What was already known
The codimension-one implication had been proved, while the remaining higher-codimension case of the David–Semmes Riesz-transform question lacked that conclusion; a stronger variation-operator hypothesis was previously known to imply rectifiability.
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
Settles the remaining higher-codimension range of the David–Semmes Riesz-transform criterion.
Limitations
The result needs Ahlfors–David regularity and a uniform L² bound over all positive hard truncations. Variation and principal-value corollaries are outside the selected Lean scope.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note gives quantitative big pieces of Lipschitz images from the stated uniform Riesz-transform bound, including for unbounded support.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- For d≥4 and 2≤n≤d−2, an n-Ahlfors–David regular measure in Rᵈ with uniformly L²-bounded positive hard truncations of its n-dimensional Riesz transform is uniformly n-rectifiable.
- 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