Kuperberg's Six-Cylinder Conjecture
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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.
Context
A known 1990 packing conjecture with decades of attention.
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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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