Recurrence, Functional Persistence, and Navigation-Layer Adversaries in Capacity-Limited Recursive Systems

This paper introduces a recurrence framework for understanding persistence and collapse in capacity-limited systems. It distinguishes between historical persistence (continuous survival along the same trajectory) and functional persistence, where structures disappear but later re-emerge when the system returns to the conditions that generate them. The work shows that survival depends on whether re-instantiation occurs before the system reaches its terminal horizon. The paper also extends the adversary taxonomy of the series, identifying three new navigation-layer threats: correlation attacks that collapse maneuverability without removing options, temporal attacks that delay recovery until the viable window closes, and recurrence attacks that alter the conditions that allow structures to regenerate. Detection mechanisms and structural tests are provided for each class. Finally, the paper introduces a six-level ontological classification describing how structures emerge, persist, and interact within viable regions of a system. Together, these results complete the series by providing a unified framework for emergence, persistence, and adversarial manipulation in bounded-capacity recursive systems.