prove-open-problem

name

prove-open-problem

description

Attack an open mathematical problem end-to-end using the Wang/Codex Erdős workflow: select tractability, craft a problem-specific proof prompt, run a long attempt→audit→repair research loop with multi-agent search, and emit LaTeX/Python/Lean artifacts. Use when the user asks to prove, disprove, resolve, or attack an open math problem (Erdős, conjectures, research questions), or when they mention prove-that-shit / open-problem proving.

Prove an open mathematical problem

Implement the workflow popularized for attacking open Erdős-type problems with coding agents (see docs/SOURCE_THREAD.md). Deep domain expertise helps for auditing, but the agent workflow itself is procedural.

Non-negotiable posture

1. Assume a complete resolution exists for the purpose of the task.
2. Do not assume the answer is yes or no in advance.
3. Do not declare the problem “open” and stop.
4. Do not treat reductions to equally hard unproved statements as progress.
5. Partial results, heuristics, and finite computations do not count unless they complete one of the exact affirmative/negative resolutions in the prompt.

Pipeline

Execute these phases in order. Persist artifacts under problems/<id>/.

Phase 0 — Intake

• Capture the exact statement, source URL/ID (e.g. Erdős problem number), and any user constraints (time budget, Lean required, computational tools).
• If the statement is ambiguous, rewrite it precisely before continuing.

Phase 1 — Selection gate

Run select-tractable-problem (or apply its checklist inline):

• Prefer problems actively discussed by working mathematicians.
• Reject (or demote) problems that are clearly equivalent to a major named conjecture, or that AI triage rates as “requires a new theory.”