Use when anticipating how an expert Annals of Mathematics referee will verify a proof — stress-testing the argument for gaps, checking external dependencies, and pre-empting the questions a careful reader will ask. Hardens the manuscript before submission; does not write the rebuttal (anmath-revision).
SkillScore100Maintained
Automatic
◆Research pack
Last verified 8/15/2026
What it changes
Passed 23 of 23 test cases with the skill, and 19 of 23 without it.
Without skill83%
With skill100%
Checks it passed that the model alone missed
Includes the field 【Next step】
Includes the field 【Weakest step】
Includes the field 【Boundary cases】
and 5 more in the full report
4 fixed19 passed either way0 still failing0 broke
Pass-rate lift
+17 pp
Tokens
+10%
Agent turns
0%
Response time
-22%
Model gemini-3.6-flashMeasured 8/15/2026v123 of 23 cases passed with skill
Tokens, turns and time describe resource use, not a dollar price.
See it in action
One of 4 test cases the skill fixed. Same model, same prompt, with and without the skill.
1 of 4
Prompt
Before submitting my paper, I need a rigorous self-adversarial assessment from the perspective of an expert referee who reconstructs every step. Please review the manuscript and give me a full referee-readiness evaluation. Include status checks on crux locatability, the weakest proof step and its strengthening, citation hypothesis matching, edge/degenerate cases, computational reproducibility, suggested referee choices with conflict status, any remaining editor-level risks, and what step to take next.
What was checked, without and with the skill
Checked
Without skill
With skill
Includes the field 【External-citation re-check】
Missed
Passed
Includes the field 【Boundary cases】
Missed
Passed
Includes the field 【Suggested referees】
Missed
Passed
case-02 · 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.md80 linessingle file
Referee Strategy (anmath-referee-strategy)
When to trigger
The manuscript is essentially final and you want to pre-empt referee objections
You want an adversarial read of your own proof before an expert does it for you
You are unsure which steps a careful referee will distrust
You want to decide what to make easier to verify before sending
How Annals referees read
Expect a referee who is an expert and verifies proofs in detail, often over a long
period (a year or more is common). They do not skim; they reconstruct each step. Their
implicit questions:
Is it important enough? Significance is judged again at the report stage.
Is every step actually valid? They will probe exactly the steps you find hardest.
Do the external results say what you claim? They will check the cited statement.
Does the theorem match the proof? Any over-claim is caught here.
Is anything hidden behind "clearly"? Softening words attract scrutiny, not less.
Self-adversarial pass
Probe
What to do before they do
Where is the crux?
Make sure it is fully spelled out and easy to locate
Which step is weakest?
Strengthen or expand it; do not hope it is overlooked
Every "clearly"/"standard"
Resolve or cite it (see anmath-writing-style)
Every external theorem
Re-read the cited source; confirm hypotheses match your use
Quantifiers / constants
Confirm order and dependence are stated and correct
Special / boundary cases
Check the degenerate cases the main argument might miss
Computer-assisted steps
Confirm code/data are archived and the claim is reproducible
Make verification easy
A clear proof overview and named lemmas let a referee navigate and check piece by
piece — this speeds a long review and reduces the chance of misreading.
Precise citations (exact theorem number and statement) save the referee from hunting
and remove a common source of objections.
Isolate any dependence on unpublished work so the referee can see exactly what rests