OpenAI · 366-01 · 2026-09-24 · Partial differential equations
Interior regularity of planar Mumford–Shah minimizers
preprints/Interior-regularity-of-planar-Mumford-Shah-minimizers-September-24-2026
Family 366. The planar Mumford–Shah regularity conjecture.
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 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.
We prove the interior regularity assertion of the planar Mumford–Shah conjecture for reduced absolute minimizers with bounded fidelity data. Every interior point of the closed discontinuity set has a neighborhood consisting of a arc, an arc ending at that point, or three such arcs meeting at 120 degrees. Only finitely many global connected components meet any relatively compact open set.
Preprint source and Lean scope
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