Phase-Front Dynamics of the Coherence Field in Static Spacetime: A Conceptual Foundation for the Cosmological Extension of Radial Coherential Dynamics

This work derives the global dynamics of the validated Wright-Fisher / Allen-Cahn kernel of Cap II (Libro X, Radial Coherential Dynamics 2. 0) in static, non-expanding reference space. We define the global coherence fraction C (t) as the volume fraction of a static reference domain in the coherent Allen-Cahn phase. Its equation of motion, derived from the kinematic identity, the planar front velocity (Aronson-Weinberger), the Cahn (1965) surface density relation, and the Bray (1994) coarsening law, takes a closed form whose exact analytical solution is a sigmoid in sqrt (t), not in t. The diffusivity DC cancels exactly in the static deterministic regime. The remaining parameters are the drift coupling g (microscopic, validated in Cap II), the asymmetry parameter mu = m - 1/2 (undetermined at present), and the global transition time t* (fixed by initial conditions). This is NOT a cosmological prediction. It is the conceptual brick of one of two parallel exploratory routes the RCD program currently maintains in the cosmological/gravitational sector. The parallel route — disformal scalar-tensor gravity within the GW170817-compatible subset, with matter-induced subluminality theorem and SPARC-calibrated bound DX > 1/g, sponge-like topology, weak multiplicative noise, static reference space). Numerical predictions for H₀, S₈, or any observable cosmological tension are not claimed.