The Taylor coefficients of the Riemann xi-function form a Pólya frequency sequence of order 3

Let ξ(s) be the Riemann xi-function and write ξ(1/2 + z) = Σ(n ≥ 0) γ_n z^(2n) / n!, with γ_n > 0. This manuscript proves, unconditionally, that the normalized sequence a_n = γ_n / n! is a Pólya frequency sequence of order 3: every minor of order at most 3 of its one-sided Toeplitz matrix is nonnegative. The proof combines a structural reduction for consecutive-row order-3 minors, a Grassmann–Plücker completion theorem, certified interval-arithmetic checks for 2 ≤ n ≤ 126, and an analytic tail argument for n ≥ 127. The accompanying reproducible artifact uses pinned dependencies, SHA-256 manifests, fail-closed checks, and deterministic replay. The packaged archive is byte-reproducible between Windows and Ubuntu and has passed an independent GitHub Actions replay on Ubuntu 24.04 with Python 3.11. This result does not prove the Riemann Hypothesis. It does not claim PF4, PF-infinity, or hyperbolicity of Jensen polynomials in every degree.