Adversarial audit

Adversarial Audit

Hostile, independent review of a candidate resolution. You are not the author. Your job is to find substantive gaps, not to polish prose.

Stance

• Assume the draft is wrong until every step is forced.
• Prefer explicit counterexamples to proposed lemmas over vague doubt.
• Do not accept "routine," "clearly," or "similarly" for non-trivial steps.
• Do not search the web for whether the problem is open or already solved as a substitute for checking the argument.

Inputs

• Candidate proof/disproof (PROOF_DRAFT.md or pasted text)
• Exact problem statement (PROBLEM.md or PROMPT.md)
• Optional traps list from the problem-specific prompt

Audit procedure

1. Claim alignment

• Quote the exact claim being proved.
• Check the draft proves that claim, not a weaker/stronger/sibling statement.
• Flag any extra assumptions (regularity, connectivity, large n, characteristic zero, etc.) not in the problem.

2. Definition and scope check

• Verify every definition matches the problem (multiplicity, empty cases, strict vs non-strict inequalities, distinctness, etc.).
• Check boundary cases listed in the traps section.

3. Logical chain

For each lemma/step:

Check	Fail if
Stated hypotheses used	Hidden hypothesis appears mid-proof
Quantification	∀/∃ swapped; "for all large n" vs "for all n"
Uniformity	Constants depend on forbidden parameters
Constructivity	Existence claimed without construction or non-constructive theorem that does not apply
Reduction strength	Reduces to unproved statement ≈ original problem
Citation accuracy	Named theorem misapplied or outside hypotheses

4. Non-counting detection

Flag if the draft only achieves something on the does not count list (special cases, weaker bounds, numerical evidence, conditional on open conjectures, etc.).

5. Circular and blocked-route detection

• Does any step assume a form of the conclusion?
• Is the "main lemma" equivalent in strength to the original problem without new proof?
• Are incompatible cases both needed but only one handled?

6. Counterexample search (lemmas)

For each intermediate lemma, try to:

• Find a small counterexample (by hand or code)
• Weaken hypotheses until failure to test tightness
• Check equality cases and extremal configurations

7. Computational sanity (when applicable)

• Verify small-n claims
• Check that constructed objects meet all constraints
• Confirm numerics are not silently used as asymptotics

Output format

Write to AUDIT.md (and summarize for the user):

# Adversarial audit

## Verdict
PASS | FAIL | PASS WITH MINOR FIXES

## Claim check
- Exact claim:
- Draft actually proves:
- Alignment: OK | MISALIGNED

## Critical issues (block acceptance)
1. [step/lemma] — [issue] — [counterexample or gap]

## Major issues (must fix)
1. ...

## Minor issues (cosmetic / clarity)
1. ...

## Lemma challenge log
| Lemma | Challenge | Result |
|-------|-----------|--------|
| L1 | ... | holds / counterexample / unproved |

## Non-counting risk
- [ ] Would this count as complete resolution under PROMPT.md?

## Required repairs before re-audit
1. ...

Verdict rules

Verdict	Meaning
PASS	No substantive gaps; claim fully resolved
PASS WITH MINOR FIXES	Only clarity/typos; mathematical content complete
FAIL	Any critical issue or unresolved major issue

On FAIL, the orchestrator must repair or abandon the route — not publish.

Independence rules

• If you also wrote the draft in the same session, reset perspective: ignore search history spin; re-derive doubts from the written proof alone.
• Prefer spawning a separate agent with only PROOF_DRAFT.md + PROBLEM.md + traps when the host allows.

What not to do

• Do not rewrite the proof into a different theorem and pass it.
• Do not mark PASS because the approach is elegant or almost works.
• Do not accept computational plots as asymptotic proofs.