meleantonio 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
- Normalize each statement (definitions + exact claim).
- Note known background (proved bounds, equivalent forms) without searching for existing full solutions to this exact problem as a substitute for work.
- Score the table above.
- Write a short recommendation: top pick(s), why, main risks, suggested approach families to try first.
- 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.