency(1,3,R2,R3,P)=True while the recursive model rejects; honest 2->3 True/True), all four apex theorem names greped from the dalek repo, the entry-13 scope block now quoted VERBATIM (was silently trimmed), the new klaus2026 citation confirmed real via the arXiv API (author order corrected to Klaus, Conejero, Tolmach), remaining 20 bibitems byte-identical to the F10-verified set. Author corrections beyond the draft: 'opaque SHA-256 function' -> uninterpreted/boundary AXIOM (matches axiom sha256 : List UInt8 -> Hash); STH field list now matches the deployed head (adds type tag); lied-size mechanism sentence from the gap ledger; six-published-heads (sizes 8-13) mirror honesty; consumers subsection (warden + Swiss Post family-level negative) per outline item 7; optimistic-accountability related-work paragraph per outline item 8; fifteen-gap ledger pointer per outline item 9; verify.py fail-closed tie-ins in artifact availability and appendix C; wired the six uncited bibitems (lean4, pnueli, eddsa, rfc8032, edwards+twisted, easycrypt); certificate listing gains the deployed 'diagnostics' field. Build: 16 pages, 0 overfull, 0 undefined. web.py: /paper/v0.2 route + loader. webdocs: paper card rewritten for v0.3 with both archived versions linked. Suite 115 green. 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The paper

-
The Lean Transparency Log: Distributing -Kernel-Checked Correctness Evidence for Deployed Ed25519 Implementations -(PDF, 19 pages, revised) — the trust model with an explicit malicious-operator adversary, -security proofs for every consumer-facing claim (inclusion soundness as an explicit -SHA-256-collision extractor, pin-store safety with transferable equivocation evidence, -verdict integrity), the self-referential signing loop, the live deployment with -its retained failure leaves, and appendices with the leaf schema, the full ~25-line -consumer verifier, and the verbatim per-fork axiom boundaries. -Previous version: v0.1 (4 pages).
+
Accountable Distribution of Machine-Checked +Correctness Evidence: A Transparency Model and the Lean Transparency Log +(PDF, 16 pages, v0.3) — the trust decomposition (expensive verification produces an +observation; transparency makes the observation accountable; consumer-local policy decides +acceptance), collision-extracting soundness for inclusion and consistency, the policy +boundary where operator labels can veto but never grant acceptance, the live thirteen-leaf +deployment whose entry 13 attests the accumulator's own mechanized model, and the measured +model/deployment seam (3,867 one-sided lied-size divergences) reported as a result rather +than hidden. +Previous versions: v0.2 (19 pages, the +system report) · v0.1 (4 pages).

Log heads are signed offline; this service is read-only and holds no key material. Provider tooling, agent tooling, and the full course (12 Jupyter

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The consumer accepts $C$ between signed heads $(n_0, r_0)$ and +$(n_1, r_1)$ iff $n_0 = 0$, or $\ConsRec(n_0, n_1, C, \top, r_0) = +(r_0, r_1)$. We verified that this recursive form agrees with the deployed +iterative RFC~9162 verifier by \emph{exhaustive} differential testing over +every pinned/current size pair $1 \le n_0 \le n_1 \le 256$, each with the +honest proof and four adversarial mutations (wrong old root, wrong new +root, truncated and padded proofs): $164{,}224$ verifier invocations, +full agreement. The inclusion verifier of Appendix~\ref{app:verifier} was +checked the same way ($164{,}479$ invocations over all $m < n \le 256$). + +The operator signs tree heads $(n, \MTH(D), t)$ with Ed25519; a +\emph{receipt} for a leaf is its index, its sibling path, and a signed +head. The signed payload is not the bare triple but the canonical JSON +serialization (sorted keys, fixed separators, UTF-8---injective on the +field set) of the head record, which additionally carries a protocol +version tag (\texttt{pacta.transparency.signed\_tree\_head.v1}) and the +log identity; +a head signature therefore transfers neither across logs nor across +protocol versions. + +\subsection{The consumer pin store}\label{sec:pinstore} + +Each consumer maintains a local pin $(n_{\mathrm{pin}}, r_{\mathrm{pin}})$, +updated by the following state machine on receiving a validly signed head +$(n', r')$: +\begin{itemize}[itemsep=1pt] +\item $n' = n_{\mathrm{pin}}$: accept iff $r' = r_{\mathrm{pin}}$; a + mismatch is reported as \emph{equivocation}, the pair of signed heads is + retained as evidence, and the state is poisoned (unrecoverable). +\item $n' > n_{\mathrm{pin}}$: accept iff a consistency proof from + $(n_{\mathrm{pin}}, r_{\mathrm{pin}})$ to $(n', r')$ verifies; then update + the pin. +\item $n' < n_{\mathrm{pin}}$: reject (rollback). +\end{itemize} +A freshness policy bounds head age; freshness, however, is an +availability policy, not an append-only property---the construction +detects rollback relative to a persisted pin, but does not prove that a +consumer sees the newest issued head (an operator can re-issue fresh +timestamps over a frozen tree). The full log is also published as a git +repository: one file per leaf, plus the signed head history since +publication began (heads signed before the mirror existed were not +retained). Any cloner can therefore recompute every prefix root from the +public leaves and check every published head against its prefix root and +signature without consistency proofs---a low-infrastructure witness +mechanism~\cite{ct2}; a standalone ${\approx}150$-line standard-library +verifier ships in the mirror. + +\section{Security analysis}\label{sec:security} + +This section proves the claims G1--G3 of \S\ref{sec:model:goals}. The +statements are not deep---inclusion and consistency security for RFC +6962/9162 trees is folklore, and was treated formally by Dowling et +al.