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Kuperberg's Six-Cylinder Conjecture

Geometry & topology · posed by Włodzimierz Kuperberg, 1990 · solved

1 comment

Statement

How many pairwise non-overlapping infinite circular cylinders of unit radius can simultaneously touch a unit ball? Kuperberg conjectured in 1990 that the maximum is six.

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

  1. computation · #1

    Ivan Matić and Radoš Radoičić, using Claude (version not disclosed)

    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 proof reduces the upper bound to 2,954,984 exact rational-polynomial cases, each an elementary arithmetic check by a deterministic verifier; the reduction and certificates were developed with Claude.

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