One Action, One Derivation, One Empirical Match: How SₑffC 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 SₑffC, 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 lK providing natural separation. For homogeneous backgrounds, the decoherence exponent reduces exactly to the quadratic sector of DK with explicit coefficient Gamma = 2 mu⁸ kappaₑnv / 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 Sconf → DK → dH → Hamming Decay for the homogeneous case. Extension to inhomogeneous backgrounds remains open. Part of the Radial Coherential Dynamics (RCD) 2. 0 program.