~\cite{dghs}---but writing them out for \emph{this} system serves two +purposes: it pins down exactly which assumption carries which consumer-facing +claim, and it produces statements in a form ready for mechanization in Lean +(\S\ref{sec:next}), where they will re-enter the log as leaves. + +We write $\Root(v, m, n, P)$ for the consumer's root reconstruction: it is +defined by $\Root(v, m, 1, [\,]) = v$ and, for $n > 1$ with $k$ the largest +power of two below $n$ and $P = P' \| [s]$, +\[ +\Root(v, m, n, P) = +\begin{cases} +\hnode\bigl(\Root(v, m, k, P'),\, s\bigr) & m < k,\\ +\hnode\bigl(s,\, \Root(v, m-k, n-k, P')\bigr) & m \ge k, +\end{cases} +\] +rejecting on any length mismatch. The consumer accepts a receipt +$(d, m, P)$ against a head $(n, r)$ iff $m < n$ and +$\Root(\hleaf(d), m, n, P) = r$. + +\begin{lemma}[Domain separation]\label{lem:domsep} +No leaf preimage equals a node preimage as a byte string: for all $d, x, y$, +$\texttt{0x00} \| d \neq \texttt{0x01} \| x \| y$. +\end{lemma} +\begin{proof} +The first byte differs. +\end{proof} + +Lemma~\ref{lem:domsep} forecloses the classic cross-type confusion in which +an adversary presents an interior node's 64-byte child concatenation as a +``leaf'' (or vice versa) to move a value between levels of the +tree~\cite{crosby,dghs}; it guarantees that whenever a leaf preimage and +a node preimage are compared, they already differ as strings, so equal +hash values across the two types constitute a collision. + +\begin{theorem}[Inclusion completeness]\label{thm:complete} +For every non-empty leaf list $D$ with $|D| = n$ and every $m < n$, +\[ +\Root\bigl(\hleaf(D[m]),\, m,\, n,\, \Path(m, D)\bigr) = \MTH(D). +\] +\end{theorem} +\begin{proof} +Structural induction on $n$. For $n = 1$: $\Path(0, [d]) = [\,]$ and +$\Root(\hleaf(d), 0, 1, [\,]) = \hleaf(d) = \MTH([d])$. For $n > 1$ with +split point $k$, suppose $m < k$ (the case $m \ge k$ is symmetric). Then +$\Path(m, D) = \Path(m, D[0{:}k]) \,\|\, [\MTH(D[k{:}n])]$, and by the +induction hypothesis +\[ +\Root\bigl(\hleaf(D[m]),\, m,\, k,\, \Path(m, D[0{:}k])\bigr) + = \MTH(D[0{:}k]), +\] +so the outer step yields +$\hnode(\MTH(D[0{:}k]), \MTH(D[k{:}n])) = \MTH(D)$. +\end{proof} + +Both soundness theorems below rest on a single collision-extraction fact, +which we isolate first. Fix the honest Merkle tree $T$ of a leaf list $D$. +A \emph{hash-fold over $T$} is a computation shaped by a connected +sub-tree $S$ of $T$ containing $T$'s root: at every internal node of $T$ +lying in $S$ it emits $\hnode$ of its two children's values; each child +lying outside $S$ is an \emph{input}, consumed as an opaque value; at +every leaf of $T$ lying in $S$ it emits $\hleaf$ of an input leaf value. +All inputs may be adversarial; only the shape is $T$'s. Three +instantiations recur below: the inclusion reconstruction +$\Root(\hleaf(\cdot), m, n, \cdot)$ ($S$ is the root path of leaf $m$; +the consumed inputs are the path's siblings); the new-root component of +the consistency verifier $\ConsRec$ (\S\ref{sec:tree}) ($S$ reaches down +to the perfect subtrees covering $[0, n_0)$; the consumed inputs are the +proof nodes and, on the leftmost spine, the pinned root); and the honest +computation of $\MTH(D')$ for any $D'$ with $|D'| = |D|$ ($S$ is all of +$T$; the inputs are the leaves of $D'$). + +\begin{lemma}[Root binding]\label{lem:bind} +Let $F$ be a hash-fold over the honest Merkle tree $T$ of a leaf list $D$, +and suppose $F$'s output equals $\MTH(D)$. Then either (i)~at some node of +$S$, $F$'s hash argument differs from $T$'s while the two hash values +agree---an explicit SHA-256 collision---or (ii)~$F$'s computation +coincides with $T$ node-for-node: every value $F$ emits, \emph{every +input it consumes}, and every leaf input it takes equals, respectively, +the corresponding node value of $T$ and the corresponding leaf of $D$. +\end{lemma} +\begin{proof} +Top-down induction on $S$, maintaining at each visited node the invariant +that $F$'s value there equals $T$'s. At the root both equal $\MTH(D)$ by +hypothesis. At an internal node of $S$ where the invariant holds, both +values are $\hnode$ of an argument pair (65-byte preimages); if the pairs +differ we are in case (i); if they coincide, each child's value is +pinned: a child inside $S$ inherits the invariant and we recurse, while a +child outside $S$ is a consumed input now known to equal $T$'s node value +there---no descent needed. At a leaf of $S$ the invariant reads +$\hleaf(d') = \hleaf(D[j])$: either $d' = D[j]$, or the two leaf preimages +differ and we are in case (i). If case (i) never fires, the accumulated +equalities at every node of $S$ are exactly claim (ii). Because $F$'s +shape is $T$'s, every comparison above is leaf-to-leaf or node-to-node; +Lemma~\ref{lem:domsep} additionally ensures that even a cross-type value +coincidence would be a collision of distinct strings, which matters in +the deployed protocol, where the same hash function commits leaves and +nodes across trees of attacker-influenced sizes~\cite{crosby,dghs}. +\end{proof} + +\begin{theorem}[Inclusion soundness: position binding]\label{thm:sound} +There is an explicit algorithm $\mathcal{E}$ (running in time $O(n)$ hash +evaluations) such that: whenever an adversary outputs a leaf list $D$ with +$|D| = n$, an index $m < n$, a leaf $d \neq D[m]$, and a path $P$ with +$\Root(\hleaf(d), m, n, P) = \MTH(D)$, $\mathcal{E}(D, m, d, P)$ outputs a +SHA-256 collision. +\end{theorem} +\begin{proof} +$F = \Root(\hleaf(d), m, n, \cdot)$ applied to $P$ is a hash-fold over the +honest tree $T_D$ whose sub-tree $S$ is the root path of leaf $m$, with +consumed inputs the entries of $P$ and leaf input $d$; by hypothesis its +output is $\MTH(D)$. Apply Lemma~\ref{lem:bind}. Case (ii) includes the +claim that the leaf input equals $D[m]$, contradicting $d \neq D[m]$; so +case (i) fires. $\mathcal{E}$ recomputes $T_D$ ($O(n)$ hashes), replays +the fold to locate the disagreeing pair, and outputs it. +\end{proof} + +\begin{remark} +Both soundness statements are unconditional in the same sense: they do not +assert forgery is infeasible, they \emph{construct} a SHA-256 collision +from any successful forgery, so append-only and position security are +\emph{precisely} ``SHA-256 is collision resistant''---no more, no less. The +two theorems share Lemma~\ref{lem:bind}, the only place hashing is reasoned +about; this factoring is deliberate, as Lemma~\ref{lem:bind} is exactly +what the Lean mechanization of \S\ref{sec:next} will carry, with collision +resistance entering only as a documented boundary axiom, audited by the log +like the SHA-512 oracle in the Ed25519 tiers. +\end{remark} + +\begin{theorem}[Consistency soundness]\label{thm:consistency} +There is an explicit algorithm $\mathcal{E}'$, running in $O(n_1)$ hash +evaluations, such that: whenever an adversary outputs leaf lists $D_0, D_1$ +with $|D_0| = n_0 \le n_1 = |D_1|$ and $D_0 \neq D_1[0{:}n_0]$, together +with a proof $C$ that the consumer's verifier of \S\ref{sec:tree} accepts, +i.e.\ $\ConsRec(n_0, n_1, C, \top, \MTH(D_0)) = (\MTH(D_0), \MTH(D_1))$, +$\mathcal{E}'(D_0, D_1, C)$ outputs a SHA-256 collision. +\end{theorem} +\begin{proof} +$\ConsRec$ returns a pair; acceptance equates its second component with +$\MTH(D_1)$ and its first with $\MTH(D_0)$. Reading the four cases, the +second component emits $\hnode$ at every split it traverses of the +size-$n_1$ tree and bottoms out on consumed values---it is a hash-fold +over the honest tree $T_1$, with consumed inputs the proof nodes and, on +the leftmost spine, the pinned root---while the first component reuses a +sub-list of those same values, namely the ones covering the index range +$[0, n_0)$, and folds \emph{only} those. We use the two components +differently, so the delicate first component never enters the lemma. + +\emph{Step 1 (the transcript values are genuine).} Apply +Lemma~\ref{lem:bind} to the second component against $T_1$. Either it hits +case (i)---output that collision---or (case ii) every value it emitted and +every input it consumed---each proof node, and the pinned root where the +fold bottoms out on it---equals the corresponding node of $T_1$. Assume +the latter; the consumed values are now known to be genuine nodes of the +honest tree $T_1$. + +\emph{Step 2 (the prefix roots collide).} The consumed values covering +$[0, n_0)$ sit at the canonical RFC~9162 decomposition of that range into +maximal perfect subtrees of $T_1$; by Step~1 they are genuine, so folding +them---which is exactly what the first component does (degenerately, when +the old tree is itself a perfect subtree of $T_1$, the ``fold'' is the +consumed pinned root alone)---yields the root of $D_1[0{:}n_0]$, +i.e.\ the first component equals $\MTH(D_1[0{:}n_0])$. But acceptance also +equates the first component with $\MTH(D_0)$. Hence +$\MTH(D_0) = \MTH(D_1[0{:}n_0])$ while $D_0 \neq D_1[0{:}n_0]$. + +\emph{Step 3 (descend).} Since $|D_0| = |D_1[0{:}n_0]| = n_0$, the two +honest trees have identical shape, so the honest computation of +$\MTH(D_1[0{:}n_0])$ is a hash-fold over $T_{D_0}$ ($S$ the whole tree; +leaf inputs the leaves of +$D_1[0{:}n_0]$). Its output is $\MTH(D_1[0{:}n_0]) = \MTH(D_0)$ by Step~2, +so Lemma~\ref{lem:bind} applies with $D = D_0$. Case (ii) would force the +leaf inputs to equal $D_0$, i.e.\ $D_1[0{:}n_0] = D_0$, contradicting the +premise; so case (i) fires---an explicit collision. $\mathcal{E}'$ outputs +whichever collision was found; recomputing $T_0$ and $T_1$, it runs in +$O(n_1)$ hash evaluations. +\end{proof} + +\begin{proposition}[Pin-store safety]\label{prop:pin} +Assume Ed25519 EUF-CMA security for the head-signing key and consider the +state machine of \S\ref{sec:pinstore}. Then, except with the probability of +a signature forgery or a SHA-256 collision: +\begin{enumerate}[itemsep=1pt] +\item (\emph{Monotonicity}) If a consumer's pin evolves through states +$(n_1, r_1), \dots, (n_t, r_t)$, then $n_1 \le \dots \le n_t$, and for any +leaf lists $D_i$ the operator can exhibit with $\MTH(D_i) = r_i$, +$|D_i| = n_i$, each $D_i$ is a prefix of $D_{i+1}$. +\item (\emph{Fork evidence}) If two consumers with the same pinned key ever +hold accepted heads $(n, r)$ and $(n, r')$ with $r \neq r'$, the pair of +signed heads is transferable, publicly verifiable evidence that the key +holder signed two conflicting views. +\end{enumerate} +\end{proposition} +\begin{proof} +(1) The machine accepts a larger size only with a verified consistency +proof, so by Theorem~\ref{thm:consistency} any exhibited leaf lists are +prefix-ordered unless a collision is found; rollback is rejected +syntactically. (2) Both heads carry valid signatures under the pinned key; +under EUF-CMA, both were produced by the key holder, and $r \neq r'$ at +equal size is precisely a split view. The evidence is transferable because +verification requires only the public key. +\end{proof} + +\begin{proposition}[Verdict integrity]\label{prop:verdict} +Fix a consumer with local allowed-set table $\allowed(\cdot)$. For every +attestation leaf $a$ and certificate $c$ in it, the consumer's +\emph{cleanliness verdict} is +the predicate $\clean(c) \Leftrightarrow \obs_a(c) = \allowed(c)$, a +function of the leaf's observed cones and the consumer's table only; the +operator's embedded pass/fail labels are not an input to it. The +consumer's \emph{acceptance policy} consults those labels at most +negatively: no operator assertion can upgrade any verdict or acceptance. +\end{proposition} +\begin{proof} +By construction of the consumer tooling: the verdict function takes +$(\obs_a, \allowed)$ and ignores the label fields in every branch; a +certificate lacking an observed cone is mapped to \textsf{unverifiable}, +not to a verdict. The acceptance policy applies the operator's +proven/failed \texttt{status} label only as a veto---a certificate the +operator does not itself mark proven can never count---and a veto cannot +upgrade; hence labels can deny but never grant. +\end{proof} + +\paragraph{What is \emph{not} proven.