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name: anmath-cover-letter description: Use when drafting the cover note to the editors for an Annals of Mathematics submission — concisely conveying the main result, its significance, scope fit, and any priority/overlap disclosures. Frames the submission; does not write the paper. Verify whether a cover letter is requested on the official submission page.

Cover Letter to the Editors (anmath-cover-letter)

When to trigger

• The manuscript is final and you are preparing the submission package
• You need a short note conveying significance and scope fit to the editor
• There is prior work, an arXiv posting, or overlap that should be disclosed up front

First verify on the official submission page whether a cover letter is expected and in what form. Some math journals want a brief note; others collect the same information in the portal. Keep it short either way — the paper carries the weight.

What an Annals cover letter does

The editors triage on importance and fit. The letter's job is to let an editor see, in under a page, why this result clears the Annals bar and which area it belongs to — not to re-prove anything.

Element	One to two sentences
Result	State the Main Theorem in plain terms (the precise version is in the paper)
Significance	Which recognized problem/program it advances and why it matters
Advance over prior work	What is new: removed hypothesis, settled conjecture, new method
Scope / area	The MSC area and why Annals is the right venue
Disclosures	arXiv id; related/overlapping work; priority context; computer-assisted parts
Logistics	Suggested area/handling editor if invited; any conflicts to declare

Drafting guidance

• Lead with the result and its significance, in language an editor outside your subfield can parse. Save technical precision for the manuscript.
• Be honest and specific about the advance; do not inflate. Editors and referees will check, and overstatement damages credibility.
• Disclose proactively: an arXiv preprint, a companion paper, partial prior announcements, or a computer-assisted step. Surprises later read as concealment.
• Keep it to a page. No proof sketches, no exhaustive literature review — that is the introduction's job.
• Suggested referees and conflicts: only if the portal asks; keep it factual.

Editor signal hierarchy

Use the cover note to answer the editor's triage questions in order:

1. What is the theorem? A plain-language version of the main result, not a slogan.
2. Why is it important now? The conjecture, program, obstruction, or method barrier that the result moves.
3. What exactly is new? Removed hypothesis, stronger range, new technique, unexpected bridge between areas, or settlement of a recognized problem.
4. Why Annals rather than a specialist journal? The mathematical audience that reaches beyond the immediate subfield.
5. What must be disclosed? arXiv history, companion papers, priority context, computational dependence, or conflicts.

If the letter cannot answer the first three without adjectives, the introduction likely needs one more pass before submission.

Checklist

• Confirmed whether a cover letter is requested (official page)
• Main result stated in plain terms in one to two sentences
• Significance tied to a recognized problem/program
• The specific advance over prior work is named, not inflated
• MSC area and rationale for Annals stated
• arXiv id and any related/overlapping work disclosed
• Computer-assisted components (if any) flagged
• Letter fits on a single page; no re-proving

Anti-patterns

• A page of hype with no precise sense of what is actually new
• Overstating significance beyond what the theorem supports
• Hiding an arXiv preprint or an overlapping companion paper
• Re-proving the theorem in the letter instead of pointing to the paper
• Generic boilerplate ("we believe this will interest your readers") with no content
• Failing to declare a known conflict or a computer-assisted dependency

Output format

【Cover letter requested?】yes / no (per official page)
【Result, plain terms】...
【Significance】advances problem/program: ...
【Advance over prior】...
【MSC area + why Annals】...
【Disclosures】arXiv: ...; related work: ...; computer-assisted: ...
【Length】≤ 1 page — confirmed
【Next step】anmath-submission