{"id":"openai-math/Sharp-one-dimensional-Lieb-Thirring-inequalities-for-matrix-potentials","pdf":"https://github.com/openai/math/blob/main/preprints/Sharp-one-dimensional-Lieb-Thirring-inequalities-for-matrix-potentials-October-5-2026/sharp-matrix-lieb-thirring.pdf","url":"https://github.com/openai/math/tree/main/preprints/Sharp-one-dimensional-Lieb-Thirring-inequalities-for-matrix-potentials-October-5-2026","tags":["mathematical-physics","spectral-theory","matrix-analysis"],"score":0,"title":"Sharp one-dimensional Lieb–Thirring inequalities for matrix potentials","domain":"Mathematical physics","family":"262","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.MP","summary":"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.","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"}