Finite Recurrent Stability and the Pre-Spacetime Structure of Horizons: Collapse, Emergence, and Recurrence as Recoverability Boundaries

This manuscript develops a mechanism-neutral theory of finite recurrent stability for closed descriptions of a universe. A closed system cannot rely on an outside clock, observer, memory, origin label, or cycle counter to explain its own persistence. If beginning, ending, recurrence, or cycle number are not recoverable from within the system, they function as external labels rather than internal structure. The paper defines persistent structured identity as recoverable relational distinction, not exact sameness or label continuity. Contraction, correction, carry-through, recurrence, collapse, and emergence are classified as recoverability conditions within a finite stability band. Stability is expressed…