What was already known
Deterministic polynomial-time white-box tests were known. For unrestricted inverse nesting, the cited black-box rational-formula hitting sets were quasipolynomial in size.
AI involvement
OpenAI authors the manuscript and credits its internal model with the construction and proof artifacts. No human origin for the central hitting-list method is documented.
OpenAI authorship and the release's model-production account support AI leadership; autonomous session provenance is absent.
Importance
The construction would reduce the black-box list size and generation time to polynomial bounds for the stated rational formulas.
Limitations
Inverse depth and rational constant heights are unrestricted. Arbitrary circuits and coefficient fields other than Q are outside the claim.
Technical verification
The cited Lean proof module states OAI.RationalHitting.main for a fixed finite-state machine, exact inverse-domain semantics, polynomial bit time, output length and matrix dimension, and an invertible hit for each admissible nonzero formula. This is source-reported machine verification, not a compilation or independent audit here.
Independent checking
Lean proof OAI.RationalHitting.main with the RationalHitting comparator statement and finite-state implementation
- Checker
- Lean 4 kernel, as reported by the OpenAI math release
- Scope
- Polynomial-time rational matrix hitting lists with exact inverse domains and invertible hits for all bounded-size admissible nonzero formulas over Q
- Basis
- Reported by the linked checker
Human understanding
No named human explanation of the model's Wronskian expansion, division-algebra lift and rational generator is documented. Few is the evidence default.
Correction and publication history
The construction would reduce the black-box list size and generation time to polynomial bounds for the stated rational formulas.
Read this published revision