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An Explicit Quintic Obstruction for the Riemann Theta Kernel
We exhibit an explicit polynomial square on which the signed derivative functional of a fixed-center Riemann theta product is negative. At the center s₀ = ¼ log(13/(4π)), the polynomial P(X) = X⁵ − 264X³ + 10952X satisfies ℒₛ₀(P²) ≤ −1,351,625,671. The certificate uses rational interval arithmetic for derivatives through order ten and an explicit bound on the complete infinite theta tail. It follows that the normalized product at this center is not positive definite and that its odd derivative Hankel block is indefinite.