Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 262-02. Sharp one-dimensional Lieb–Thirring inequalities for matrix potentials
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OpenAI@2026-10-07#rem:oai-p-262-02
Authors: OpenAI. Family 262.
Title: Sharp one-dimensional Lieb–Thirring inequalities for matrix potentials.
Abstract: We prove the sharp one-dimensional Lieb–Thirring inequality for every finite matrix size and every exponent $1/2{}lt {}gamma{}lt 3/2$. The optimal constant is the scalar one-bound-state constant, independently of the matrix size. The inequality bounds the full sum of negative eigenvalue moments for every measurable Hermitian positive semidefinite potential W satisfying ${}int_{}mathbb R{}mathop{{}mathrm{tr}}{}nolimits (W{}{{}gamma+1/2}){}lt {}infty$. The matrices may have arbitrary rank and need not commute at different points.
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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