# Craft Proof Prompt

> 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.

- Skill: `meleantonio/craft-proof-prompt` (Agent Skill)
- Install (CLI): `npx skillmds@latest add meleantonio/craft-proof-prompt`
- Raw SKILL.md: https://api.skillmd.com/api/skills/meleantonio/craft-proof-prompt/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: AI & ML
- Author: meleantonio (https://skillmd.com/u/meleantonio)
- Updated: 2026-09-17
- Page: https://skillmd.com/skills/meleantonio/craft-proof-prompt

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# 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:

   ```text
   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