The Structural Persistence Principle Generated Admissibility, Physical Support, and Remaining Maneuverability Under Irreversible Dynamics

This working note states a corrected Structural Persistence Principle for constraint-defined systems. For a specified system boundary, observational resolution, operating context, and horizon, persistence capability is determined jointly by the effective admissible geometry generated by the operative requirements, available capability, and couplings, and by the physically realizable dynamics available to remain within that geometry. Persistence over the specified horizon requires at least one admissible continuation. At regular boundary points, standard viability theory supplies the corresponding local condition: a single physically realizable support action must satisfy all active boundary requirements simultaneously. Positive support magnitude alone and linear spanning of the active constraint normals alone are not sufficient. Passive first exit provides a separate reference diagnostic: persistence beyond the exit predicted by a specified passive model establishes departure from that reference but does not by itself identify the physical mechanism, since state dynamics and admissibility-boundary motion are distinct possible sources of first-exit change. A retained representation is sufficient for a selected persistence-capability record only when that record is invariant across all full realizations identified by the representation. A September 2026 thermodynamic refinement shows, for constrained finite-state Markov networks with specified locally detailed-balanced support channels, how finite entropy-production supply bounds the remaining direction-resolved disturbance-rejection capability. The principle is therefore presented as a structural synthesis built on established viability theory, not as a new statement of the Nagumo theorem or as a universal thermodynamic law.