The Weierstrass Decomposition of the Zeta Metric: gₒ₈₆₌₀ ₒ₈₆₌₀ = -wpᵦeta + Cₐn, the Lamé Equation, and the Spectral Identification

We prove that the metric component gₒ₈₆₌₀ ₒ₈₆₌₀ (1/2, t) of the pseudo-Riemannian zeta metric decomposes as: gₒ₈₆₌₀ ₒ₈₆₌₀ (1/2, t) = -wpᵦeta (t) + Cₐn (t) where wpᵦeta (t) = sumₙ 1/ (t - tₙ) ² is the Weierstrass-type sum over non-trivial zeros, and Cₐn (t) -> 0 as t -> infinity. The function Cₐn (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/t²). This decomposition transforms the eigenvalue equation squareg f = lambda*f into an asymptotic Lamé equation: f'' (t) + lambda * wpᵦeta (t) - lambda * Cₐn (t) f (t) = 0 which, in the limit t -> infinity, becomes exactly the generalized Lamé equation f'' + lambda * wpᵦeta (t) * f = 0. The Lamé equation has a completely known spectrum: its eigenvalues are the resonances where the monodromy around each pole tₙ is trivial, which occurs if and only if lambda = tₙ². This conditionally proves Spec (squareg) subset tₙ² in the asymptotic regime, subject to the convergence of the perturbation expansion in Cₐn. The Riemann Hypothesis reduces to the spectral theory of a quasiperiodic Schrödinger operator with Weierstrass-type potential wpᵦeta (t) = sumₙ 1/ (t - tₙ) ².