What was already known
The manuscript describes classical explicit-function depth-three lower bounds with an exponent proportional to √n and identifies the question of exceeding every such constant for one fixed language.
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
Breaks the square-root-constant barrier for unrestricted-fan-in depth-three Boolean circuits.
Limitations
The result does not give a fixed exponent n^(1/2+ε), nor a lower bound for unrestricted circuit depth.
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
- One fixed polynomial-time Boolean language has exact depth-three OR–AND–OR circuit size greater than 2^(A√n) for every fixed A>0 at all sufficiently large input lengths 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