Constraint-Preserving Recursion Under Finite Capacity

This preprint introduces a constraint-theoretic framework for understanding delayed and phase-like failure in recursive adaptive systems operating under finite coordination capacity. The framework distinguishes between two feasibility conditions: operational coherence, governing whether unified action is possible in the present, and structural coherence, governing whether retained commitments can be reconciled through finite coordinated rewrite over time. These conditions are asymmetric: operational coherence must be preserved continuously for execution to continue, while structural coherence may fail silently without immediate disruption of action. Under persistence and finitude, internal incompatibility among retained constraints is unavoidable. Once executability must be preserved, admissible responses to contradiction are shown to be structurally exhausted by exactly two operator classes: suppression, which preserves action by deferring incompatibility without altering retained structure, and integration, which rewrites retained structure to eliminate incompatibility at the cost of coordination and temporary destabilization. No admissible response exists that both preserves executability and resolves contradiction without structural rewrite. The paper formalizes admissible structural change, introduces structural events as the atomic units of feasibility-preserving transition, and derives long-run consequences of recursive admissibility under finite capacity. These include characteristic regimes of operation, loss of warning signals under prolonged suppression, and collapse as a binary feasibility boundary rather than a gradual degradation of performance. The framework makes no assumptions about dynamics, optimization, representations, or mechanisms. It specifies feasibility predicates, operator closure, and binary falsifiers, and is intended as a structural constraint layer within which empirical, dynamical, or control-theoretic models must operate.