What was already known
Stein’s directional singular-integral question asked for weak-(2,2) control at a scale governed by the reciprocal Lipschitz seminorm; earlier results treated restricted vector-field structures.
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
Gives an affirmative strong-L² form of Stein’s short-scale directional Hilbert-transform question.
Limitations
The selected estimate is short-scale; the constant-field K=0 case and all scales are not part of this formalized statement.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note covers short-scale uniform L² hard-truncation bounds and, at normalized scale, weak-(2,2) and principal-value estimates.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- For a planar Lipschitz unit vector field with Lipschitz constant K>0, short Hilbert transforms with outer scale at most 1/(10⁶K) have a universal L² bound independent of the inner hard truncation, including fields depending on both coordinates.
- 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