Spectral Exclusion Results for Operators Whose Eigenvalue Multiset Would Equal the Riemann Zero Ordinates

We prove two spectral exclusion results showing that no operator in a natural geometric class can have its eigenvalue multiset equal to {gamma_n}, the positive ordinates of the nontrivial zeros of the Riemann zeta function. Theorem D: No positive classical elliptic pseudodifferential operator of order m > 0 on any closed smooth manifold of dimension d >= 1 has eigenvalue multiset {gamma_n}. The Weyl counting law forces a pure-power leading term N_H(T) ~ C_H * T^(d/m) in the eigenvalue counting function, while the zero-ordinate heat sum satisfies Z_zeta(t) ~ (1/(2*pi)) * t^(-1) * log(1/t) as t -> 0+, which has an unavoidable logarithmic factor incompatible with any pure-power Weyl law. Theorem D': The exclusion extends to the class C_sub of operators whose symbol has a classical positive elliptic principal part and strictly lower-order log-polyhomogeneous corrections (in the sense of Lesch 1999), via a min-max squeeze argument comparing heat-trace asymptotics. Both results are unconditional; neither assumes nor concludes the Riemann Hypothesis. The paper also includes a non-elliptic escape example showing the class boundary is sharp, and an open problem section on symbol classes whose counting law could match T*log(T).