# Select Open Problem

> 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.

- Skill: `meleantonio/select-open-problem` (Agent Skill)
- Install (CLI): `npx skillmds@latest add meleantonio/select-open-problem`
- Raw SKILL.md: https://api.skillmd.com/api/skills/meleantonio/select-open-problem/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: Coding & Dev Tools
- Author: meleantonio (https://skillmd.com/u/meleantonio)
- Updated: 2026-09-17
- Page: https://skillmd.com/skills/meleantonio/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.