A computer-assisted proof of Kuperberg's six-cylinder conjecture

2026/07/27 by Ivan Matić, Rados Radoičić
Mathematics · #math.CO

paper · pdf

arxiv created 2026/07/29 · arxiv updated 2026/07/30

Abstract

We prove that at most six pairwise non-overlapping infinite unit cylinders can simultaneously touch a unit ball. Six is achievable, so the answer to Kuperberg's question is exactly six. The proof is computer-assisted in the following sense: the statement is reduced to a finite case analysis with 2,954,984 cases, and in each case a program verifies that one of three inequalities between explicit polynomials with rational coefficients holds throughout a box. Each case is an elementary arithmetic check, and the complete list of cases is provided with the paper.

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