What was already known
Earlier lower bounds from Erdős–Rado, Schmidt, Berlekamp, and later constructions did not settle Erdős’s superexponential-growth question for fixed r, including two colors.
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
Answers Erdős’s superexponential-growth question with a bound uniform in the number of colors.
Limitations
The threshold K is existential, and the Lean scope does not include sharper intermediate estimates in the manuscript.
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
- There is an absolute K such that W(r,k)>k^(k⌊log₂ r⌋/100000) for all k≥K and r≥2, so W(r,k)^(1/k) diverges for each fixed r≥2.
- 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