} Propositions~\ref{prop:pin} and +\ref{prop:verdict} together with Theorems~\ref{thm:complete}--% +\ref{thm:consistency} discharge G1--G3. They do not---and cannot---exclude +an operator who fabricates observations (\S\ref{sec:model:residual}), and +they say nothing about the mathematical content of the attested corpus, +whose guarantees rest on the Lean kernel and the assumption set enumerated +in \S\ref{sec:deployment}. The division of labor is deliberate: the +cryptographic layer makes the operator's claims \emph{exact, immutable, and +attributable}; the deductive layer is what makes them \emph{true}. +Table~\ref{tab:claims} decomposes the end-to-end chain: each consumer +conclusion, the mechanism that establishes it, and the assumption that +remains. The architecture does not pretend to eliminate trust; it +decomposes trust into independently visible components---including two +rows it deliberately does \emph{not} establish. + +\begin{table}[t] +\centering\small +\begin{tabular}{@{}p{0.31\textwidth}p{0.28\textwidth}p{0.33\textwidth}@{}} +\toprule +consumer conclusion & established by & remaining assumption \\ +\midrule +leaf bytes sit at index $m$ under head $h$ & inclusion proof (Thm~\ref{thm:sound}) & SHA-256 collision resistance; authentic head \\ +head was authorized under the log key & Ed25519 verification & correct key pin; EUF-CMA \\ +new local head extends the old one & consistency proof (Thm~\ref{thm:consistency}) & SHA-256 collision resistance \\ +equal-size heads conflict: equivocation & two valid signatures, unequal roots (Prop~\ref{prop:pin}) & correct key pin \\ +observed cone matches local policy & set equality (Prop~\ref{prop:verdict}) & semantic identity of the named declarations at the pinned commit \\ +the kernel produced the observation & operator replay attestation & replay-pipeline honesty, or independent replay (\S\ref{sec:model:residual}) \\ +deployed binary matches verified source & \emph{not established} & reproducible build / binary attestation \\ +signing binary is the claimed implementation & \emph{not established} & execution provenance (\S\ref{sec:selfref}) \\ +\bottomrule +\end{tabular} +\caption{The end-to-end claim matrix. Every consumer conclusion, what +establishes it, and what remains assumed. The last two rows are +deliberate non-claims (\S\ref{sec:intro}, \S\ref{sec:limitations}).} +\label{tab:claims} +\end{table} + +\section{The self-referential signing loop}\label{sec:selfref} + +Tree heads are Ed25519 signatures, and this creates an opportunity for +coherence: the log contains correctness certificates for an Ed25519 +implementation. The LTL's heads are therefore signed by a binary built from +the pinned source tree of exactly the implementation attested in the log +(serial backend pinned, matching the verified extraction), and---before +signing---the operator runs the same Merkle inclusion verification a +consumer runs, on the newest leaf attesting the signing implementation, +against the tree about to be signed. The verdict is embedded in the +signature block: +\begin{quote}\ttfamily\small +signing\_backend: verified-dalek-serial\\ +signing\_library\_source\_commit: aa0f6ab...\\ +signing\_library\_leaf\_index: 8\\ +signing\_library\_certificates\_proven: 16/16\\ +self\_inclusion: verified +\end{quote} +(These provenance fields ride alongside the signature as operator-provided +context; they are not part of the signed payload, and a consumer relies on +none of them---the acyclic chain below rests only on the signature and the +leaf's inclusion.) +The signature vouches for the tree; the tree vouches for the code that +produced the signature; and the two vouchings are different proof modalities +(cryptographic and deductive), so the loop is self-referential without being +circular. Concretely, a consumer's verification order is a directed acyclic +chain, no step trusting its own output: pin the operator key (assumed, once) +$\to$ check the head signature (EUF-CMA) $\to$ verify the signing library's +leaf is included in that head (hashes only, no signature) $\to$ optionally +rebuild that library from its pinned commit and re-check its certificates +(Lean kernel). The self-reference is only that the code producing signatures +also \emph{appears as a subject} in the log; no check consumes the result it +is establishing. The self-check always references the \emph{newest} leaf +attesting the signing library: after the re-attestation of +\S\ref{sec:deployment}, the referenced index advanced from~4 to~8 +automatically, the loop re-anchoring itself to the fresh attestation +without operator intervention. + +\paragraph{The honest extent of this claim.