Admissibility-Gated Interaction as a Structural Condition in Cognitive Systems

This paper formalises interaction as an admissibility-gated process within cognitive systems. Engagement is reframed as a constraint-governed continuation problem rather than a behavioural or communicative phenomenon. Interaction persists only while structural compatibility between participants remains sufficient to support continued state transitions. A minimal interaction state is defined by alignment (A), value (V), and energy cost (E), establishing the admissibility condition (A + V) > E as necessary for continuation. Interaction modes are shown to arise from constraint configurations, and termination is defined as incompatibility-conditioned collapse, consistent with the Constraint-Incompatibility Collapse Law (CICL). This work positions interaction as a Tier-7 instantiation of the Paton System, demonstrating that admissibility, constraint accumulation, and boundary formation operate equivalently in cognitive systems as in physical and mathematical domains. The result is a domain-neutral structural account of engagement persistence, independent of behavioural or psychological interpretation.