OpenAI · 262-03 · 2026-09-23 · Mathematical physics
Sharp one-dimensional Lieb–Thirring constants
preprints/Sharp-One-Dimensional-Lieb-Thirring-Constants-September-23-2026
Family 262. Sharp one-dimensional Lieb–Thirring inequalities.
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
Proves the sharp one-dimensional Lieb–Thirring inequality for and arbitrary finite-matrix potentials with : the optimal constant is the scalar one-bound-state value, independent of matrix size. All equality cases are direct sums, in one constant unitary basis, of scalar solitons with independent scales and centers, and zero channels.
We resolve affirmatively the remaining cases of the scalar one-dimensional Lieb–Thirring conjecture: for every , the optimal constant is the one-bound-state constant. The estimate holds for every nonnegative potential in , with all negative eigenvalues included.
Preprint source and Lean scope
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This preprint is named in the Lean scope note for 262: Sharp finite-matrix Lieb–Thirring inequalities and all equality cases. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.