From 78eea145127153c524f629e592986981332227f2 Mon Sep 17 00:00:00 2001 From: mrwulf Date: Thu, 9 Jul 2026 20:02:51 +0200 Subject: [PATCH] =?UTF-8?q?paper:=20Socratic=20proof-rigor=20pass=20?= =?UTF-8?q?=E2=80=94=20close=20Lemma=202=20gap,=20fix=20Step=203=20object,?= =?UTF-8?q?=20argue=20=C2=A77=20acyclicity?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Adversarial re-read of the security section found three exposition gaps (no math errors, but the kind a referee pounces on), all fixed: - Lemma 2 (Root binding): Theorem 3 Step 1 asserted 'every proof node consumed is genuine', but the lemma's STATED conclusion only mentioned values F emits, not siblings F consumes. Strengthened case (ii) to pin the consumed siblings explicitly (it follows from argument-pair coincidence, now stated, not just proved). - Theorem 3 Step 3: 'hash-fold over itself' named the wrong object — for Lemma 2, T_{D1[0:n0]} must be a hash-fold over T_{D0}; justified by equal size => identical shape, leaf inputs = D1[0:n0]. - §7: 'self-referential without being circular' was asserted; now argued via the explicit acyclic verification order (pin key -> check sig -> verify inclusion by hashes -> optionally rebuild+recheck source), no step consuming its own output. 17 pages, refs resolve, 104 tests green (verifier defs untouched). Co-Authored-By: Claude Fable 5 --- paper/ltl.pdf | Bin 556320 -> 557593 bytes paper/ltl.tex | 60 +++++++++++++++++++++++++++++++------------------- 2 files changed, 37 insertions(+), 23 deletions(-) diff --git a/paper/ltl.pdf b/paper/ltl.pdf index 4a65fc0eb18c0280df6da7deafa207ae0fc40682..bf2b6c80e4625eff229196ea3996b7c576197386 100644 GIT binary patch delta 54620 zcmV(=K-s^b`XQNwBC!2@12Hf)mx1{QD1X&FU325Ok?;N$s=O>+WpRmba3*_I$xddI z)F!nz>#BS3_<@#bn;D66NXZ^2`{UD%1}TE#hrBbn+&$PNKmgrnG#dQ{C5!t-viRXF z@z391o_+g1l?x_gAvIrI-YrZT^Mz3?HezvkySR$<`I0fNqM!5CzAAR-f<-UqOMhWh zl$F`~r7r68>&riX``#oAmc(h2G8~4*Nn!v7R4$B-ZDJROn^+jTxZJ>~mk-cyDMS+0 z`D#~eODa58+jDNCr*m$i+&9=g{=okEgMe3_M%z0=fHB?0;L5f8$fd#0 zXNXD?>qT|HXkI`3aMnlrDgsLQ_J2eosEW^*QZhi<<5BOjUB1anL~`fx$twS`-0tY* zHqRe_DazG)U$@iC%3B;9pr^JWj-xjdvE?a|X0NrsEl z0Se0>3m(F~{^e%xK|ccp5mg5sSZYJnTlXERkfg-NeJ+y7g2P-6UyX_C7g((g4O8dU zfqAi~BNEnZsp4^8J)SSITz}{F8{jO>qvD)J9?i$1^gVC4*z38Zar4jFY6r{EaE}Q0 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zN6T6M-UdfEprOCV!*F=h=F7Nzq^y7i^O5-=@Pzru5=GdECNKB)*B>>-;ZKV5HALJ_ zHAm${7X2!bJ$>=Cg5O+0I1`9VYT7U;7FyV%HCke_-CBZ-FnK3l?p8cG*j9)fSXT=u zK&DUrJx$K{z?~myR5d&7*k2rZb}dTSUyP^h?fgZhM`Grm2$*{Ao9td zdh8WU>|2e}%?m>_7f-ao1~h8DZ00FaEHcNsh|Qfr1=yg%nS$;9M$Gt*L$;LyM{C;8 ziZhG51kD`NhnC!^pgOWKmj44Z{<0X`YRF!NJPGN*;NMssu=#|&h7~=_XxRs1Qo2Wr d;sxF6+Vkr4-5?4sYKXkN92FnmeFJT(e*uF2Ur7J} diff --git a/paper/ltl.tex b/paper/ltl.tex index 0875ca0..3037592 100755 --- a/paper/ltl.tex +++ b/paper/ltl.tex @@ -573,24 +573,29 @@ may be adversarial; only the \emph{shape} matches $T$. \begin{lemma}[Root binding]\label{lem:bind} Let $F$ be a hash-fold over the honest Merkle tree $T$ of a leaf list $D$, -run on otherwise adversarial inputs, and suppose $F$'s output equals -$\MTH(D)$. Then, walking $F$ and $T$ in parallel from the root, either -(i)~at some internal node $F$'s $\hnode$ argument pair differs from $T$'s -while the two $\hnode$ values agree---an explicit SHA-256 collision---or -(ii)~every value $F$ emits equals the