Coherence-Conditioned Temporal Ordering in Dissipative and Informational Systems

This paper defines effective temporal ordering as a coherence-conditioned structural relation among effective descriptions in dissipative and informational systems. It is situated after the temporal architecture framework developed in Time as Architecture: Temporal Points, Non-Linear Adjacency, and Readability Without Control, where time is defined as an architecture of temporal points and temporal relations, and chronology as local traversal or indexing within that architecture. The paper addresses the narrower formal question of when a family of effective descriptions supports temporal ordering rather than chronological, parametric, computational, or archival sequence alone. It argues that temporal ordering requires three jointly satisfied conditions: a recoverable structural relation between descriptions, positive orientation relative to a declared reference condition, and sufficient coherence support above threshold. The central relation is defined as: X_i <_T X_j iffR(K_ij) ≥ R_c,Θ_O(X_i, X_j) > 0,Ω_eff ≥ Ω_c. On this basis, the paper distinguishes chronological succession from effective temporal order, recoverable continuity from storage or index sequence, and temporal fragmentation from the cessation of dynamical evolution. It also defines temporal collapse as the loss of recoverable oriented relation under coherence support at a declared level of description. The framework is intended for use in dissipative systems, informational systems, nonlinear dynamics, memory and archival structures, hybrid biological or cognitive regimes, and formal temporal theory. It supplies the pairwise ordering layer on which later analyses of corridor admissibility, passage, anchoring, support satisfaction, external instantiation, prediction-like readability, and control may depend.