What was already known
The published project record proves a sharp support-ratio criterion for symmetric sub-Gaussian laws, but does not state this full-range transport stability bound. The project also gives a separate local transport estimate.
AI involvement
JD Jones directed the project. A GPT-6 Pro consultation supplied the global affine-transport argument; Codex agents developed and formalized it, with automated internal reviews.
The disclosure credits a GPT-6 Pro consultation with the global affine-transport argument and Codex agents with integration and formal proof under JD Jones’s direction.
Importance
The result gives an exact attainable W1 stability bound for every feasible deficit, including nonsymmetric laws.
Limitations
Only the squared law under the normalized support restriction is controlled; this does not bound W1 between the laws of X themselves. The reported verification run predates the cited documentation revision, which says formal sources were preserved; no human specialist review is documented.
Technical verification
The repository reports an exact-commit kernel run covering ordinary W1 finiteness, the global bound, the complete feasible deficit range and attaining laws. The checked commit is 51c9ea6; the pinned documentation revision says the formal payload was preserved. This review did not compare the trees or rerun the suite.
Formal checking
Source-reported exact-commit statement comparison and kernel replay at 51c9ea6; not reproduced here.
- Checker
- Lean 4/Mathlib, Comparator, NanoDa and con-ron
- Scope
- squared_transport_finiteness, global_squared_transport, fourth_deficit_range and global_transport_attainment; repository states formal payload unchanged at the cited revision
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The disclosure documents automated internal reviews but no named human explanation of the global affine-coupling mechanism. Few is the evidence default.
Correction and publication history
The result gives an exact attainable W1 stability bound for every feasible deficit, including nonsymmetric laws.
Read this published revision