acta-mathematica - SKILL.md Agent Skill

name: acta-mathematica description: Use when targeting Acta Mathematica (Acta Math.) or deciding whether a pure-mathematics manuscript meets the bar of one of the most selective journals in the field. Encodes the journal's fit, framing, proof-and-rigor bar, house style, official-submission re-check, and desk-reject heuristics.

Acta Mathematica (acta-mathematica)

Journal positioning

Acta Mathematica, published by the Institut Mittag-Leffler (distributed by International Press), is among the most selective pure-mathematics journals in the world. Its defining character is exceptional results, not topical breadth: it publishes a small number of papers per year, drawn from across all of mathematics, that resolve major problems, introduce methods of lasting influence, or open new directions. There is no thematic restriction — analysis, geometry, number theory, algebra, dynamics, topology, and mathematical physics all appear — but the importance bar is uniform and extremely high. Readership is the research mathematics community at large, and a paper is judged on the depth, correctness, and significance of its theorems and on the durability of the techniques it introduces. This skill is a fit / venue-selection / re-framing tool. It does not replace the journal's current official submission guidelines or the editorial board's judgment. Before submitting, re-check the live author instructions on the Acta Mathematica / Institut Mittag-Leffler site.

When to trigger

The author believes a result resolves a long-standing problem or introduces a method of broad and lasting significance, and is considering the very top general venues.
A manuscript is being weighed between Acta Mathematica and Annals of Mathematics or Inventiones Mathematicae.
An author needs a candid read on whether a strong, correct result is also significant enough for an extremely selective generalist journal rather than a strong specialist one.
The author needs Acta Mathematica's expectations on full rigor, exposition, and submission norms before committing.

Scope & topic fit

Major advances in analysis: harmonic analysis, PDE, functional analysis, complex analysis, and ergodic theory at the level of resolving central problems.
Number theory and arithmetic geometry: deep results in analytic or algebraic number theory, automorphic forms, and arithmetic of varieties.
Geometry and topology: differential and algebraic geometry, geometric analysis, low-dimensional and geometric topology with field-shaping consequences.
Dynamical systems and probability: structural theorems, rigidity, and probabilistic results of broad importance.
Algebra, representation theory, and mathematical physics where the contribution reshapes a research area.
Cross-cutting work that introduces a technique used widely afterward, regardless of its home subfield.

Method & evidence bar

Results must be complete and fully proved: every theorem is established rigorously, with no gaps, no appeals to unpublished or "folklore" claims without proof, and no reliance on unverified computation.
Significance is the binding constraint: correctness alone is insufficient; the work must resolve an important problem or introduce methods of lasting, cross-area influence.
Proofs must be referee-verifiable in full; the exposition must let an expert referee check every step, with technical lemmas either proved or precisely cited.
The Mathematics Subject Classification (MSC) should be assigned accurately to situate the work for editors and referees.
arXiv posting is standard and encouraged in mathematics; there is no data- or code-deposition norm, but any computer-assisted proof must be documented so it can be independently checked.
Priority and context must be honest: prior and concurrent results are credited precisely, and the advance over the state of the art is stated exactly.

Structure & house style

Standard pure-mathematics structure: abstract, introduction stating the main theorems and their significance, preliminaries, the body of proofs, and references; length follows the needs of a complete, rigorous argument.
The introduction must state the main results precisely and explain why they matter and how they relate to prior work; for a top generalist venue this framing carries real weight.
Exposition must be of the highest quality: definitions precise, notation consistent, and proofs organized so a reader can follow the architecture before the technical detail.
Long or technical arguments may be modularized into lemmas and propositions; auxiliary computations or routine verifications may go to appendices.
Statements of theorems should be self-contained and quotable; hypotheses and conclusions must be unambiguous.
LaTeX is expected; bibliographic and formatting conventions follow the journal's current style.

Official-submission checklist

Before giving submission-ready advice, read ../../resources/source-basis.md and ../../resources/official-source-map.md; start from the official source anchors for this journal family, then cite the current journal-specific page you checked.
Search the live site for "Acta Mathematica submission instructions" and follow the current Institut Mittag-Leffler / International Press version.
Re-check the submission procedure, file-format and LaTeX requirements, and any editor-handling or pre-screening conventions.
Re-check MSC classification requirements and the journal's expectations on exposition and length.
Re-check authorship, competing-interests, and any AI-use disclosure requirements; confirm arXiv/preprint posting policy and documentation expectations for computer-assisted proofs.
If the live official instructions conflict with this skill, the official instructions win.

Pre-submission self-check

One sentence — the main theorem and why it is a major advance across mathematics, not only within its subfield.
Every proof is complete and referee-verifiable, with all lemmas proved or precisely cited and no unverified computation.
The introduction states results precisely and positions them honestly against prior and concurrent work.
MSC classification is assigned accurately.
Any computer-assisted component is documented for independent verification; the preprint/arXiv status is consistent with policy.
The work is genuinely at the significance level of Acta Mathematica, not merely strong and correct.

Common desk-reject triggers

A correct and solid result that is not significant enough for an extremely selective generalist journal — a specialist or strong field journal is the right home.
A proof with gaps, hand-waved steps, or reliance on unproved "folklore" or unverified computation.
Overstated significance or imprecise positioning relative to known results.
A manuscript whose exposition is too disorganized for a referee to verify the argument.
Incremental improvement of an existing theorem without a method or consequence of lasting, cross-area importance.

Re-routing decision

A field-defining result that is an equally natural fit for the other apex generalist venue: annals-of-mathematics.
A major advance, especially in geometry, number theory, or arithmetic geometry, at top generalist level: inventiones-mathematicae.
A strong, correct, but more specialized result: the leading journal of the relevant subfield.
Computation-at-the-interface results with rigorous foundations rather than pure-math significance: foundations-of-computational-mathematics.

Output format

[Fit] High / Medium / Low (one-line reason)
[Target] Acta Mathematica
[Topic tags] <2–3 closest areas / MSC themes>
[Method/evidence] <are the proofs complete and referee-verifiable, and is the result significant enough for an apex generalist journal?>
[Top risk] <the single most likely reason for rejection>
[Official items to re-check] <submission/LaTeX format / MSC classification / exposition & length / arXiv & computer-proof documentation / disclosure>
[Re-route suggestion] <if not a fit, a better-matched venue>