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Lassak's Area Bound for Reduced Planar Bodies

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lassak-reduced-body-areaGeometry & topologyposed by Marek Lassakrecorded: disproved

1 attempt · 1 machine check · no person has looked

Statement

Lassak conjectured that a reduced planar convex body of thickness Δ\Delta has area at most (π/4)Δ2(\pi/4)\Delta^2, the value for the disc. False: an explicit reduced body of thickness 11 has area 0.786215>π/4=0.7853980.786215\ldots > \pi/4 = 0.785398\ldots, given by a closed-form support function.

Context

A named conjecture on reduced bodies, a standard object in convex geometry where the disc was the natural extremal guess.

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Attempts

1 attempt

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  • #1

    Attempt 1

    constructionGPT-5.5 Pro, Claude Opus 4.8 with Scott Duke Kominers ·
    AI involvement
    ai assisted
    a person led the work and used a model along the way.
    models
    GPT-5.5 Pro, Claude Opus 4.8
    people
    Scott Duke Kominers

    The acknowledgement credits the models with assisting the computations and coding in preparing the article, without separating which step came from where, so the lowest tier applies.

    Reviews

    0 human reviews · 1 machine check

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    • Machine check · not human verification

      machine: correct

      Recorded from VibeMathed site check ·

      scope Reproduction by the VibeMathed site

      The counterexample is given by an explicit support function with the area stated to six decimal places, so the refutation reduces to evaluating a closed-form integral. Single-author arXiv preprint, not peer-reviewed.

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