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OpenAI reports: The chromatic number of the plane

The manuscript reports that five colors cannot suffice, implying that the plane’s chromatic number is six or seven if the result holds.

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Sources for this record

What was already known

The target is excluding every five-coloring, not finding a graph that is difficult for a coloring heuristic.

What changed and why it matters

Addresses a substantive research target in the specified setting; this is a reported advance whose correctness and novelty remain subject to mathematical assessment.

The AI contribution

OpenAI attributes the manuscript to an internal frontier model. This entry does not infer the exact human contribution to this individual result from the release-wide description.

Limitations

This would not determine whether six or seven colors are necessary. The lack of regularity assumptions is part of the claim. Preprint. AIProofWatch reviewed the source statement and scope, not the full proof, and has not independently run a formal checker.

Verification evidence

Evidence labels show what supports the claim. Importance rates its impact if correct.

Author claim

Reported theorem in the pinned manuscript. This records the claim, not an independent proof check.

Accessible artifact / proof

Manuscript proof is accessible. Formalization availability alone is not labelled as successful formal verification.

Correction and publication history

2026-10-11 · amendment

Editorial importance reassessment: rate the scoped impact if correct independently from verification. The claim, limitations, sources, and verification evidence are unchanged.

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