select-tractable-problem

name	select-tractable-problem
description	Filter open math problems for agent attackability: prefer actively discussed problems, demote those tied to major conjectures or requiring new theory. Use before long proof runs or when the user asks which Erdős/open problems to attempt.

Select a tractable open problem

Problem selection is the first secret of the workflow: burn long compute only on problems that are cared about and plausibly within reach of current agent search, not on fortress conjectures.

Prefer

• Problems with recent active discussion by working mathematicians (forums, blogs, Tao/Bloom-style commentary, seminar notes).
• Sharply stated yes/no or exact-constant questions (clear success criterion).
• Problems where finite checks, constructions, or elementary/analytic toolkit pieces are known to matter.
• Instances where weaker order-of-magnitude results already exist (room for a sharp resolution without inventing a field).

Demote or reject

• Clear special cases of RH, Twin Prime, Collatz-class, or other celebrity conjectures unless the user explicitly wants a partial conditional result.
• Problems whose community notes say “equivalent to …” a major open statement.
• Vague “describe the structure of all …” targets without a principal binary or asymptotic question.
• Problems that triage (below) rates as needing a new theory or decades of domain-specific machinery.

AI triage prompt

Run this against one or more strong models; keep independence if using several:

You are triaging an open mathematical problem for an autonomous proof agent.

Problem statement:
[STATEMENT]

Source / community notes:
[NOTES]

Answer with:
1. Care score (0–5): how much active research attention this problem has.
2. Fortress score (0–5): how tightly it is tied to a major named conjecture.
3. Theory-need score (0–5): likelihood a solution needs a new theory vs known tools.
4. Success-criterion clarity (0–5): how crisp the yes/no or exact-target is.
5. Agent-attackability (0–5): candid estimate for long multi-agent search with
   adversarial audit, not single-shot prompting.
6. Go / Conditional / No-go recommendation with one paragraph of reasons.
7. If Conditional: what narrowed principal question would be attackable.

Decision rule

Care	Fortress	Theory-need	Clarity	Action
≥3	≤2	≤3	≥4	Go
≥3	≤3	≤4	≥3	Conditional (narrow the principal question)
else				No-go (propose alternatives)

Record the triage table in problems/<id>/STATUS.md before any long run.