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 for this record

What was already known

OpenAI’s result 172 supplied the classification and its formal proof. Earlier work established algebraic spherical cases and certificate-level invariance; the project’s claimed advance is invariance of the Ramsey property itself.

AI involvement AI-led

Strinz directed the work. Claude agents produced the proofs, ported the supporting OpenAI development and performed checks; an exploratory Claude conversation produced the theorem and argument.

Strinz’s disclosure locates Theorem C and its proof in a Claude conversation and allocates proof production to agents; OpenAI’s classification remains a separately credited foundation.

Importance Notable

Extracts a geometric invariance principle from the existing classification and makes the stated implication formally checkable.

Limitations

The author describes this as a short consequence of OpenAI’s classification, not an independent replacement for it. Identification of the Lorentz model with the full Möbius group for sphere dimensions covered by d≥2 is cited rather than formalized; d=1 has a separate interpretation. No independent human expert review is reported. AIProofWatch has not rebuilt the formal development or audited the complete proof. Palomar reports mechanical checking of a pinned statement; its automated statement review is not human peer review. The reported date records this registry checkpoint; the earlier first-report date of the formalization has not been established.

Technical verification Formal (Lean)

A completed rigorous check is documented for the scoped statement. Palomar: Lean, NanoDa and con-ron (reported): ramsey_iff_ramsey_mobius_full and the three recorded corollaries at 52284ddf3db595776b0d651c844fbeaf7b34a641; finite distinct unit-sphere configurations and O(1,d) maps, using the standard axioms.

Formal checking

Registry-reported Comparator and kernel checking; not reproduced by AIProofWatch.

Checker
Palomar: Lean, NanoDa and con-ron (reported)
Scope
ramsey_iff_ramsey_mobius_full and the three recorded corollaries at 52284ddf3db595776b0d651c844fbeaf7b34a641; finite distinct unit-sphere configurations and O(1,d) maps, using the standard axioms.
Basis
Reported by the linked checker
Check date
2026-10-13
Evidence source

Checking a formal statement does not establish that it matches the original problem.

Human understanding Few

Few is the default when evidence for a higher level is insufficient. No sufficient account of a named human explaining the scoped central reasoning is established in this assessment. Missing disclosure is not evidence of little understanding.

Correction and publication history

2026-10-14 · publication

Source-statement, baseline, AI-role and verification-scope review, 14 October 2026. New curated contribution; eligible for matching consented digests.

Read this published revision