select-open-problem

name	select-open-problem
description	Filter and score candidate open math problems for AI-assisted attack. Prefer actively discussed problems; deprioritize those tied to major open conjectures or clearly out of reach. Use when choosing among Erdős problems, open problems lists, or deciding whether a problem is a good target. Triggers: /select-open-problem, problem selection, which problem to try, filter open problems.

Select Open Problem

Implement the first secret of the Wang/Erdős workflow: problem selection.

Goal

Rank candidate open problems by fitness for a long multi-agent proof search, not by prestige alone.

Inputs

• One or more problem statements, links, or IDs
• Optional domain constraints (combinatorics only, number theory only, etc.)
• Optional user priority (must attempt X regardless of score)

Scoring dimensions

Score each candidate 1–5 on:

Dimension	High score means
Community attention	Discussed by active mathematicians; forum activity; recent interest
Statement cleanliness	Precise, finite or well-posed asymptotic claim; clear yes/no or exact constant
Locality	Not equivalent to a major landmark conjecture
Partial structure	Known partial results, order-of-magnitude bounds, or structural reformulations exist
Approach diversity	Multiple plausible technique families (not a single brittle path)
Checkability	Small cases computable; intermediate lemmas falsifiable; possible formalization later
Trap surface	Traps are listable (definitions, edge cases) rather than amorphous

Hard filters (default deprioritize)

Flag and lower rank if the problem:

• Is essentially RH, BSD, P vs NP, Navier–Stokes regularity, etc., or a thin rephrasing thereof
• Requires assuming another open conjecture of comparable strength to make progress
• Has no clear success criterion (purely aesthetic open-ended exploration)
• Is known only as a vague "something like X might be true"

Do not hard-block if the user insists; document the risk in the report.

Process

1. Normalize each statement (definitions + exact claim).
2. Note known background (proved bounds, equivalent forms) without searching for existing full solutions to this exact problem as a substitute for work.
3. Score the table above.
4. Write a short recommendation: top pick(s), why, main risks, suggested approach families to try first.
5. If only one problem was given, still produce a feasibility memo (attempt / attempt with caution / poor fit).

Output format

Write to the conversation and, if a workspace exists, to problems/<slug>/NOTES.md under a ## Selection heading:

## Selection

### Candidates ranked
1. **[name]** — score S/35 — recommendation: attempt | caution | skip
   - Why:
   - Risks:
   - Seed approach families:

### Chosen problem
- Statement summary:
- Success = complete proof of ___ OR complete disproof of ___
- Non-counting partial results (seed list):

Heuristics from the source workflow

• Prefer problems mathematicians already care about (active discussion beats dusty lists).
• Use AI (you) to filter extremely difficult or conjecture-tied items before spending a multi-hour run.
• A ~50% hit rate on a curated shortlist is more valuable than random attacks on the hardest open problems.

What not to do

• Do not claim a problem is solved based on web chatter.
• Do not rewrite the mathematical claim to make it easier.
• Do not discard a problem solely because it is hard if the user prioritizes it.