Craft Proof Prompt

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

1. Copy templates/problem-specific-prompt.md.

2. Fill sections 1–4 with problem-specific content. Do not leave generic placeholders in the final PROMPT.md.

3. Keep sections 5–6 (search management + persistence) essentially intact; only specialize the adversarial checklist and computational tools.

4. 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.
   

5. 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.

6. 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:

• Precise restatement
• Exact complete resolutions (yes and no)
• Insufficient weaker results listed
• Traps / invariants listed
• Multi-agent + adversarial instructions present
• Persistence / no-quit / no-“it is open” policy present
• Statement integrity verified