This revised theoretical preprint develops phase coherence as an effective order parameter in coupled dissipative systems. Building on the preceding formalization of resonance coherence Ω and its conditional projection beyond the gravitational domain, the paper restricts the analysis to systems in which phase-like variables, nonlinear coupling, dissipation or irreversible reduction, perturbation, scale separation, and coarse-graining conditions can be explicitly declared. The paper treats synchronization as a coherence-supported regime of effective dynamics rather than as perfect phase locking, centralized timing, global control, or externally imposed temporal order. Within this framework, Ω classifies the degree to which phase organization remains macroscopically available after microscopic phase trajectories, local fluctuations, and fine-grained dynamical details have been averaged, dissipated, or integrated out. The analysis distinguishes coherent, partially coherent, metastable, intermittent, fragmented, and incoherent regimes by the behavior of Ω relative to declared thresholds, fluctuations, recovery times, and correlation structure. Candidate observable signatures include fluctuation amplification, critical slowing down, hysteresis, path dependence, cluster fragmentation, recovery-time increase, and loss of long-range phase correlation. These signatures are treated as empirical constraint regimes, not as direct prediction or control mechanisms. The resulting framework supplies a bounded diagnostic grammar for retained phase organization in coupled dissipative dynamics. It prepares later analyses of coherence-conditioned information encoding and coherence-conditioned temporal structure while preserving the distinction between synchronization dynamics, information retention, temporal organization, external realization, prediction, and control.
Son et al. (Fri,) studied this question.