--- name: duke-mathematical-journal description: Use when targeting Duke Mathematical Journal (Duke Math. J.) or deciding whether a pure mathematics manuscript fits this top-tier broad-scope Duke University Press venue. Encodes the journal's fit, framing, proof standard, house style, official-submission re-check, and desk-reject heuristics. --- # Duke Mathematical Journal (duke-mathematical-journal) ## Journal positioning Duke Mathematical Journal, published by Duke University Press, is one of the leading general journals in pure mathematics, with a long-standing reputation for publishing deep, high-quality research across the full range of mathematical fields. Its defining character is depth at top-tier breadth: Duke publishes results of major significance from algebra, geometry, topology, number theory, analysis, dynamics, and mathematical physics, and is regarded as sitting near the very top of the general-journal hierarchy. The journal rewards substantial, conceptually significant theorems and methods presented with full rigor; it is not a home for routine extensions or narrowly technical notes. This skill is a **fit / venue-selection / re-framing** tool. It does not replace the journal's current official submission guidelines. Before submitting, re-check the live author instructions on the Duke Mathematical Journal site (Duke University Press) and confirm submission procedures. ## When to trigger - The author is considering Duke Mathematical Journal for a deep, significant pure-mathematics paper. - A result is of major significance and the author is choosing among Duke, `annals-of-mathematics`, and `inventiones-mathematicae`. - A strong paper spans sub-fields or sits in a core area (number theory, geometry, analysis) where Duke has particular strength. - The author needs Duke's significance and rigor bar, plus common rejection reasons, before submission. ## Scope & topic fit - Pure mathematics across all major areas: number theory and arithmetic geometry, algebraic and differential geometry, topology, representation theory, analysis and PDE, probability, dynamical systems, mathematical physics. - Deep theorems of major significance and methods whose impact reaches across sub-areas. - Results that resolve substantial open questions or build new theory in a core mathematical field. - Work bridging sub-fields at a high level of depth and significance. - Survey or purely expository work is not the focus; contributions must be primary research with new, fully proved results. ## Method & evidence bar - The primary standard is mathematical correctness: every claim must be fully proved; no proof sketches, unresolved cases, or conditional results in place of complete arguments (unless conditionality is the explicit contribution). - Significance is judged on depth and importance to mathematics broadly, not on citation counts or problem fame alone; the bar is comparable to the top general journals. - Novelty of result or technique is expected; incremental extensions of known arguments are unlikely to clear the bar. - Exposition must let expert referees verify correctness: precise statements, complete proofs, and clear separation of new from standard material. - MSC (Mathematics Subject Classification) codes must be assigned correctly to signal scope and assist referee assignment. - arXiv posting is standard practice; most submissions appear on arXiv before or contemporaneously with submission. ## Structure & house style - No imposed structural template beyond mathematical convention: introduction (context, precise statement of results, proof strategy), preliminaries, core proof sections, optional appendices. - The introduction should state main results precisely, explain significance to a broad mathematical audience, and outline key proof ideas — read first by referees and the editorial board. - LaTeX is standard; Duke University Press formatting conventions apply — re-check the current style file and reference style on the submission site. - References must be complete and correctly formatted; preprint citations should carry stable arXiv identifiers. - Length is set by mathematical necessity; there is no fixed page limit, but unnecessary length attracts scrutiny — concise, complete arguments are valued. ## 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. - Check the current Duke Mathematical Journal submission instructions on the Duke University Press site and re-verify the submission system and procedure. - Assign MSC primary and secondary classification codes. - Post to arXiv (or confirm prior posting) with the identifier ready for correspondence. - Prepare a cover letter stating the main result, its significance, and suggested/excluded referees with conflicts noted. - Confirm all co-authors have approved the submission and re-check any current fee/open-access arrangements. - If the live official instructions conflict with this skill, the official instructions win. ## Pre-submission self-check - [ ] One sentence stating the main theorem and why it is of major importance to mathematics broadly. - [ ] Every claim is fully proved; no gaps, sketches, or unresolved cases. - [ ] The result is genuinely significant and novel, not a routine extension of known arguments. - [ ] The introduction states results precisely, explains significance, and outlines proof ideas for a broad audience. - [ ] The paper is posted or ready to post on arXiv with correct MSC codes. - [ ] An honest assessment: is this best at Duke, or does its significance warrant `annals-of-mathematics` or `inventiones-mathematicae` first? ## Common desk-reject triggers - A correct but incremental result extending known techniques without a substantially new idea. - A narrowly specialized paper of interest only to a small sub-community, better suited to a field journal. - An incomplete proof: any identifiable gap, unresolved case, or unjustified claim. - An introduction that fails to convey major significance to a broad editorial board. - Expository or survey material submitted as primary research without new theorems. ## Re-routing decision Result of exceptional, field-reshaping significance → `annals-of-mathematics`. Top-tier general advance of comparable depth → `inventiones-mathematicae`. High-quality broad research perhaps slightly below the Duke bar → `advances-in-mathematics`. Deep analysis / PDE / applied-analysis with substantial theorem content → `communications-on-pure-and-applied-mathematics`. Narrowly specialized result → an area-specific society journal. ## Output format ```text [Fit] High / Medium / Low (one-line reason) [Target] Duke Mathematical Journal [Topic tags] <2–3 MSC areas> [Method/evidence] [Top risk] [Official items to re-check] [Re-route suggestion] ```