The Weierstrass Decomposition of the Zeta Metric: gsigma sigma = -wp_zeta + C_an, the Lamé Equation, and the Spectral Identification

We prove that the metric component gsigma sigma(1/2, t) of the pseudo-Riemannian zeta metric decomposes as: gsigma sigma(1/2, t) = -wp_zeta(t) + C_an(t) where wp_zeta(t) = sum_n 1/(t - t_n)^2 is the Weierstrass-type sum over non-trivial zeros, and C_an(t) -> 0 as t -> infinity. The function C_an(t) is computed explicitly from the Hadamard product of zeta: it consists of contributions from Gamma(s/2), the pole at s = 1, and the trivial zeros, each decaying as O(1/t^2). This decomposition transforms the eigenvalue equation square_g f = lambda*f into an asymptotic Lamé equation: f''(t) + [lambda * wp_zeta(t) - lambda * C_an(t)] f(t) = 0 which, in the limit t -> infinity, becomes exactly the generalized Lamé equation f'' + lambda * wp_zeta(t) * f = 0. The Lamé equation has a completely known spectrum: its eigenvalues are the resonances where the monodromy around each pole t_n is trivial, which occurs if and only if lambda = t_n^2. This conditionally proves Spec(square_g) subset {t_n^2} in the asymptotic regime, subject to the convergence of the perturbation expansion in C_an. The Riemann Hypothesis reduces to the spectral theory of a quasiperiodic Schrödinger operator with Weierstrass-type potential wp_zeta(t) = sum_n 1/(t - t_n)^2.