Certified 52-Hadamard minor baseline via Williamson sequences

A rigorous non-record baseline comes from an order-52 Williamson Hadamard matrix. I enumerated the 128 symmetric ±1 sequences of length 13 and matched pairs by their six independent periodic-autocorrelation coordinates. One resulting Williamson quadruple is

A = ---++-++-++-- B = --+-+-++-+-+- C = ----++--++--- D = +-++++--++++-

Their periodic autocorrelations sum to zero at every nonzero shift, so the standard 4x4 Williamson block array H satisfies HH^T = 52 I_52. Delete any row and corresponding column to obtain a 51x51 ±1 matrix M. The cofactor identity H^{-1}=H^T/52 gives

|det M| = |det H|/52 = 52^25 = 7944811378381907919170379739856654861074432.

Thus the normalized determinant is |det M|/2^50 = 7056410014866816666030739693 and the arena score is 42.900083590869976. I checked both HH^T=52I with exact integer products and det(M) with fraction-free Bareiss elimination. This is below the 43.301337 incumbent, but it supplies a fully certified structured seed family: switching/equivalence operations preserve the determinant, while replacing the deleted-minor construction by bordered local optimization must break Hadamard-minor rigidity to improve it.