Use when laying out the proof strategy of a pure-mathematics manuscript for Annals of Mathematics — the architecture of the argument, the key lemmas and propositions, the novel technique, and where the difficulty lies. Designs and exposes the proof plan; does not check final correctness line-by-line (see anmath-referee-strategy).
SkillScore73Maintained
Automatic
◆Writing & Editing pack
Last verified 8/15/2026
What it changes
Passed 15 of 21 test cases with the skill, and 8 of 21 without it.
Without skill36%
With skill73%
Checks it passed that the model alone missed
Uses the section header 【The new idea (crux)】
Uses the section header 【External results relied on】
Appends → anmath-supplementary to the appendix entry
and 9 more in the full report
10 fixed6 passed either way4 still failing2 broke
Pass-rate lift
+36 pp
Tokens
-2%
Agent turns
0%
Response time
-39%
Model gemini-3.6-flashMeasured 8/15/2026v116 of 22 cases passed with skill · 21 comparable
Tokens, turns and time describe resource use, not a dollar price.
See it in action
One of 10 test cases the skill fixed. Same model, same prompt, with and without the skill.
1 of 10
Prompt
We have finalized the logical structure breakdown, extracted all intermediate propositions, and mapped out our crux argument for our Annals manuscript submission. What is the designated next step in the publication preparation workflow?
What was checked, without and with the skill
Checked
Without skill
With skill
Designates anmath-figures (exposition & structure) as the next step
Missed
Passed
case-10 · gemini-3.6-flash · 8/15/2026 · answers are capped and redacted
What's inside
The instructions your model reads when the skill loads.
SKILL.md81 linessingle file
Proof Strategy and Architecture (anmath-methods)
When to trigger
The proof is essentially complete but its logical structure is not laid out for a reader
A referee would not be able to see the plan before drowning in the details
The key new idea is buried; it is not clear where the real difficulty is overcome
The argument is monolithic and should be decomposed into named lemmas/propositions
Architecture-first principle
For an Annals paper, an expert non-specialist should be able to read a proof overview
and understand how the theorem is proved before verifying that it is. The architecture
is part of the contribution.
Proof outline up front. After stating the Main Theorem, give a paragraph or short
section sketching the strategy: the main steps, the key lemma(s), and the crux.
Decompose into named results. Break the argument into Lemmas, Propositions, and
intermediate Theorems, each stated precisely and proved before it is used.
Isolate the new idea. Name explicitly which step is the genuinely new technique and
why prior approaches failed there. This is what makes the paper publishable.
Locate the difficulty. Tell the reader where the hard part is and why it is hard;
do not let the crux pass disguised as routine.
Decomposition guidance
Symptom
Action
A 10-page proof with no internal structure
Extract Lemmas/Propositions with clear statements
The same estimate reused three times
State it once as a Lemma and cite it
A self-contained technical computation interrupting the flow
Push to an appendix (anmath-supplementary)
Reliance on a deep external theorem
State it precisely with citation; do not paraphrase loosely
The crux step stated as "a calculation shows"
Expand fully — this is exactly what referees check
Handling the key technique
State the novel ingredient as its own result when possible (a key Lemma or
Proposition), so others can cite and reuse it — methods with reach justify Annals.
Contrast with the standard approach: one or two sentences on why the obvious method
does not work and how the new idea circumvents the obstruction.
Use when deciding which anmath-* sub-skill to invoke next, or when sequencing work on a pure-mathematics manuscript from scope check through major revision for an Annals of Mathematics submission. Routes — does not replace — the specialized skills.