One Action, One Derivation, One Empirical Match: How S_eff[C] Produces Exponential Decoherence Without Modifying Quantum Mechanics

We derive the exponential suppression of off-diagonal coherences predicted in Conjecture 1 of P1 v1.1 from the parent action S_eff[C], using the Feynman-Vernon influence functional within the Schwinger-Keldysh formalism. The coherential field C is decomposed into long-wavelength system modes and short-wavelength environment modes, with the kernel scale l_K providing natural separation. For homogeneous backgrounds, the decoherence exponent reduces exactly to the quadratic sector of D_K with explicit coefficient Gamma = 2 mu^8 kappa_env / C_*^2. In the binary discrete limit, this reproduces the Hamming-weighted exponential decay established experimentally in P0-a (GHZ-Bridge). No modification of quantum mechanics is assumed; no new parameters are introduced. The derivation closes the structural bridge S_conf → D_K → d_H → Hamming Decay for the homogeneous case. Extension to inhomogeneous backgrounds remains open. Part of the Radial Coherential Dynamics (RCD) 2.0 program.