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arXiv · 2607.22398

A counterexample for the polar conjecture of Spencer-Brown

Scott Baldridge·Louis H. Kauffman·Ben McCarty
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Abstract

In 1976, George Spencer-Brown announced a proof of the four color theorem, using operations on Tait colorings for trivalent plane graphs. In subsequent work he formulated these operations in terms of an algorithm that he called a parity-pass and claimed that when the parity pass algorithm is performed on a non-polar pentagon region, it necessarily terminates in an edge coloring that is extendable to the entire graph. We provide here a counterexample to show that this claim is false. We then raise questions related to the existence of this sort of counterexample.

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Scott Baldridge, Louis H. Kauffman, Ben McCarty. 2026-07-24. A counterexample for the polar conjecture of Spencer-Brown. https://arxiv.org/abs/2607.22398

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