Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: Family 365. Joint metric and connection recovery from one boundary patch
Family claims › Partial differential equations · lines 2363–2368
OpenAI@2026-10-07#rem:oai-365
Zero-frequency measurements on any nonempty open boundary patch determine a smooth metric and smooth unitary connection on a trivial Hermitian rank-two bundle over a compact connected manifold of dimension at least three, up to diffeomorphism and gauge fixed on that patch. Inputs and observations use the same patch. In contrast, distinct uniformly positive bounded measurable scalar conductivities on a three-dimensional ball can have identical full-boundary data.
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 366. The planar Mumford–Shah regularity conjecture
- 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