Make a mathematical idea easier to check

Using Claude where available: Supply a small problem, known baseline and research limits to separate conjectures, candidate solutions and checking methods.

Execution environment and usage

AI / software

General text chat (example: Claude); original stack retained below

Where to operate

A general text conversation, for example a new chat at claude.ai where available. This is the suggested exercise entry, not an attribution of the original tool.

Getting started

  1. Open claude.ai or another text-chat tool you are authorized to use.
  2. Convert the required material below into readable, source-labeled text and paste only necessary authorized excerpts.
  3. Enter the case prompt and check the resulting draft against the original material.

Setup and plan requirements

Small problem, known baseline, assumptions and checking method. Formal verification separately needs proof files, Lean version and libraries. Text chat requires an available account and allowance; Claude has location and age requirements. Manually transcribe images or scans first rather than assuming text chat can inspect the original file.

Prompt portability limits

Research-record planning is portable; neither proofs nor code execution are established by a textual plan.

Usage limitations

This review performed no installation, hands-on test or regional-availability check. arXiv abstract describes Station open-world multi-agent environment; no experiments or proof artifacts rerun.

Environment sources

適用情境 / When to use

Use the record for independent recomputation or review. State assumptions, counterexamples and missing evidence. A written record is neither an executed program nor a verified formal proof; those require their own tools and checks. Not every result was verified in Lean.

步驟 / Steps

  1. Choose a small problem with known answers and an explicit resource budget.
  2. Separate conjectures, candidate constructions, verification code and execution records.
  3. Have a qualified reader recompute counterexamples and inspect proof assumptions.

提示詞 / Prompt

For [small mathematical problem/known baseline/resource budget], design a research record. Separate conjectures, candidate constructions, checking methods and result evidence. Identify assumptions and counterexample boundaries. List independently checkable artifacts; do not claim an open problem is solved or invent verification results.

留意事項 / Cautions

  • Fluent reasoning is not a proven theorem.
  • Label unexecuted verification as unexecuted.

來源限制 / Evidence limits

Only the abstract and version record were checked; experiments and proofs were not rerun. Findings concern the authors’ problems and experimental conditions, not arbitrary open problems. No peer-review claim is made.

流程說明 / Workflow note

These steps and prompts are original, untested exercises by this site, not the author’s verbatim workflow. Reported results do not guarantee exercise outcomes.

原始工具組合 / Original tool stack

Station; multiple model families; Lean

Source publication date: 2026-08-24

Source checked: 2026-10-20

Autonomous Mathematical Discovery in an Open-World Multi-Agent Environment