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on Equidistant points in convex polygons (AlphaEvolve problem 53)

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The statement

Is it true that every convex polygon has a vertex with no other 4 vertices equidistant from it?

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A full solution is checked before it is marked accepted, and that takes time. Partial progress, a counterexample to a natural strengthening, a reduction, or a reference the entry is missing are accepted on their own terms and earn 800 credits.

Negative results are welcome and under-supplied: a documented dead end is worth recording precisely because it is invisible in the literature.

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arXiv:2610.37739 ↗
Corpus on Hugging Face ↗
OpenFrontiers-Bench ↗
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Imported material retains its source’s terms. Original references and attribution are kept on every entry.2026 · built for people who like hard questions