Say at what scale the encoding audit holds, wherever it is summarised - #7
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Section 5.1 is accurate: the CNF was compared against a direct transcription of the definition "on instances small enough to enumerate exhaustively", on 11 cases at n = 8 to 12, j = 0 to 3. Four summary sentences elsewhere compressed that into "proven equal to the definition by exhaustion", "proven to lose no orbit" and "guarantees apply", which read as claims for all n. The published values sit at n = 45 to 84, j = 4 to 19. The audit is still strong evidence -- the same generator emits the CNF at every size, so exhaustive agreement at small n bears directly on large n -- but it is a check at a scale, not a proof for all n, and only section 5.1 said so. Now the summaries say so too. No evidence changed and no value is affected. verify_all.py: 108 passed, 0 failed. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_011dH16KSogC4aDoxznH1d5n
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No evidence changed. No value is affected. This aligns four summary sentences with what §5.1 already says correctly.
The gap
§5.1 is accurate and careful:
Those cases are
n= 8 to 12,j= 0 to 3. The published values sit atn= 45 to 84,j= 4 to 19.Four summary sentences elsewhere compressed that into:
Read alone, each says the encoding is proven correct for all
n. It isn't — you cannot exhaust infinitely manyn, and the audit doesn't try to.What changed
Each of the four now names the scale. §7 reads "checked equal to the definition by exhaustion at the scale of section 5.1 (11 cases,
n= 8 to 12)", and so on.paper/main.texdoesn't contain these sentences and needed no change.vdw/encoding_audit.py's own docstring was already accurate — "audited by exhaustion on instances small enough to enumerate" — so the code was more careful than the prose summarising it.What this does not say
The audit remains strong evidence. The same generator emits the CNF at every size, so exhaustive agreement at small
nbears directly on the encoding used atn = 57. That argument is unchanged. What changed is that the summaries no longer overstate it as a proof.Verification
python verify_all.py→ 108 passed, 0 failed🤖 Generated with Claude Code
https://claude.ai/code/session_011dH16KSogC4aDoxznH1d5n
Generated by Claude Code