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Use when polishing the prose and rigor of a pure-mathematics manuscript for Annals of Mathematics — eliminating gaps, removing "clearly"/"it is easy to see", precise quantifiers, and consistent mathematical English. Late-stage polish; run only after the proof and architecture are fixed.
Passed 21 of 22 test cases with the skill, and 8 of 22 without it.
and 14 more in the full report
13 fixed8 passed either way1 still failing0 broke
Tokens, turns and time describe resource use, not a dollar price.
One of 13 test cases the skill fixed. Same model, same prompt, with and without the skill.
After successfully resolving all 'clearly' phrases, stating all constant dependencies, verifying quantifier order, and matching theorem statements to proofs with zero open gaps remaining, what is the mandatory final output tag and next step?
| Checked | Without skill | With skill |
|---|---|---|
| Outputs 【Next step】anmath-length-management at the end of the summary | Missed | Passed |
The instructions your model reads when the skill loads.
At Annals, an expert referee verifies the proof in detail. A logical gap — especially one hidden behind softening words — is fatal. Treat every "clearly" as a debt to be paid or deleted.
| Phrase | What to do |
|---|---|
| "It is easy to see that ..." | Either show it in one line, or delete the claim if truly immediate |
| "Clearly / obviously ..." | Replace with the actual one-line reason, or cite the lemma |
| "A standard argument shows ..." | Name the standard argument and cite it precisely |
| "By a similar argument ..." | State exactly which prior argument and what changes |
| "It can be shown that ..." | Show it, or move it to a lemma with a proof |
| "Modulo routine modifications ..." | Spell out the modifications or do them |
If a step really is immediate, a single clause giving the reason is better than "clearly".
Before:
Clearly f is uniformly continuous on K, so by a standard compactness argument the bound (3.2) holds with a constant independent of ε.
After:
Since K is compact and f is continuous, f is uniformly continuous on K. Covering K by finitely many δ-balls with δ as in (3.1) and taking the maximum of the local bounds yields (3.2) with C = C(K, f) independent of ε.
Two debts are paid for one extra line: "clearly" becomes the one-clause reason, and
test cases passed, vs 8 / 22 without
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