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Erdős Problem #1151

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erdos-1151Analysisposed by Paul Erdős, 1999recorded: candidate

1 attempt · 1 machine check · no person has looked

Statement

Let Lnf\mathcal{L}^nf be the Lagrange interpolation polynomials of a continuous ff on the Chebyshev nodes. Prove that, for any closed A[1,1]A\subseteq [-1,1], there exists a continuous function ff such that AA is the set of limit points of Lnf(x)\mathcal{L}^nf(x).

Context

An elementary solution via a primitive-row decomposition of the Chebyshev-node measures; the main theorem is formalized in Lean, but erdosproblems.com still lists the problem open

A numbered problem from the Erdos catalog: real and documented, with a specialist audience. Checked against erdosproblems.com: no prize attached and a modest reference trail, so it sits at the band's baseline.

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Projects

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Interest

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Attempts

1 attempt

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  • #1

    Attempt 1

    constructionGPT-5.5 Pro, Codex with Przemysław Chojecki, Allen Hart ·
    AI involvement
    ai co developed
    a person and a model developed the result together.
    models
    GPT-5.5 Pro, Codex
    people
    Przemysław Chojecki, Allen Hart

    The solution was obtained with GPT-5.5 Pro using an explicit primitive-row decomposition of the Chebyshev-node measures; Theorem 1.1(a), the main contribution, was subsequently formalized largely autonomously by ChatGPT and Codex.

    An elementary solution via a primitive-row decomposition of the Chebyshev-node measures; the main theorem is formalized in Lean, but erdosproblems.com still lists the problem open

    Reviews

    0 human reviews · 1 machine check

    No person has reviewed this attempt. 1 machine check below — a machine check is not human verification.

    • Machine check · not human verification

      machine: correct

      Recorded from Lean ·

      scope Lean formalization of the result

      Theorem 1.1(a), the main part of the contribution, is formalized in Lean and the formalization was confirmed correct on the forum; part (b) is unformalized because it depends on an Erdős result absent from mathlib. erdosproblems.com still lists the problem open.

      No ProbXiv account is credited for this check. Nobody has put their name to it, so it carries no personal accountability and does not count as verification by a person.

    Endorsements

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    Discussion of this attempt

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Discussion

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