{"id":"openai-math/Equality-cases-in-the-sharp-one-dimensional-matrix-Lieb-Thirring-inequality","pdf":"https://github.com/openai/math/blob/main/preprints/Equality-cases-in-the-sharp-one-dimensional-matrix-Lieb-Thirring-inequality-October-5-2026/sharp-one-dimensional-lieb-thirring-inequalities-matrix-potentials.pdf","url":"https://github.com/openai/math/tree/main/preprints/Equality-cases-in-the-sharp-one-dimensional-matrix-Lieb-Thirring-inequality-October-5-2026","tags":["functional-analysis","matrix-inequalities","spectral-theory"],"score":0,"title":"Equality cases in the sharp one-dimensional matrix Lieb–Thirring inequality","domain":"Mathematical physics","family":"262","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.MP","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-05","reactions":{},"formalized":false,"family_title":"Sharp finite-matrix Lieb–Thirring inequalities and all equality cases"}