Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 158-01. The Euclidean plane is not five-colorable
Manuscript map · lines 5415–5424
OpenAI@2026-10-07#rem:oai-p-158-01
Authors: OpenAI. Family 158.
Title: The Euclidean plane is not five-colorable.
Abstract: We prove that every coloring of the Euclidean plane with five colors has a monochromatic unit-distance pair, with no regularity assumption on the color classes. Consequently, the chromatic number of the plane is either six or seven.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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