What was already known
Earlier work supplied a field criterion and an at-most-six-point result. Pálvölgyi ruled out one non-Ramsey certificate for a wider class without proving this theorem.
AI involvement
Claude agents developed the proof and Lean port under Will Strinz’s direction. Strinz reviewed the note as owner and chose the release scope; earlier field-criterion results remain separately credited.
Claude generated the central new theorem's proofs and development under Strinz's direction; the precise independence of the initial idea is not documented for this theorem alone.
- Supporting source (palomar-registry.org) — Assigned registry pointer and version; page was not retrievable in this review
Importance
The theorem adds an unbounded-size class of planar Ramsey configurations.
Limitations
Reported Lean, Comparator and negative-control checks cover this theorem. A separate Möbius-image extension uses another theorem by hand. No human expert review or explanation of the central certificate is documented, and the novelty search is incomplete.
Technical verification
The cited disclosure reports kernel and Comparator checks of the two theorem statements at Lean 4.35.0-rc2, standard-axiom audits, and rejected negative controls. The original rope was also checked at Lean 4.34.1. This covers B(b), not the by-hand Möbius-image combination or the claimed sharpness of three. The reported runs were performed by AI agents; this review did not reproduce them.
Formal checking
Lean 4.35.0-rc2 kernel checking, standard-axiom audit, statement and definition comparison against Challenge.lean, and refusal of five negative controls
- Checker
- Lean, NanoDa and con-ron kernels through Comparator on a GitHub runner
- Scope
- Theorem B(b) in OpenAI and Mathlib vocabulary for planar concyclic configurations with at most three nonalgebraic-coordinate points
- Basis
- Reported by the linked checker
Fresh-runner Comparator at Lean 4.34.1 with ten expected checks; the port compares statements with the originating challenges
- Checker
- Stock Comparator with Lean kernel on the originating rope AV5
- Scope
- The same B(b) statements and proofs before the module-system port
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Default for missing evidence of human explanation: the hand proof and fidelity notes were AI-produced or AI-reviewed, while Strinz's owner review was not line by line. No human expert explanation of the certificate argument is documented.
Correction and publication history
A distinct theorem for arbitrarily large concyclic sets with at most three nonalgebraic points.
Read this published revision