What was already known
The exact-extremizer form of the Gotsman–Linial conjecture had counterexamples, but the manuscript says the asymptotic O(d√n) bound remained 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
Proves the asymptotic Gotsman–Linial sensitivity bound uniformly in degree and dimension.
Limitations
The sign convention assigns +1 at zero. The result does not identify exact extremizers or settle the refuted stronger formulation.
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
- Every degree-at-most-d real polynomial threshold function on the uniform n-dimensional Boolean cube has average sensitivity at most 8d√n for 1≤d≤n.
- 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