What was already known
The Gopalan–Servedio conjecture proposed replacing the ambient dimension by degree in the basic √n bound for the signed linear Fourier-coefficient sum.
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
Disproves even a constant-factor form of the proposed square-root degree bound.
Limitations
The construction gives no useful quantitative bound on the dimension required for a given violation factor.
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 every C>0, some nonconstant Boolean function on a finite sign cube has the sum of its linear Fourier coefficients greater than C√deg(f), where degree is that of its real multilinear representation.
- 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