corresponding node of $T$, down to -the leaves, whence $F$ read the true leaf bytes of $D$. +run on otherwise adversarial inputs (a leaf value and sibling nodes it +folds in), and suppose $F$'s output equals $\MTH(D)$. Then either (i)~at +some internal node $F$'s $\hnode$ argument pair differs from $T$'s while the +two $\hnode$ values agree---an explicit SHA-256 collision---or (ii)~$F$'s +computation coincides with $T$ node-for-node: every value $F$ emits and +\emph{every sibling node $F$ consumes} equals the corresponding node of +$T$, and $F$'s leaf inputs are the true leaves of $D$. \end{lemma} \begin{proof} Induction on the height of $T$. At the root both values equal $\MTH(D)$ by -hypothesis, and each is $\hnode$ of an argument pair (for $F$ by the -hash-fold property, for $T$ by definition of $\MTH$ at an internal node). -Equal $\hnode$ values of \emph{distinct} argument pairs are a collision -(case i); otherwise the pairs coincide, so $F$'s two child values equal -$T$'s two children, and the hypothesis applies to each child subtree. At a -leaf, $F$ emits $\hleaf(d')$ and $T$ has $\hleaf(D[j])$; equality with -$d' \neq D[j]$ is again a collision, and Lemma~\ref{lem:domsep} rules out -a leaf value coinciding with an internal-node value by type, so the two -cases are exhaustive and exclusive. +hypothesis, and each is $\hnode$ of an argument pair---for $F$ that pair is +(its recursive child value, the sibling it consumed there); for $T$ it is +$(\MTH$ of the left block, $\MTH$ of the right block$)$. Equal $\hnode$ +values of \emph{distinct} argument pairs are a collision (case i); +otherwise the two pairs coincide \emph{as pairs}, so simultaneously $F$'s +recursive child value equals $T$'s child \emph{and the sibling $F$ consumed +equals $T$'s other child}, and the hypothesis applies to the child subtree. +At a leaf, $F$ folds $\hleaf(d')$ where $T$ has $\hleaf(D[j])$; equality +with $d' \neq D[j]$ is again a collision, and Lemma~\ref{lem:domsep} rules +out a leaf value coinciding with an internal-node value by type, so the two +cases are exhaustive and exclusive. In case (ii) the argument-pair +coincidence at every level is exactly the claim that both emitted values +and consumed siblings match $T$. \end{proof} \begin{theorem}[Inclusion soundness: position binding]\label{thm:sound} @@ -656,13 +661,15 @@ 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).} Apply Lemma~\ref{lem:bind} once more, this time -with the honest hash-fold $F = T_{D_1[0{:}n_0]}$ (the honest tree of -$D_1[0{:}n_0]$, trivially a hash-fold over itself) against the honest tree -$T = T_{D_0}$: their roots are equal but their leaf lists differ, so case -(ii) is impossible and case (i) fires---an explicit collision. -$\mathcal{E}'$ outputs whichever collision was found. It recomputes $T_0$ -and $T_1$, so it runs in $O(n_1)$ hash evaluations. +\emph{Step 3 (descend).} Since $|D_0| = |D_1[0{:}n_0]| = n_0$, the two +honest trees have identical shape, so $T_{D_1[0{:}n_0]}$ is a hash-fold +over $T_{D_0}$ (same shape; its leaf inputs are 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} @@ -736,7 +743,14 @@ self\_inclusion: verified 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. The self-check always references the \emph{newest} leaf +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