What was already known
Earlier target-uniform results had weaker exponents or constants depending on nondegenerate atomic geometry. Letrouit conjectured a uniform square-root estimate for convex uniform sources, and had shown an obstruction above one-third for a nonconvex source.
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
Determines the exact uniform stability exponent and refutes the proposed square-root exponent.
Limitations
The constant depends on the fixed source body and target compact set, not on individual targets. Targets may be atomic or singular. Both the upper bound and sharpness are in the pinned Lean scope.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned solution proves the one-third upper bound and cube three-atom obstruction to every larger exponent.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- For the uniform measure on any compact convex body with nonempty interior in ℝᵈ, d≥2, and targets supported in one fixed compact set, the L² distance between their quadratic optimal maps is at most C times the one-third power of the targets’ 2-Wasserstein distance. No larger uniform exponent works in general, even for three-atom targets on a fixed cube.
- 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