Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: Family 366. The planar Mumford–Shah regularity conjecture
Family claims › Partial differential equations · lines 2369–2374
OpenAI@2026-10-07#rem:oai-366
Resolves the interior regularity conjecture for reduced absolute planar Mumford–Shah minimizers with bounded fidelity data. Locally, the closed discontinuity set is a arc, a regular crack tip, or three arcs meeting at ; only finitely many global connected components meet any compact interior region.
The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.
Nearby in this section
- remark: Remark: Family 362. Global smoothness for relativistic Vlasov–Maxwell
- remark: Remark: Family 363. Boltzmann nonuniqueness with exact local conservation
- remark: Remark: Family 364. Kinetic limits and fluctuations over the Boltzmann lifespan
- remark: Remark: Family 365. Joint metric and connection recovery from one boundary patch
- remark: Remark: Family 367. The critical dimension for the one-phase Bernoulli problem
- remark: Remark: Family 368. The three-dimensional Ball–Evans approximation problem
- remark: Remark: Family 369. The hot spots conjecture for simply connected planar domains
- remark: Remark: Family 370. The subcritical Lane–Emden and Hénon–Lane–Emden conjectures