{"id":"palomar/PALOMAR-2026-08-27-000007","url":"https://github.com/hkjtsgmc79-boop/colombo-odd-lean/tree/250ff20a0c2edae8f37e5733b439bf9128a877bd","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-08-27-000007-v1.json","repo":"https://github.com/hkjtsgmc79-boop/colombo-odd-lean","tags":["math.CA","math.CO","msc:15A15","msc:15B48","msc:41A15","matrix-theory","lean","total-positivity","determinants"],"score":0,"title":"hkjtsgmc79-boop/colombo-odd-lean","trust":"high","domain":"math.CA","source":"palomar","authors":["Qianli Ma"],"reviews":0,"subject":"math.CA","summary":"This project formalizes the odd-exponent branch of Colombo's determinant problem for even matrix size. For every m at least one, every strictly increasing x : Fin (2*m) → ℝ, and every r at least m - 1, it proves that the determinant of the matrix with entries (x_j - x_i)^(2*r+1) is strictly positive. The proof development passes through paired truncated-power determinants, B-spline and Marsden factorization, total nonnegativity, Volterra propagation, and Beta--de Bruijn and Pfaffian identities.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-08-27","reactions":{},"formalized":true,"formalizes":[{"title":"Colombo's Determinant Problem","identifier":"doi:10.5281/zenodo.21993537","relationship":"formalizes"}]}