} The Lean certificates cover +the \emph{verification} path of the library (the theorems' subject is the +extraction image of that path); the \emph{signing} path is not covered by +any certificate and is declared trusted base. The deployed operator +\emph{enforces and records} the invariant that the signing binary is +built from the attested artifact rather than an unrelated third +implementation; a consumer can check that the claimed source is attested +in the signed tree, but---an Ed25519 signature reveals nothing about the +program that produced it---cannot independently establish that this +binary produced a given signature. Establishing that would require +reproducible builds or execution attestation +(\S\ref{sec:limitations}). Signature verification +on consumer machines can optionally run through the same certified-source +binary, with the backend that actually ran recorded in every result and a +fail-closed policy flag available. First-append bootstrapping is handled +honestly: heads signed before the signing library's attestation enters the +log record \texttt{self\_inclusion: library\_not\_in\_log}. + +\section{Deployment and evidence}\label{sec:deployment} + +The LTL is deployed\footnote{Service: \url{https://ltl.zkdefi.org} +(read-only HTTP API and documentation). Mirror: +\url{https://github.com/saymrwulf/lean-transparency-log}. Operator and +consumer tooling: \url{https://github.com/saymrwulf/proof-aware-crypto-tooling-agent}. +The underlying proof corpora are in the +\texttt{saymrwulf/*-ed25519-verified} repositories; every claim in this +paper is re-checkable from these artifacts.} with twelve leaves, +produced by three full replay runs (one attestation per fork per run; +58--64 Lean files and ${\approx}1{,}800$\,s per fork, under hard memory +caps and core pinning; the per-fork duration is corroborated by the +inter-leaf \texttt{issued\_at} spacing in the published log, whose +uninterrupted within-run gaps fall between 29m35s and 30m40s). Each +successful run reports 16/16 certificates +proven with boundary-exact cones, pinned to exact commits. The three runs +correspond to three states of the world, and their coexistence in one +append-only ledger is the point of the system: + +\begin{itemize}[itemsep=2pt] +\item \textbf{Leaves 0--3 (failed run).} The first run's audit step failed + on two defects in the operator tooling (a path issue and a parser that + mishandled Lean's line-wrapped axiom lists for the eleven-axiom cones). + The operator signed attestations \emph{recording the failure} rather + than suppressing the run. Both defects were fail-closed: valid proofs + were rejected, invalid ones never accepted. +\item \textbf{Leaves 4--7 (clean run).} After the fix, all four forks + attested 16/16 boundary-exact at that day's commits. +\item \textbf{Leaves 8--11 (clean run, new commits).} A subsequent + documentation-only rewrite of the subject repositories' histories + changed their commit hashes. Because a leaf pins an exact commit + (\S\ref{sec:leaves}), the operator re-ran the full corpus and appended + fresh attestations at the new commits rather than editing leaves 4--7. + That the proof \emph{files} survived the rewrite unchanged is + corroborated from the log itself: leaves 4--7 and 8--11 carry identical + certificate lists and identical observed axiom cones, re-checked by the + kernel at both commit generations. (The pre-rewrite trees themselves are + no longer distributed, so a direct tree diff is not among the public + artifacts.) +\end{itemize} + +\noindent This last event is a live exercise of the append-only +discipline (G2): a change that a naive operator would have hidden by +overwriting is instead absorbed by \emph{addition}, leaving a permanent, +publicly verifiable record that the subject histories changed and that +the mathematics survived the change. The ledger---four failure leaves and +eight success leaves across two commit generations---is a feature of the +trust model, not clutter to be pruned (Figure~\ref{fig:tree}). + +\begin{figure}[t] +\centering +\begin{tikzpicture}[ + every node/.style={font=\footnotesize}, + leaf/.style={draw, minimum width=0.62cm, minimum height=0.42cm, inner sep=1pt}, + fail/.style={leaf, draw=black!45, text=black!55, fill=black!7}, + ok/.style={leaf, draw=black!85, fill=black!3}, + node/.style={draw, circle, minimum size=0.34cm, inner sep=0pt, fill=black!4}, + edge/.style={draw=black!55}, xscale=0.92] + % leaves 0..11 + \foreach \i in {0,...,3} \node[fail] (l\i) at (\i,0) {\i}; + \foreach \i in {4,...,11} \node[ok] (l\i) at (\i,0) {\i}; + % exact RFC 9162 shape for n = 12: root splits 8 | 4 + \foreach \i/\a/\b in {0/0/1, 1/2/3, 2/4/5, 3/6/7, 4/8/9, 5/10/11} + \node[node] (m\i) at ({(\a+\b)/2},1.0) {}; + \node[node] (q0) at (1.5,1.95) {}; % leaves 0-3 + \node[node] (q1) at (5.5,1.95) {}; % leaves 4-7 + \node[node] (q2) at (9.5,1.95) {}; % leaves 8-11 + \node[node] (o0) at (3.5,2.9) {}; % leaves 0-7 + \node[node, minimum size=0.4cm] (root) at (6.5,3.85) {}; + \node[right=1pt of root, font=\small] {\ signed tree head $\;\sigma = \mathrm{Sig}(sk,(12,r,t))$}; + % edges + \foreach \i/\a/\b in {0/0/1, 1/2/3, 2/4/5, 3/6/7, 4/8/9, 5/10/11} + { \draw[edge] (l\a)--(m\i); \draw[edge] (l\b)--(m\i); } + \draw[edge] (m0)--(q0); \draw[edge] (m1)--(q0); + \draw[edge] (m2)--(q1); \draw[edge] (m3)--(q1); + \draw[edge] (m4)--(q2); \draw[edge] (m5)--(q2); + \draw[edge] (q0)--(o0); \draw[edge] (q1)--(o0); + \draw[edge] (o0)--(root); \draw[edge] (q2)--(root); + % brackets under leaf ranges + \draw[decorate,decoration={brace,mirror,raise=3pt}, black!45] + (l0.south west) -- (l3.south east) + node[midway,below=7pt, black!55]{run 1: failed audit}; + \draw[decorate,decoration={brace,mirror,raise=3pt}, black!70] + (l4.south west) -- (l7.south east) + node[midway,below=7pt]{run 2: clean, commits $g_1$}; + \draw[decorate,decoration={brace,mirror,raise=3pt}, black!70] + (l8.south west) -- (l11.south east) + node[midway,below=7pt]{run 3: clean, commits $g_2$}; +\end{tikzpicture} +\caption{The deployed twelve-leaf log. Grey leaves 0--3 record the first +run's audit failure (retained, not erased); leaves 4--7 and 8--11 are two +clean runs, at commit generations $g_1$ and $g_2$ across a subject-history +rewrite. The interior is the exact RFC~9162 shape of \S\ref{sec:tree} for +$n = 12$ (root split $8 \mid 4$; $r$ denotes the root value). Every value +in the figure is recomputable from the public leaves.