Exact_Primality_Verification_for_the_Goldbach_Tensor.

This paper delivers a complete, self-contained proof that the Goldbach Spectral Tensor, equipped with a coupled primality sensor, admits only verified prime pairs and annihilates every composite channel identically. The external sensor ΨGoldbach(2n,p)=1−sgn⁡(ξ(p)+ξ(2n−p))\Psi_{\mathrm{Goldbach}}(2n,p) = 1 - \operatorname{sgn}(\xi(p)+\xi(2n-p))ΨGoldbach(2n,p)=1−sgn(ξ(p)+ξ(2n−p)) evaluates to unity if and only if both ppp and 2n−p2n-p2n−p are prime, releasing the full invariant energy density; otherwise the contribution is the absolute mathematical zero. The construction requires no iterative primality testing beyond the definition of the indicator ξ\xiξ.