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hkjtsgmc79-boop/colombo-odd-lean

Qianli Ma

Palomar Registrypalomar/PALOMAR-2026-08-27-000007Aug 27, 2026math.CAscore 0

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.

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