OpenAI · 368-02 · 2026-09-24 · Partial differential equations
Strong diffeomorphic approximation in three dimensions for p>2
preprints/Strong-diffeomorphic-approximation-in-three-dimensions-for-p-gt-2-September-24-2026
Family 368. The three-dimensional Ball–Evans approximation problem.
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 three-dimensional Ball–Evans approximation problem: every homeomorphism between arbitrary bounded domains in , for , is a strong limit of smooth diffeomorphisms onto the same target.
We resolve the three-dimensional Ball–Evans approximation problem for every finite p > 2. Every homeomorphism between arbitrary bounded domains in ℝ3 can be approximated strongly in by smooth diffeomorphisms onto the same target.
Preprint source and Lean scope
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No Lean scope note is in the repository for this family. The preprint source below is still the full manuscript, not only the abstract. No compilation is asserted.