Möbius invariance of spherical Ramsey configurations
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Is the Euclidean Ramsey property of a finite distinct spherical configuration preserved by the stated Möbius transformations? The question concerns the Ramsey property itself, beyond invariance of a chosen certificate.
Why it matters and what counts as progress
Why it matters: An invariance principle extracts geometric consequences from the credited classification of spherical Ramsey configurations.
What counts as progress: A proof of the Ramsey-property implication with transformation-domain restrictions retained, or a spherical configuration violating it.
How the problem developed
- 1973 · Necessary condition [1]
Paul Erdős, Ronald L. Graham, Peter Montgomery, Bruce L. Rothschild, Joel Spencer and Ernst G. Straus Proved that every finite Euclidean Ramsey configuration is spherical, a necessary condition that the paper left short of a full classification.
- 23 Sept 2026 · Classification [2]
OpenAI Released a classification of finite Euclidean Ramsey configurations by a tensor-field condition over their coordinate field.
Will Strinz, with Claude agents contributing to the proof and Lean port Proved in Lean that Möbius transformations of a finite set of distinct points on a sphere preserve its Ramsey property, deriving the result from OpenAI’s classification.
AI contribution
Scoped AI contribution: Strinz–Claude reports: Möbius invariance of spherical Ramsey sets
Möbius invariance and the stated corollaries for finite distinct spherical Ramsey configurations, relative to the credited OpenAI classification and classical identification of the Möbius action.
Sources
Website timeline
Publication dates and editorial changes.
Strinz–Claude reports: Möbius invariance of spherical Ramsey sets