Admissibility-Limited Systems Unified Explanation of Boundary Behaviour

This paper presents a unified structural explanation of boundary behaviour within admissibility-limited systems in the Paton framework. A system is defined by what information can pass through its boundary into stable, usable structure. The framework distinguishes between admissible propagation, where information passes constraint and stabilises at the datum, and post-return regimes, where propagation exceeds admissibility and boundary traversal is no longer permitted. Under admissible conditions, information is accessible, stabilised, and externally usable. When propagation exceeds admissibility, information is not destroyed but becomes inaccessible to external observation. It persists within the system while remaining outside admissible access. This establishes a key distinction between information existence and information accessibility. The paper introduces a refined gradient of boundary behaviour, showing transitional regimes where information becomes increasingly compressed and difficult to access as the admissibility limit is approached. Near the boundary, minimal structured leakage may occur. Beyond the boundary, access ceases entirely and only indirect inference remains possible. This interpretation unifies boundary behaviour across systems by showing that limits do not remove information but restrict its admissibility for external use. The result aligns with broader Paton System principles, including admissibility gating, datum stabilisation, and constraint-governed continuation. The framework introduces no new domain-specific laws. It provides a structural account of how information behaves at system boundaries, clarifying the distinction between persistence and accessibility.