Local Phase-Time, Anchoring Conditions, and External Realization Constraints in Coherence-Conditioned Systems

This paper defines local phase-time, anchoring conditions, and external realization constraints in coherence-conditioned systems. It is positioned downstream of the domain-independent definition of lawhood, the temporal architecture framework, the effective temporal-ordering relation, and the corridor-admissibility framework. Its central contribution is to distinguish route accessibility from local stabilization and to distinguish local stabilization from externally realized occurrence.The paper introduces a bounded local temporal subdomain 𝒟_loc, a restricted local temporal relation <_(T,loc), a local temporal structure TA_loc(𝒟_loc; O), a recoverable structure Y, local retention Ret_loc(Y, 𝒟_loc), local support B_loc(Y, 𝒟_loc), local coherence Ω_loc(Y, 𝒟_loc), observable trace Tr(Y), and trace persistence Pers(Tr(Y)). Anchoring is defined as local stabilization under temporal admissibility, retention, support, and coherence constraints. External realization is defined as anchoring together with observable trace and trace persistence above threshold.The resulting framework supplies the local-stabilization and trace-realization layer between corridor admissibility and later analyses of passage, support satisfaction, external instantiation across domains, prediction-like readability, intervention, and control. It remains formal and classificatory: external realization is treated as persistent trace-bearing occurrence, not as prediction, control, global stabilization, or cross-domain instantiation.