An explicit uniform cubic wedge for consecutive Toeplitz minors of the Riemann xi coefficients

Let (a_k) be the positive coefficient sequence of the normalized Riemann xi-function, and let D_{r,k} denote its consecutive Toeplitz minors.

The Riemann Hypothesis is equivalent to (a_k) being a Polya frequency sequence of infinite order, and hence to nonnegativity of all Toeplitz minors.

We prove that D_{r,k} > 0 for every r >= 2 and k >= 10^18 r^3.

This gives an explicit cubic tail scale uniform in r, in contrast with Katkova's fixed-order asymptotic positivity.

The proof does not use numerically verified zeros of the Riemann zeta-function.

It combines a certified complex saddle-point analysis of the moment transform, an exact q-Pascal dilation semigroup controlling every degree simultaneously, and a weighted Banach-algebra majorant for the nonlinear remainder, closed by an inertia-preservation argument.

All analytic constants are certified with directed rounding in Arb ball arithmetic, and all algebraic identities are verified in exact rational arithmetic.

The ancillary files reproduce every certificate.

The result concerns only the tail regime k much larger than r^3 and makes no progress on the Riemann Hypothesis, which concerns the complementary region.