anmath-revision

Business

Use when responding to an Annals of Mathematics referee report — revising the manuscript to close gaps or strengthen results and writing a point-by-point reply. Drafts the revision and response after the text is fixed; does not invent significance the result lacks (see anmath-scope-fit).

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Source SKILL.md: https://github.com/brycewang-stanford/Awesome-Journal-Skills/blob/HEAD/Annals-of-Mathematics-Skills/skills/anmath-revision/SKILL.md

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Revision and Response (anmath-revision)

When to trigger

A referee report has arrived (revision requested, or queries to address)
A referee found a gap, a questionable step, or a missing citation
You need to revise the manuscript and write a point-by-point reply
A correction is needed and you must show exactly what changed

Math reviews are slow and thorough. A report may identify a genuine gap; the right response is to fix the mathematics first, then explain — never to argue a gap away.

Order of operations

Fix the text first. Resolve every gap, error, or imprecision in the manuscript before drafting a single line of reply. The reply describes changes that already exist.
Triage the report. Classify each point: (a) genuine gap/error — must fix; (b) request for clarification — add exposition; (c) disagreement — respond with a precise mathematical argument, respectfully.
Verify the fix does not break anything. A repaired step must be re-checked against the whole argument (re-run the self-adversarial pass from anmath-referee-strategy).
Then write the reply, point by point, pointing to exact locations in the revision.

Point-by-point reply structure

Element	Content
Opening	Brief thanks; summary of the main changes
Each point	Quote the referee remark, then state the change and where it appears (section/line/Lemma)
Gaps/errors	Acknowledge plainly, give the corrected argument, point to the new text
Disagreements	A precise, courteous mathematical rebuttal; concede where the referee is right
Marked-up version	Provide a `latexdiff` PDF so changes are easy to verify

Handling a real gap

If the gap is fixable, fix it fully and show the new argument; do not paper over it.
If the fix weakens the theorem (e.g. an extra hypothesis is needed), state the new, correct theorem honestly and explain the change — a correct weaker result beats a wrong strong one.
If the gap is not fixable, the honest course may be withdrawal or a substantially scaled-back result; consult anmath-scope-fit on whether the salvaged result still fits.
Never respond to a gap with "it is easy to see" — that is what created the problem.

Tone and conduct

Respectful and precise. Referees give a great deal of unpaid time on long reviews.
Concede points the referee gets right; defend points you are sure of with mathematics, not assertion.
Address every point; silence on a remark reads as evasion.

Checklist

Every referee point is classified (gap / clarification / disagreement)
All genuine gaps and errors are fixed in the manuscript first
Each fix re-checked against the whole argument (no new gap introduced)
Reply addresses every point, pointing to exact locations in the revision
Any weakened/corrected theorem is stated honestly with the change explained
A latexdiff marked-up version is included
Tone is respectful; defenses are mathematical, not rhetorical
If unfixable, scope/withdrawal reconsidered via anmath-scope-fit

Anti-patterns

Writing the reply before actually fixing the mathematics
Arguing a genuine gap away instead of repairing it
Patching a gap with "it is easy to see" — the original sin, repeated
Silently ignoring a referee remark you find inconvenient
Claiming the original (now-known-wrong) theorem still holds without a valid proof
Defensive or dismissive tone toward a careful, time-intensive review

Output format

【Report points】N total → gaps: a; clarifications: b; disagreements: c
【Gaps fixed】point i: corrected by ..., now in §...
【Theorem changed?】no / now reads ... (honest restatement)
【Re-check after fix】no new gap / FIX
【Reply drafted】point-by-point, with locations
【latexdiff attached】yes
【If unfixable】reconsider via anmath-scope-fit
【Next step】resubmit revision + response