} +\label{fig:tree} +\end{figure} + +\begin{table}[t] +\centering\small +\begin{tabular}{@{}lrrl@{}} +\toprule +fork & Lean files & apex cone (axioms, total) & SHA-512 in the boundary \\ +\midrule +upstream \texttt{dalek} & 64 & 11 & 3-call streaming (\texttt{new/update/finalize}) \\ +Solana (\texttt{anza}) & 58 & \phantom{0}7 & one \texttt{ed\_sigs.sha512\_hash3} \\ +RISC~Zero & 63 & \phantom{0}8 & one \texttt{verifying.sha512\_hash3} \\ +Betrusted & 63 & \phantom{0}8 & one \texttt{verifying.sha512\_hash3} \\ +\bottomrule +\end{tabular} +\caption{The four subject implementations. Each replay re-checks 16 +certificates in ${\approx}1{,}800$\,s under memory caps and core pinning. +The apex-cone count is the full allowed axiom set at the signature +tiers---Lean's three standard axioms plus the fork's enumerated oracle +boundary (Appendix~\ref{app:axioms}); it differs by fork because the +SHA-512 surface and the byte-accessor shape differ. Proof-script +divergence across forks is quantified in the portability paragraph below; +the pure-mathematics files are byte-identical across all four.} +\label{tab:forks} +\end{table} + +\paragraph{What a verified receipt establishes.} Under the assumptions +enumerated below, a consumer who verifies a receipt knows: \emph{the +operator whose key I pinned attests that the Lean certificates of repository +$X$ at commit $Y$ re-check, with per-certificate observed axiom cones as +included---and this statement is part of the log presented to every other +consumer.} Combined with local verdict re-derivation +(Proposition~\ref{prop:verdict}), this yields source-level assurance for the +pinned commit. It deliberately does \emph{not} establish: correctness of any +binary (consumers build from the pinned source; compilers are trusted base), +correctness of SHA-512 (an opaque oracle in the theorems), correctness of +the wire-format parsers (their outcomes are hypotheses of the signature +tiers), signing-side correctness, or side-channel properties. + +\paragraph{The assumption set, in full.} The Lean kernel and its three +axioms plus mathlib; faithfulness of the Charon/Aeneas +extraction~\cite{aeneas}; each fork's documented oracle boundary; operator +key custody and trust-on-first-use key distribution (mitigated by publishing +the key in two independent locations); collision resistance of SHA-256 for +the log (Theorems~\ref{thm:sound}, \ref{thm:consistency}); unforgeability +of Ed25519 for the heads (Proposition~\ref{prop:pin}); and the consumer's +own ${\approx}25$-line verifier (Appendix~\ref{app:verifier}). + +\paragraph{An observational by-product: proof portability.} Because the +four corpora prove the same theorems against four independent extractions, +the diff between proof files measures how portable proofs are across real +forks. Pure-mathematics files (e.g., a carry-telescope lemma file) are +byte-identical across all four; extraction-facing proof scripts diverge +sharply where the forks' code or the extractor's naming differs (e.g., 215 +changed lines for the byte-parser proofs on the two forks whose extraction +produces a closure-based loader; 121 lines for the signature-glue proofs on +the same-crate fork; 27 lines between the two structurally closest forks, +tracking one fork's \texttt{black\_box} optimization barrier and the +operation reordering it induces). Per-target +verification, in other words, is doing +measurable work exactly where the targets actually differ. + +\section{Limitations}\label{sec:limitations} + +The deployment is small (one operator, twelve leaves, four subject +repositories) and the operator is a single party; split-view defense +currently rests on consumer-side pinning (Proposition~\ref{prop:pin}) plus +the public git mirror rather than an independent witness network. Key +distribution is trust-on-first-use. The signing path of the dogfood binary +is unverified (declared, not proven). The residual trust of +\S\ref{sec:model:residual}---honesty of the operator's kernel +observations---is mitigated only by targeted independent replay, and +replayability presupposes retrievability: a leaf whose pinned commit is +no longer distributed (leaves 0--7 after the subject-history rewrite, +\S\ref{sec:deployment}) decays from a replayable claim to a historical +record, and consumers act on the newest, retrievable attestations. The corpus +itself stops at source-level assurance: reproducible builds and side-channel +evidence remain open, and ML-DSA slots in the head format are deliberately +recorded as unavailable rather than backed by an unverified implementation. + +\section{Next step: verifying the accumulator itself}\label{sec:next} + +The natural continuation applies the corpus's own discipline to the log's +cryptographic half. Theorems~\ref{thm:complete}--\ref{thm:consistency} and +Proposition~\ref{prop:pin} were stated so as to make their mechanization +direct; we expect the principal work to be specification alignment and +proof engineering rather than new cryptographic argument: (i) inclusion completeness +(Theorem~\ref{thm:complete}) is assumption-free; (ii) inclusion soundness +becomes the explicit extractor of Theorem~\ref{thm:sound}, with SHA-256 +collision resistance a documented boundary axiom audited exactly like the +SHA-512 oracle in the Ed25519 tiers; (iii) likewise consistency +(Theorem~\ref{thm:consistency}); (iv) domain separation +(Lemma~\ref{lem:domsep}) is a one-line lemma; and (v) total