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 D_C 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 D_X < 0.21 — is documented in Paper XVI v2.1 (DOI 10.5281/zenodo.19744527). The program does not commit to either route at the present stage; the decisive criterion for consolidation is empirical and will be applied as subsequent Cuadernos produce (or fail to produce) quantitative observational predictions. Six explicit kill switches are declared ex ante: expansion test under metric expansion (KS-C10-1), front planarity (KS-C10-2), topology assumption (KS-C10-3), noise-induced coarsening modification (KS-C10-4), barrier shift origin (KS-C10-5), and deferred observational falsification (KS-C10-6, operative only after subsequent Cuadernos). The manuscript was revised across three rounds of internal critical review (Panel Cerezo methodology). The closed-form result is established under explicit regime conditions (t >> 1/g, sponge-like topology, weak multiplicative noise, static reference space). Numerical predictions for H_0, S_8, or any observable cosmological tension are not claimed.