This revised theoretical preprint defines coherence-conditioned information encoding as the admissible retention of structured correlations under dissipative coarse-graining within a declared effective domain. It follows the development of phase coherence as an order parameter in coupled dissipative systems and introduces the additional predicate required for structured correlations to qualify as information encoding at the effective level. The paper treats information encoding as a domain-relative regime property. A candidate structured correlation qualifies as encoding only when retained correlation, coherence support, retention timescale, and domain admissibility are jointly satisfied. The resulting condition is formalized through the predicate Enc_𝒟 (Y), where Y denotes a candidate correlation-bearing structure and 𝒟 denotes the declared domain of evaluation. Within this framework, Ω_𝒟 functions as a coherence-support order parameter inherited from the dissipative synchronization layer. Its role is to classify whether the effective regime can sustain retained structured correlation after dissipation, perturbation, and reduction. The paper distinguishes encoding-admissible regimes, partially retained or fragmented regimes, intermittent encoding regimes, and encoding-inadmissible regimes. The analysis is diagnostic and classificatory. It provides a constrained framework for evaluating information persistence across physical, biological, neural, informational, and computational systems while preserving domain-specific thresholds, variables, reduction procedures, and admissibility conditions. It thereby supplies the information-encoding layer between dissipative synchronization and later analyses of coherence-conditioned temporal structure.
Son et al. (Fri,) studied this question.