correctness of +the consumer's pin-store state machine (Proposition~\ref{prop:pin}). +Verified Merkle implementations in F*~\cite{evercrypt} and machine-checked +transparency-protocol analyses~\cite{cheval} show these proofs are well +within reach; the LTL-specific closure is where the certificates go: +\emph{into the log they defend, checked by the certified checker they +specify}, alongside a consumer policy flag requiring the certified verifier. +At that point both proving traditions in the composition run on certified +code, and the remaining trusted base is two hash assumptions, a compiler, an +extraction pipeline, and one key. + +\section*{Acknowledgments} + +The author designed the system, directed the verification effort, and is +solely accountable for every claim in this paper. Claude (Anthropic) was +used as an assistant in developing the proof corpora, tooling, and text, +and adversarial reviews by both Claude and GPT (OpenAI) shaped the final +manuscript; all +proofs, measurements, and claims have been reviewed by the author and are +independently re-checkable from the public artifacts and the referenced +check scripts. +% \authortodo{The sentence above must be true before you submit it. +% Review every proof in Section 6 line by line and re-run every number in +% Section 8 yourself.} + +\begin{thebibliography}{20} +\itemsep2pt + +\bibitem{ct1} B. Laurie, A. Langley, E. K\"asper. Certificate Transparency. +RFC 6962, 2013. + +\bibitem{ct2} B. Laurie, E. Messeri, R. Stradling. Certificate Transparency +Version 2.0. RFC 9162, 2021. + +\bibitem{crosby} S. A. Crosby, D. S. Wallach. Efficient Data Structures for +Tamper-Evident Logging. USENIX Security, pp. 317--334, 2009. + +\bibitem{dghs} B. Dowling, F. G\"unther, U. Herath, D. Stebila. 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Yang. +High-speed high-security signatures. J. Cryptographic Engineering 2(2): +77--89, 2012. + +\bibitem{rfc8032} S. Josefsson, I. Liusvaara. Edwards-Curve Digital +Signature Algorithm (EdDSA). RFC 8032, 2017. + +\bibitem{edwards} D. J. Bernstein, T. Lange. Faster addition and doubling on +elliptic curves. ASIACRYPT, LNCS 4833, pp. 29--50, 2007. + +\bibitem{twisted} D. J. Bernstein, P. Birkner, M. Joye, T. Lange, +C. Peters. Twisted Edwards curves. AFRICACRYPT, LNCS 5023, pp. 389--405, +2008. + +\bibitem{pnueli} A. Pnueli. The temporal logic of programs. IEEE FOCS, pp. +46--57, 1977. + +\end{thebibliography} + +\appendix + +\section{Leaf schema}\label{app:leaf} + +Each leaf is the canonical JSON serialization (sorted keys, no +insignificant whitespace, UTF-8) of an attestation. Below is leaf~8 of +the deployed log---the re-attestation of the upstream fork. The +16-certificate array is elided to its first (foundational) and last +(apex) entries; long values (hashes, timestamps, version strings, +paths) are shortened, and omitted fields are marked, with ellipses; and +fields are shown in logical rather than canonical (sorted-key) order +for readability. The +field names and values shown, and the axiom lists, are verbatim, and the +unelided leaf is one \texttt{jq} invocation away in the public mirror. +\begin{quote}\ttfamily\scriptsize +\{ "type": "pacta.attestation", "schema\_version": 1,\\ +\hspace*{0.6em}"attestation": \{\\ +\hspace*{1.2em}"provider": "local-pacta-provider",\\ +\hspace*{1.2em}"issued\_at": "2026-07-07T...Z",\\ +\hspace*{1.2em}"subject": \{ "component": "dalek-ed25519-verified",\\ +\hspace*{2.4em}"repo\_commit": "33fb8bb2311c70ead2e83c0...",\\ +\hspace*{2.4em}"repo\_url": ..., "verified\_backend": "serial/u64",\\ +\hspace*{2.4em}... \},\\ +\hspace*{1.2em}"environment": \{\\ +\hspace*{2.4em}"lean\_version": "Lean (version 4.30.0-rc2, ...)",\\ +\hspace*{2.4em}"lake\_version": ..., "env\_script": ...,\\ +\hspace*{2.4em}"lean\_project\_dir": ... \},\\ +\hspace*{1.2em}"machine\_protection": \{ "lean\_guard": ...,\\ +\hspace*{2.4em}"note": "All Lean compiles route through the\\ +\hspace*{2.4em}repo's lean-guard (memory cap, core pinning,\\ +\hspace*{2.4em}timeout, single-flight lock) ..." \},\\ +\hspace*{1.2em}"replay": \{ "checked\_files": 64, "failed\_files": [],\\ +\hspace*{2.4em}"check\_ok": true, "axiom\_ok": true, ... \},\\ +\hspace*{1.2em}"certificates": [\\ +\hspace*{2.4em}\{ "name": "CurveFieldProofs.fieldImplementation",\\ +\hspace*{3.0em}"status": "proven", "axiom\_status": "clean",\\ +\hspace*{3.0em}"observed\_axioms": ["propext",\\ +\hspace*{3.6em}"Classical.choice","Quot.sound"],\\ +\hspace*{3.0em}"expected\_axioms": [...], ... \},\\ +\hspace*{2.4em}... \; \emph{(14 certificates elided)} \; ...\\ +\hspace*{2.4em}\{ "name":\\ +\hspace*{3.0em}"CurveFieldProofs.verify\_accepts\_iff\_decompress",\\ +\hspace*{3.0em}"status": "proven", "axiom\_status": "clean",\\ +\hspace*{3.0em}"observed\_axioms": ["propext","Classical.choice",\\ +\hspace*{3.6em}"Quot.sound","ed25519.Signature","sha2.Sha512",\\ +\hspace*{3.6em}"verifying.sha512\_finalize\_bytes",\\ +\hspace*{3.6em}"verifying.sha512\_new","verifying.sha512\_update",\\ +\hspace*{3.6em}"ed25519.Signature.to\_bytes",\\ +\hspace*{3.6em}"signature.error.Error",\\ +\hspace*{3.6em}"signature.error.Error.new"], ... \} ],\\ +\hspace*{1.2em}"signature": \{ "scheme": "openssl-ed25519", ... \},\\ +\hspace*{1.2em}... \} \} +\end{quote} +The \texttt{observed\_axioms} field is the exact output of +\texttt{\#print axioms} for that theorem. Operator labels +(\texttt{replay.check\_ok}, per-certificate \texttt{status} and +\texttt{axiom\_status}) are recorded for the audit trail, but the +cleanliness verdict is $\obs = \allowed$ computed against the consumer's +own table in every case, with a missing cone mapped to +\textsf{unverifiable} (Proposition~\ref{prop:verdict}). The +\texttt{status} label is consulted