A Bounded Coherence Field with Wright–Fisher / Allen–Cahn Dynamics: Numerical Validation of the RCD C(x,t) Core

We report the numerical validation of a bounded scalar field C (x, t) ∈ 0, 1 governed by a stochastic partial differential equation with factored Wright–Fisher / Allen–Cahn dynamics. The field arises in the RCD 2. 0 program (Radial Coherential Dynamics, Cerezo, Quantum Benchmark Insights) as an effective coherence variable; here we focus exclusively on the mathematical and numerical properties of its dynamical core. A first attempt at the dynamics, using an unconstrained Landau quartic potential with three free parameters, fails a structural smoke test: the deterministic attractor sits at C* ≈ 1. 170820, outside the declared physical domain 0, 1. We document this failure, identify its algebraic root cause, and replace the potential by a factored cubic drift F (C) = g·C (1−C) (C−m) whose attractors at C ∈ 0, 1 are guaranteed by construction. The replacement reduces the kernel parameter count from five to four and preserves domain compatibility with multiplicative Wright–Fisher noise σ·√ (C (1−C) ) in the Stratonovich sense. We then validate the resulting equation in three escalating blocks: (i) a deterministic diffusion control reproduces ∂ₜ λ² (t) = 2 DC with relative error 0. 00% within reported precision; (ii) an 81-point parameter-space sweep confirms operational robustness across the declared regime; (iii) a bistable front velocity test recovers the closed-form Allen–Cahn / Nagumo prediction v* = √ (DC·g/2) · (1−2m) with relative error 0. 01% in the deterministic regime, ~1% at σ = 0. 05, and ~3% at σ = 0. 10, totaling 153 official trajectories. A residual stochastic velocity shift of order σ², with non-trivial m-dependence not fully explained by the standard Stratonovich–Itô drift correction, is reported as a secondary observation. We do not claim a complete theory of the quantum-classical transition, gravity, or cosmology. We report a bounded effective coherence-field core whose internal dynamics, domain preservation, diffusion limit, and bistable front velocity are numerically validated under a disciplined falsification protocol.