select-open-problem

# 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: ```markdown ## 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.