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The Odd Area Conjecture for Unit Disks

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odd-area-unit-disksGeometry & topologyposed by conjectured in the discrete geometry literaturerecorded: disproved

1 attempt · 1 machine check · no person has looked

Statement

For a family FF of an odd number nn of unit disks in the plane, let OA(F)\mathrm{OA}(F) be the area covered by an odd number of disks. It was conjectured that OA(F)≥π\mathrm{OA}(F) \ge \pi, the area of a single disk. False: configurations exist with smaller odd area.

Context

A clean and much-repeated conjecture about odd covering area of unit disks, the kind of statement that looks obviously true until it is not.

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Attempts

1 attempt

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  • #1

    Attempt 1

    computationAlphaEvolve with Stefan Steinerberger ·
    AI involvement
    ai co developed
    — a person and a model developed the result together.
    models
    AlphaEvolve
    people
    Stefan Steinerberger

    The counterexample configurations, at 51 and 151 disks, were investigated using AlphaEvolve. The author notes the behaviour differs between small and large numbers of disks, which is what the search surfaced.

    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 refutation is explicit finite disk configurations, so the odd area is a direct computation. Single-author arXiv note, not peer-reviewed.

      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.

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