Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: Family 373. Nonattainment in three-marginal Coulomb transport
Family claims › Partial differential equations · lines 2411–2416
OpenAI@2026-10-07#rem:oai-373
An optimal three-particle Coulomb configuration need not be a deterministic function of the first particle, even for smooth identical spatial densities. The Monge and Kantorovich infima agree, but the Monge infimum is not attained. The same phenomenon occurs for every inverse-power Riesz exponent in each dimension at least two, with a suitable density in each case.
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 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