What was already known
Earlier lower bounds were quadratic in m for this measure; the manuscript claims a cubic asymptotic bound.
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
Improves the known asymptotic lower-bound order for exact and border determinantal representations of the permanent.
Limitations
The selected claim concerns determinantal complexity. The paper’s algebraic-branching-program consequences are outside the pinned Lean scope and are not included in this assessment.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note gives an explicit cubic lower bound for exact and border affine-linear determinant representations for m≥1408.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- The complex border determinantal complexity of the m×m permanent is Ω(m³), allowing affine-linear determinant representations and coefficientwise limits.
- 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