A uniform quadratic wedge for consecutive Toeplitz minors of the Riemann ξ-coefficients

Let ⅛ ξ(½ + ix/2) = Σ_{k≥0} (−1)^k a_k x^{2k}, so that a_k > 0, and let D_{r,k} = det[a_{k+j−i}]_{i,j=0}^{r−1} be the consecutive Toeplitz minors of the coefficient sequence. The Riemann Hypothesis implies that (a_k) is a Pólya frequency sequence, hence D_{r,k} ≥ 0 for all r, k. Michałowski recently proved unconditionally that D_{r,k} > 0 whenever r ≥ 2 and k ≥ 10^18 r^3. We prove that D_{r,k} > 0 for all r ≥ 2 and k ≥ 10^11 r^2. The improvement comes from replacing the three-point log-quadratic comparison sequence by a four-point q-Pochhammer comparison sequence c_s = (1−α)^s/(α; q)_s that reproduces the normalized coefficients at four consecutive indices exactly. The reversed Hankel block of this reference is diagonally congruent to a matrix with an exact q-Pascal LDL^T factorization (a consequence of the q-Chu–Vandermonde summation) with alternating pivots, so the dilation/whitening argument applies to it unchanged, while the logarithmic mismatch now has four interpolation zeros. The weighted remainder therefore starts at fourth order and scales like r^2/k instead of (r^3/k)^{1/2}. The only analytic inputs are Michałowski's all-degree Taylor bound for log a and the Liu–Mao asymptotic for the log-curvature of (a_k); all remaining constants are certified in interval arithmetic. Verification code: see the related software record. AI models used in the preparation of this work: Astra (GPT, OpenAI) and Claude (Anthropic).