OpenAI · 081-01 · 2026-09-24 · Real and complex analysis
Riesz transforms and uniform rectifiability in higher codimension
preprints/Riesz-transforms-and-uniform-rectifiability-in-higher-codimension-September-24-2026
Family 081. The David–Semmes Riesz-transform problem in higher codimension.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Resolves the remaining higher-codimension Riesz-transform rectifiability problem: for and , an -Ahlfors–David regular Radon measure on is uniformly -rectifiable whenever its -dimensional Riesz transform is uniformly -bounded over all positive hard truncations. The rectifiability bounds depend only on dimension, regularity and operator bounds.
We prove that an n-Ahlfors–David regular Radon measure on ℝd is uniformly n-rectifiable if its n-dimensional Riesz transform is uniformly bounded from scalar to vector-valued over all positive hard truncations, for integers d ≥ 4 and . This gives a positive answer to the David–Semmes Riesz-transform question in its remaining higher-codimension range. The conclusion gives uniform big pieces of Lipschitz images of Euclidean balls.
Preprint source and Lean scope
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This preprint is named in the Lean scope note for 081: Riesz transforms and rectifiability in higher codimension. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.