Coherence Field Dynamics and the Emergence of Metric Structure

This revised theoretical preprint formulates a reduced local dynamics for coherence-bearing domains within an emergent metric framework. It introduces Ωₗoc as a bounded effective order parameter defined after macroscopic reduction on a declared support domain. Ωₗoc represents retained local phase organization within an effective regime and is formally distinguished from the statistical state section Ψ, the information metric h_μν, the global coherence functional CglobalΨ, the spacetime metric g_μν, and downstream resonance-induced gravitational correction structures. The paper develops an effective dynamical equation for Ωₗoc combining coherence transport, nonlinear stabilization, and resonance-mediated interaction: ∂_σΩₗoc = κ_ΩΔₑffΩₗoc + F_Ω (Ωₗoc) + R_ΩΩₗoc. It analyzes stationary configurations, perturbative stability, coherence-domain formation, support gradients, fragmentation, and threshold-sensitive regime classification. A restricted metric-support predicate is then introduced to specify when stabilized local coherence may supply support for later metric admissibility. The analysis preserves the distinction between reduced local coherence dynamics, metric support, metric admissibility, metric closure, effective gravitational comparison, empirical validation, prediction, external realization, and operational control. The contribution of the paper is structural and classificatory. It provides the local coherence-dynamical layer between pre-metric information-geometric organization and later analyses of metric admissibility, metric closure, and effective resonance-coherence gravitation.