What was already known
Erdős, Faudree, Rousseau, and Schelp conjectured the formula. Prior work covered n≤7 and ranges such as m≥n²−2 or sufficiently large m relative to n, leaving the full parameter range open.
AI involvement
OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.
OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.
Importance
Resolves the cycle–clique Ramsey conjecture for every parameter pair.
Limitations
The claim concerns an exact cycle C_m, not an arbitrary cycle of length at least m; the manuscript reports additional exact finite case checking for its proof.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned OpenAI Lean scope note identifies this selected claim.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- For all integers m≥n≥3 except (m,n)=(3,3), R(C_m,K_n)=(m−1)(n−1)+1; the exceptional value is R(C₃,K₃)=6.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.
Correction and publication history
Primary manuscript, attribution, prior-work, and scoped checking review for non-notifying local inclusion.
Read this published revision