Admissible Persistence Theory (APT): A Layered Formalization of Admissible Continuation, Realization, Dissipation, and Semantic Persistence

Admissible Persistence Theory (APT) is a layered formalization framework for admissible continuation, realizability, dissipation, irreversibility, embodied persistence, maintenance, and observer-relative semantic persistence. The framework is organized as a strict inheritance architecture in which each layer introduces only the minimum additional structure required for new persistence phenomena to emerge. The publication defines: admissible continuation relations, persistence reachability geometry, boundary and obstruction structures, quantitative admissibility margins, feasibility interaction geometry, admissible trajectories, realization compatibility, realized evolution, dissipation accumulation, irreversibility as reconstruction failure, fragmentation and proto-entropic sectorization, physical persistence realization, maintenance/metabolic persistence, observer-relative semantic persistence. The framework is intended as a foundational architecture for admissible computation, governed state transition systems, persistence geometry, verifier-governed execution systems, semantic continuity analysis, and resource-aware intelligent systems. This release includes: publication-grade manuscripts, notation registries, semantic firewall registries, theorem dependency structures, release metadata, supplementary layered PDFs, and Zenodo archival metadata. License: CC BY-NC 4.0 (Attribution-NonCommercial)