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Claude Code traces preview

Thu, Jul 30

# Audit spec: registered-claim reproduction, clean room You are auditing one paper's registered claims. Everything you need is in this directory. You have no network beyond your own API, and nothing here is secret. ## Inputs - `source.tex` — the author's LaTeX, byte-exact from the arXiv e-print, hash-pinned in `SOURCE_PIN.txt` - `CLAIMS.txt` — the registered claims, verbatim. **These are what you are scored against.** ## Match claims to results by content and `\label`, never by number Theorem numbers are typeset by LaTeX at build time and are usually absent from source. An unnumbered `\begin{theorem}` renders as "Theorem 4.2" in the PDF. A number a claim cites and the source lacks is a version gap, never a falsification. Quote the exact LaTeX you matched, with its line number, in `THEOREMS.md`, and resolve any macro before you read a formula. ## The rule that decides whether this audit is worth anything **Before you write `falsified`, read the registered claim text again and ask whether the defect you found is inside what that claim actually asserts.** This is not a formality. On 2026-07-25 an audit on this project found a real defect: a theorem printed a step size `τ = 1/(3L)` that carries no horizon dependence, while the proof of that same theorem opened by assuming a step size that depends on the horizon `T`. Simulation confirmed it, twice, independently. It was graded `falsified`, and that was wrong, because the registered claim read: > "Section 4.4 applies the framework to a BlockProx algorithm for graph-guided regularizers used > in multi-task and federated learning, proving last-iterate convergence without assuming bounded > gradients." Every word of that is true, and it never mentions a step size. The audit had falsified its own restatement of the claim. A `falsified` verdict on a true claim scores **0**. The honest `toy` scores 1. Inflating a finding costs points and costs credibility. So there are two separate questions and you answer both: 1. **Is the registered claim true as written?** That decides the verdict. 2. **Did you find a defect in the paper regardless?** That gets reported plainly as a negative result on the claim page, whatever the verdict is. A real defect outside the claim's scope is worth writing down. It is not worth relabelling the claim to accommodate. A genuine falsification looks like the paper contradicting **itself on the thing the claim asserts**: a stated rate that disagrees with the paper's own table, an exponent in the claim that the source's own formula contradicts, a bound described as matching that visibly does not match. ## When a printed quantity looks wrong, check the paper's OTHER statements of it Do this before you decide anything, and report it whatever the verdict turns out to be. It is the cheapest step in this spec and it was worth more than the simulation. Grep the source for every other site where the same quantity is set: the sibling theorems, the general lemmas in the appendix, and the step sizes used in the paper's own experiments. Then ask whether the suspect value is the odd one out. On `last-iterate-prox` the answer decided how the finding could be described. Its BlockProx theorem prints `\tau = 1/(3L)`, and *every other* step size in that paper carries `\sqrt{T}`: `1/(3 L \sqrt{T})` in one sibling theorem, `1/(5L\sqrt{T})` in the other, `1/(C L \sqrt{T})` and `1/(C L T^\beta)` in the lemmas it invokes, `1/(4L\sqrt{T})` in the experiments. The suspect value even shares the constant 3 with the sibling that has the factor. That turns a vague "the theorem and its proof disagree" into a specific, localised, checkable statement: one `\sqrt{T}` is missing from one theorem statement, and five independent sites in the paper agree on what it should read. A reader can verify each of those lines against the same bytes you did. Put them in a small table in `RESULTS.md` with line numbers. Two more ways a falsification goes fake, both of which have happened here: - **A dropped or loose constant.** If the source states the result as `\lesssim` or "up to constants" nearby, its printed constants are not tight and cannot be falsified. - **You measured noise.** A difference at the numerical noise floor has no sign. If the effect is a fraction of a percent of the quantities involved, you have not measured it, and the honest label is `inconclusive`. ## The work `audit.py`, numpy and scipy only. One function per claim returning pass or fail plus the numbers. 20 seeds unless a claim is about worst-case behaviour; report the worst case, never the mean. Give the most load-bearing claim a negative control: an instance where the theorem's hypothesis fails, showing the conclusion fails there too. Say plainly in `RESULTS.md` which claims have none. A check that passes on every input you can construct certifies nothing, and a control that refuses to break is a failed instrument you report as one rather than quietly weaken. **Do not let a summary flag outrun its data.** If you compute a boolean like "consistent" or "holds" from a tolerance, state the tolerance and the margin. A check that returns True on a quantity that is visibly growing is worse than no check. Run it, tee to `results.log`, and write `RESULTS.md` with one `## CLAIM N` section per claim holding: the verbatim claim text, the pass criterion you fixed **before** running, what differs from the paper's setup and why, the measured numbers, and a line `- Verdict: **<verdict>**`. ## Verdicts `verified` = an exact identity, a closed form you evaluated, or a quantity you computed directly. Confirming an asymptotic order or a qualitative trend is `toy`. `inconclusive` if you could not measure it. Never leave a claim unlabelled: a labelled small-scale attempt scores, silence does not. ## Boundaries Do not print or inspect environment variables. Do not run `env`, `printenv`, or `set`. Nothing here needs them, and the transcript of this session is a published artifact. Write only into this directory. Report what you produced and the verdict for each claim. 1 message 94 tools

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