| name | craft-proof-prompt |
| description | Build a problem-specific open-problem proof prompt that defines success, bans weaker substitutes, lists traps, and configures multi-agent adversarial search. Use when preparing Codex/Cursor/Claude goals for proving or disproving a conjecture, or when asked to generate prompts in the Wang/OpenAI cycle-double-cover style. |
Craft a problem-specific proof prompt
The second secret of the workflow is prompt construction: define exactly what
counts as solving the problem.
Inputs
- Exact problem statement (and ID/URL if any)
- Known background results and their limits
- Optional: 1–3 successful example prompts from prior wins (same style)
Procedure
-
Copy templates/problem-specific-prompt.md.
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Fill sections 1–4 with problem-specific content. Do not leave generic
placeholders in the final PROMPT.md.
-
Keep sections 5–6 (search management + persistence) essentially intact;
only specialize the adversarial checklist and computational tools.
-
If example prompts are available, ask a strong model:
Here is an open problem statement, and here are successful problem-specific
prompts in the target style. Generate a new prompt for this problem in the
same style. Preserve the original mathematical statement exactly — do not
strengthen, weaken, or silently rephrase the claim. Return only the prompt.
-
Statement integrity check (mandatory):
- Diff the original claim against the restatement.
- Confirm affirmative/negative resolutions partition the original question.
- Confirm every listed “insufficient” item is actually weaker / off-target.
-
Write problems/<id>/PROMPT.md and a one-paragraph integrity note in
STATUS.md.
Quality bar
A good prompt is long, precise, and slightly paranoid. Short vibes prompts
fail this workflow. If the filled prompt is under ~80 lines for a research
problem, it is probably missing traps or insufficient-outcomes.
Output
Return the path to PROMPT.md and a checklist:
