Escribe una PREreview

Prior work established Chollet’s conjecture for arbitrary complex Hermitian positive semidefinite matrices only for orders q ≤ 4. We prove Chollet’s permanent conjecture through order six: for 1 ≤ q ≤ 6 and complex Hermitian positive semidefinite q × q matrices A, B, per(A ◦ B) ≤ per(A) per(B). After reducing to the self-conjugate formulation, we encode a normalized border by two permanent polynomials whose relevant coefficients are represented by nonnegative sums of squared norms over orthogonal symmetric-tensor sectors. Evaluating the doubled polynomial along (a, b) = (t, t²) at t = √2 closes the induction, and a permutation-monomial Cauchy–Schwarz inequality transfers the result to arbitrary pairs.