only \emph{negatively}: a certificate +the operator itself does not mark proven can never count toward +acceptance, so labels can deny but never grant. + +\section{The consumer verifier}\label{app:verifier} + +The consumer-side inclusion check, in full (Python, standard library only); +this is the recursive form proved in \S\ref{sec:security} and is equivalent +to the iterative algorithm of RFC~9162 \S2.1.3.2. + +\begin{quote}\ttfamily\small +import hashlib\\[2pt] +def H(b): return hashlib.sha256(b).digest()\\ +def h\_leaf(d): return H(b'\textbackslash x00' + d)\\ +def h\_node(x, y): return H(b'\textbackslash x01' + x + y)\\[2pt] +def largest\_pow2\_below(n):\\ +\hspace*{1em}k = 1\\ +\hspace*{1em}while 2 * k < n: k *= 2\\ +\hspace*{1em}return k\\[2pt] +def root(v, m, n, path):\\ +\hspace*{1em}if n == 1:\\ +\hspace*{2em}if path: raise ValueError\\ +\hspace*{2em}return v\\ +\hspace*{1em}if not path: raise ValueError\\ +\hspace*{1em}*rest, s = path\\ +\hspace*{1em}k = largest\_pow2\_below(n)\\ +\hspace*{1em}if m < k:\\ +\hspace*{2em}return h\_node(root(v, m, k, rest), s)\\ +\hspace*{1em}return h\_node(s, root(v, m - k, n - k, rest))\\[2pt] +def verify\_inclusion(leaf, m, n, path, head\_root):\\ +\hspace*{1em}return m < n and root(h\_leaf(leaf), m, n, path) == head\_root +\end{quote} +Signature verification of the head (Ed25519) and the pin-store logic of +\S\ref{sec:pinstore} complete the consumer; the deployed +${\approx}150$-line standalone verifier in the mirror additionally checks +consistency proofs and recomputes prefix roots from the public leaves. + +\section{Allowed axiom sets}\label{app:axioms} + +Foundational certificates (12 of 16) must carry exactly Lean's three +standard axioms: +\begin{quote}\ttfamily\small +propext \quad Classical.choice \quad Quot.sound +\end{quote} +The four signature-tier certificates additionally carry a per-fork +enumerated boundary: an opaque SHA-512 oracle and opaque wire-format +types (the signature type, its byte accessors, and---where the fork's +API surfaces it---the error type). The +boundary is not identical across forks---it reflects each fork's actual +extracted surface---and auditing is exact against the fork's own set. The +three distinct boundaries in the deployed corpus, verbatim from the +repositories' check scripts, are as follows (the three standard axioms +above, plus): + +\smallskip +\noindent\textbf{Upstream \texttt{curve25519-dalek}} (11 axioms total; +this fork exposes SHA-512 as three streaming operations): +\begin{quote}\ttfamily\scriptsize +ed25519.Signature \quad sha2.Sha512\\ +verifying.sha512\_finalize\_bytes\\ +verifying.sha512\_new \quad verifying.sha512\_update\\ +ed25519.Signature.to\_bytes\\ +signature.error.Error \quad signature.error.Error.new +\end{quote} + +\noindent\textbf{RISC~Zero and Betrusted forks} (8 axioms total; +identical to each other---SHA-512 is a single \texttt{hash3} oracle): +\begin{quote}\ttfamily\scriptsize +ed25519.Signature \quad verifying.sha512\_hash3\\ +ed25519.Signature.to\_bytes\\ +signature.error.Error \quad signature.error.Error.new +\end{quote} + +\noindent\textbf{Solana (anza) fork} (7 axioms total; its own +\texttt{ed\_sigs} namespace, and \texttt{R}/\texttt{s} byte accessors +rather than a whole-signature encoder): +\begin{quote}\ttfamily\scriptsize +ed25519.Signature \quad ed\_sigs.sha512\_hash3\\ +ed25519.Signature.r\_bytes \quad ed25519.Signature.s\_bytes +\end{quote} + +A consumer's local table (\S\ref{sec:auditing}) contains exactly these +sets. That a boundary differs by fork is itself audited: an +upstream-shaped cone appearing under the anza label, or vice versa, fails +$\clean$ in the ``unexpected axiom'' direction. + +\section{The four verification tiers: Lean theorem names}\label{app:tiers} + +The lifting ladder T1--T4 and the mathematical facts it turns on are +stated in \S\ref{sec:corpus}. For reproducibility we record here the +verbatim Lean theorem name backing each tier in the upstream corpus +(namespace \texttt{CurveFieldProofs} elided; the forks use the same names +against their own extractions); a reader can +\texttt{\#print axioms} any of these to reproduce the cones of +Appendix~\ref{app:axioms}. +\begin{center}\small +\begin{tabular}{@{}ll@{}} +\toprule +tier (\S\ref{sec:corpus}) & Lean theorem \\ +\midrule +T1 \enspace byte apex & \texttt{verify\_accepts\_iff} \\ +T2 \enspace canonical half-lift & \texttt{verify\_accepts\_iff\_point} \\ +T3 \enspace injectivity / point eq. & \texttt{verify\_accepts\_iff\_point\_eq} \\ +T4 \enspace constructive full lift & \texttt{verify\_accepts\_iff\_decompress} \\ +\bottomrule +\end{tabular} +\end{center} +All four are proven under the wire-format hypotheses $\mathcal{W}$ of +\S\ref{sec:corpus}; a consumer reasoning about the underlying group +element relies on their conjunction (the ladder up to T4), and all four +cones are audited against the same per-fork boundary of +Appendix~\ref{app:axioms}. + +\end{document} diff --git a/paper/ltl.pdf b/paper/ltl.pdf index 2747bf43c99fa93b1fbd5aa35de5e4056dc0b59a..21dbda7608099c16f872d04fe62d8e9920460c2b 100644 GIT binary patch delta 374348 zcmZsiQ*bT-vt?tOC$??dwv!XvcD~rQZQHhOpV&6%zcY8HYO3yAzwVc=Ub|MGFA?{@ zV^WYQii*=Q(R09%%`cCv!!WV26EYIo8(G2d^1?94n%bGWSP-%>Gbb5-PyuqZwqmzO zk$u-Rrgb<65N1wtW!3fyhHygi(o z(dF(Fem1;*FRu|bnO>SWH}Qn4ZJf03XBcB!Grf7_n5VYJN?UzR&y(tQ$;`|dxut|R zABmXK2d)svk9#h25tY)t+CH~Ej5id@oQ7W&h`$}z2?nRDY-O&eX#n09N>iUc&CF*# zbl%8@iFfa$w_%WK`FBB_J9vftanT9K0IMl)td|`|{+pzAn$sd1{wTK){bIvO?>Sh3 zU}yx+TjJTaINx{rlG~sA&#}!P3dRP3XhhBn%E<0Kzg=T<``%xOs(dUkA;|%Ob}zqdC>BwLOfX9JfwmMD&HgCSwil40Q9|6 zIH`yMe*%#f5xu2#fz(jy!ebt zutV)B#jqXAsKye}U^&EOhI4b$cz*m1#u;cNNN4$Y54exoC#EBs9UipQ_Qy=I-n|!s zJ5t$Bm9RDE8EiR&qt=6;{ 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