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The Odd Area Conjecture for Unit Disks

Geometry & topology · posed by conjectured in the discrete geometry literature · disproved

2 comments

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.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. computation · #1

    Stefan Steinerberger, using AlphaEvolve

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    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.

  2. Recorded elsewhere on #1 · not checked here

    recorded: correctVibeMathed 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 Single-author arXiv note, not peer-reviewed.

    Repeated from the source; nothing was checked here.

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