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Use when strengthening the reproducibility of a COLT (Conference on Learning Theory) paper, where reproducing means re-deriving — complete proofs, explicit assumptions, tracked constants, correctly invoked external results, self-contained notation — plus seeds and scripts for any numerical illustration the paper carries.
Passed 19 of 23 test cases with the skill, and 10 of 23 without it.
and 8 more in the full report
9 fixed10 passed either way4 still failing0 broke
Tokens, turns and time describe resource use, not a dollar price.
One of 9 test cases the skill fixed. Same model, same prompt, with and without the skill.
Before submitting our COLT paper, who should perform step 2 of the pre-submission re-derivation drill, and what specific task must they perform on the statement list?
| Checked | Without skill | With skill |
|---|---|---|
| Specifies that a non-author coauthor should attempt the check | Passed | Passed |
| Requires verifying whether statements can be fully understood without reading proofs | Missed | Passed |
The instructions your model reads when the skill loads.
At COLT, reproducibility means a competent reader can re-derive every claim from the PDF alone. There is no reproducibility checklist form in the COLT 2026 CFP (checked 2026-07-08) — the venue enforces the property the hard way, through referees who attempt the re-derivation during review. This skill is the pre-submission audit that makes that attempt succeed.
A theorem is reproducible when all of the following hold:
| Failure mode | Typical symptom in the PDF | Repair |
|---|---|---|
| Hypothesis smuggling | Proof uses independence never assumed | Add the assumption to the statement, or redo the step |
| External-result misuse | "By [X], ..." where [X] needs bounded support you don't have | Check [X]'s hypotheses; find the right variant or prove a lemma |
| Constant drift | C doubles silently between two displays | Number constants (C_1, C_2, ...) and track them in a ledger |
| Case leakage | "The case d=1 is analogous" when it is not | Write the case or prove the reduction |
| Notation overload | Same symbol for a filtration and a function class | One notation table, enforced globally |
| Silent regime switch | Bound proved for T large, quoted for all T | State the threshold explicitly in the theorem |
Give assumptions their own numbered environment and cite them by label everywhere:
\newtheorem{assumption}{Assumption}
test cases passed, vs 10 / 23 without
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