Hecke Theta-Integral Kernels and Single-Mode Damping in General Degree L-Functions versus Off-Line Zero Diagnostics in the Davenport-Heilbronn Counterexample

Separates Archimedean functional-equation identities (Hecke theta-integral dilation, high-frequency tetragamma branch damping, and the single-mode hyperbolic identity) that hold identically for zeta(s), L(s,Delta), and D_DH(s) from the non-multiplicative defect delta_DH(m,n) = +-(1+kappa^2), the complete 8-mode + Riemann-Siegel remainder vector balance (38.81780% primes, 54.02700% composites, 7.25126% RS remainder) at the first off-line zero (d_*, gamma_*) = (0.3085171825, 85.6993484854), and four classical off-line zero-detection contrapositives.