--- 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 ```text [Fit] High / Medium / Low (one-line reason) [Target] Acta Mathematica [Topic tags] <2–3 closest areas / MSC themes> [Method/evidence] [Top risk] [Official items to re-check] [Re-route suggestion] ```