anmath-referee-strategy

# 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: 1. **Is it important enough?** Significance is judged again at the report stage. 2. **Is every step actually valid?** They will probe exactly the steps you find hardest. 3. **Do the external results say what you claim?** They will check the cited statement. 4. **Does the theorem match the proof?** Any over-claim is caught here. 5. **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 - **Isolate any dependence on unpublished work** so the referee can see exactly what rests on it; reduce or remove such dependence where possible. ## Suggested / opposed referees - If the portal allows suggestions, propose genuine experts without conflicts of interest; do not pack the list with close collaborators. - Declare conflicts honestly. Editors decide; transparency builds trust. ## Checklist - [ ] The crux is fully spelled out and easy to find - [ ] The weakest step has been strengthened or expanded, not hidden - [ ] Every "clearly"/"standard" is resolved or precisely cited - [ ] Every external theorem's hypotheses match your use (re-checked at source) - [ ] Quantifier order and constant dependence verified - [ ] Degenerate/boundary cases handled - [ ] Computer-assisted steps reproducible (archived code/data) - [ ] Suggested referees are genuine, conflict-free experts; conflicts declared ## Anti-patterns - Hoping a referee will not check the step you yourself are unsure about - Citing an external theorem without re-reading its exact hypotheses - Leaving the crux hard to locate in a long, unstructured proof - Suggesting only close collaborators as referees - Treating significance as settled at submission — it is re-judged in the report - Relying on "it is easy to see" to get past a careful reader (it will not) ## Output format ``` 【Crux locatable & complete】yes / fix: ... 【Weakest step】... → strengthened / expanded 【External-citation re-check】hypotheses match use: yes / fix: ... 【Boundary cases】covered / add: ... 【Computer-assisted reproducible】n/a / yes 【Suggested referees】names (conflict-free); conflicts declared: ... 【Residual risks to flag to editor】... 【Next step】submit, then await report → anmath-revision ```