What was already known
Deterministic polynomial-time white-box noncommutative-rank tests were known. Garg, Gurvits, Oliveira and Wigderson asked for a black-box singularity construction.
AI involvement
OpenAI credits its internal model with the source manuscript and its rational-formula construction. The affine-pencil deduction has no separately documented human origin.
OpenAI authorship and model-production provenance cover the source manuscript and its pencil corollary; autonomous prompting history is unavailable.
- Supporting source (github.com) — Model-production and verification account
Importance
The affine-pencil corollary would give a deterministic rational black-box test for this stated question.
Limitations
The result does not cover arbitrary coefficient fields or circuit black boxes. Lean checks the parent rational-formula hitting-list theorem; no complete check of the pencil and rank corollaries is documented.
Technical verification
The cited Lean development proves the parent rational-formula hitting-list theorem with exact domain and polynomial resource bounds. The black-box homogeneous-pencil and rectangular-rank deductions are stated in the manuscript, but no matching completed formal or human check of those corollaries is documented.
Formal checking
Lean proof of OAI.RationalHitting.main in the cited proof module
- Checker
- Lean 4 kernel, as reported by the OpenAI math release
- Scope
- The parent polynomial-time rational hitting-list theorem for admissible nonzero rational formulas
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
No named human explains the new universal pencil and rank-detection construction. Few is the evidence default.
Correction and publication history
The affine-pencil corollary would give a deterministic rational black-box test for this stated question.
Read this published revision