Agent Skills
› brycewang-stanford/Awesome-Journal-Skills
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anmath-figures
GitHub用于优化纯数学手稿（Annals风格）的论述结构与可读性。涵盖章节规划、符号一致性、定理前置及交叉引用规范。仅在能比文字更高效传达结构时使用图表，不验证证明正确性。
Trigger Scenarios
论文逻辑难懂但证明正确
符号使用不一致或引入混乱
定理与证明交错导致困惑
需用交换图清晰表达对象关系
决定是否需要极少数的实际图表
Install
npx skills add brycewang-stanford/Awesome-Journal-Skills --skill anmath-figures -g -y
SKILL.md
Frontmatter
{
"name": "anmath-figures",
"description": "Use when organizing the exposition and structure of a pure-mathematics manuscript for Annals of Mathematics — sectioning, notation, statements-before-proofs, commutative diagrams, and readability for an expert non-specialist. Figures are optional and rare; this skill is about exposition first. Does not assess the proof's correctness."
}
Exposition and Structure (anmath-figures)
When to trigger
- The paper is hard to follow even though the proof is correct
- Notation is inconsistent or introduced after first use
- Theorems and their proofs are interleaved confusingly
- A relation between objects would be far clearer as a commutative diagram
- You are deciding whether the rare case of an actual figure is warranted
In pure mathematics, papers are theorem-and-proof and usually have no experiments and few or no figures. "Figures" here means exposition and structure: a figure or diagram is included only when it conveys structure more efficiently than prose.
Exposition principles (Annals readability)
- Statements before proofs. State each definition, lemma, proposition, and theorem in full before proving it. The reader should always know the target before the argument.
- Notation introduced once, used consistently. Define every symbol at first use; keep a fixed convention throughout; avoid overloading the same symbol for two things.
- Logical sectioning. Preliminaries → key constructions → main lemmas → proof of the Main Theorem → consequences. Each section has a clear job and a one-line opener.
- Self-contained where reasonable. Recall the precise external statements you use so a reader need not reconstruct them from memory.
- Readable by an expert non-specialist. Someone strong in an adjacent area should be able to follow the architecture; gloss the field-specific shorthand the first time.
Sectioning template
| Section | Contents |
|---|---|
| Introduction | Problem, Main Theorem, what is new, method sketch, organization |
| Preliminaries / Notation | Conventions, recalled definitions, cited external results |
| Constructions / setup | The objects the proof manipulates |
| Key lemmas | The intermediate results, stated then proved |
| Proof of Main Theorem | Assembling the lemmas into the headline result |
| Consequences | Corollaries and remarks |
| Appendices | Auxiliary/technical material (see anmath-supplementary) |
Numbering and cross-reference conventions
- Number theorem-like environments in one per-section sequence (Theorem 3.1, Lemma 3.2, Corollary 3.3) so a referee deep in a long verification can locate any statement from its number alone.
- Give the headline result a stable early label — Theorem 1.1, or letters (Theorem A, B, …) in a long paper — and use it everywhere.
- Number displayed equations only when referenced; an unnumbered-but-needed display forces "the equation above," which breaks silently under revision.
- Open each section with what it proves and what it consumes: "In this section we prove Proposition 3.1, using Lemma 2.4."
Diagrams and figures (when justified)
- Commutative diagrams: use
tikz-cd(oramscd) when a chain of maps or an exact sequence is clearer drawn than written. Keep arrows labeled and consistent. - A genuine figure (a configuration, a region, a graph): include only when it removes real ambiguity. Use vector output (PDF/EPS), label everything, and reference it in text.
- Tables: occasionally useful for case enumerations or notation summaries; keep clean.
- Most Annals papers have zero figures — do not add one for decoration.
Micro-example: when a diagram earns its place
Prose version: "The map φ factors through the quotient, and the induced map commutes with the two projections of Section 2."
As a tikz-cd square with labeled arrows, the same content is checkable at a glance.
That is the admission test — the referee verifies commutativity faster from the
picture than from the sentence. A picture that merely restates a relation the prose
already makes precise is decoration.
Checklist
- Every definition/lemma/proposition/theorem is stated before it is proved
- Numbering is one per-section sequence; the headline theorem has a stable label used everywhere
- Every symbol is defined at first use and used consistently
- Sections are logically ordered with clear one-line openers
- External results used are recalled precisely (statement + citation)
- Commutative diagrams (if any) are typeset with labeled, consistent arrows
- Any figure is vector, labeled, referenced, and genuinely necessary
- An expert in an adjacent area could follow the overall architecture
Anti-patterns
- Using a symbol before defining it, or redefining a symbol mid-paper
- Interleaving proof fragments with statements so the target is unclear
- A wall of unsegmented text with no sectioning logic
- Adding a decorative figure that conveys nothing the prose does not
- Field jargon used without a single gloss for the adjacent-area reader
- Sloppy diagram arrows (unlabeled, inconsistent direction) that obscure the maps
Output format
【Section plan】1 Intro · 2 Prelim · 3 ... · n Appendix
【Notation issues fixed】...
【Statements-before-proofs】compliant / fix: ...
【Diagrams】none / commutative diagram in §... via tikz-cd
【Figure justification】none needed / figure in §... because ...
【Next step】anmath-supplementary (appendix triage) or anmath-writing-style
Version History
- 1839142 Current 2026-07-05 12:22
