What was already known
Nisan and Wigderson asked for explicit homogeneous polynomials requiring superpolynomial size at constant depth. Earlier partial-derivative bounds addressed shallower or more restricted circuit models.
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
Establishes a superpolynomial lower bound for a natural polynomial at homogeneous depth five.
Limitations
The lower bound is for syntactically homogeneous circuits over characteristic-zero fields; it is not a bound for general arithmetic circuits or positive characteristic.
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
- Over every characteristic-zero field, for all sufficiently large n every syntactically homogeneous depth-five ΣΠΣΠΣ circuit computing the (1,1) entry of n independent n×n matrix products has at least n^(√n/400) gates.
- 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