Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 262-01. Equality cases in the sharp one-dimensional matrix Lieb–Thirring inequality
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OpenAI@2026-10-07#rem:oai-p-262-01
Authors: OpenAI. Family 262.
Title: Equality cases in the sharp one-dimensional matrix Lieb–Thirring inequality.
Abstract: We classify all equality cases in the sharp one-dimensional Lieb–Thirring inequality for every finite matrix size and $1/2{}lt {}gamma{}lt 3/2$. For measurable Hermitian positive semidefinite potentials W with ${}int_{}mathbb R{}mathop{{}mathrm{tr}}{}nolimits (W{}{{}gamma+1/2}){}lt {}infty$, equality holds precisely for direct sums, in one constant unitary basis, of scalar one-bound-state solitons and zero channels. The nonzero solitons may have independent scales and centers.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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