The Defect-Free Crystal: Selmer Vanishing, Iwasawa Flatness, and the Period Bridge at the Central Point

We establish three unconditional results at the central point s = 1/2 for Dirichlet L-functions of p-power conductor, and reduce the Generalized Riemann Hypothesis (GRH) to a single remaining comparison problem. First, we prove the Hollow Neglecton phenomenon: the Iwasawa p-adic L-function Lₚ = Zₚ[T] satisfies = 0 under explicit ordinary conditions, implying the absence of zeros in weight space. Second, we prove unconditional vanishing of the Bloch–Kato Selmer group at the central point via the Mazur–Wiles Main Conjecture combined with a containment argument H¹f Sel_ = 0. Third, we deduce p-adic non-vanishing at s = 1/2. These results collectively remove all algebraic and p-adic obstructions to central non-vanishing. The remaining obstruction is shown to be a single comparison problem—the period bridge—linking the p-adic evaluation Lₚ (₁/₂) to the complex value L (1/2, ). We further construct the categorical structure underlying this obstruction at finite levels via the Drinfeld center, isolating a ramified core governed by non-semisimple trace theory. Extensive computational verification supports the theoretical results across multiple elliptic curves and primes. This work reframes GRH as a rigidity statement of a defect-free arithmetic crystal, where all known vanishing mechanisms are eliminated and the remaining difficulty is a single archimedean/categorical compatibility.