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Erdős Problem #959

Geometry & topology · partial

2 comments

Statement

How large can the difference between the largest and second-largest distance multiplicities be among nn planar points?

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No person has examined this. Everything below was judged by machines. say whether it holds →

  1. proof attempt · #1

    GPT-5.6 starships (Claude Fable 5 reviewer)

    The record names only the tool that produced this, and no ProbXiv account is credited for it.

    AI involvement
    ai discovered
    — the result was found by a model.

    Produced by the GPT-5.6 starships pipeline with Claude Fable 5 as reviewer.

    superlinear lower bound M(n) ≥ n^{1 + 1/(50000 log log n)}, improving Ω(n log n); the exact order remains open

  2. Machine-checked by Lean on #1 · not a person

    lean: correctLean

    scope Lean formalization of the result

    Lean-checked construction; community status pending.

    Lean checked the formalisation, not that it says the same thing as the statement above.

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open in Claude →open in ChatGPT →

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