Recursive Continuity Governance: A Graph-Theoretic Topology for Recoverability Under Asynchronous Recursive Transmissibility Conditions presents a constrained conceptual framework for analyzing governance instability in recursive AI systems. The paper argues that recursive systems fail first at provenance, authorization continuity, and recoverability long before they fail semantically.The framework introduces six non-equivalent continuity layers — semantic, behavioral, identity, authorization, provenance, and recoverability continuity — and demonstrates how recursive propagation, delegation, synchronization lag, and identity branching generate graph-level governance failures even while systems remain coherent and operationally stable.Nine recursive governance failure classes are identified, including circular provenance, recursive consensus poisoning, recursive delegation collapse, recursive revocation failure, and recursive identity fragmentation. The paper further proposes a central theorem candidate: recursive systems become irrecoverable when propagation, delegation, synchronization, and identity branching asymmetries collectively outpace provenance compression and lineage reconciliation.A major architectural result is the External Anchor Condition: recursive recoverability requires at least one acyclic provenance anchor established before fragmentation occurs. Without such an anchor, legitimacy becomes historically negotiable rather than computationally recoverable.The framework is explicitly bounded. It applies only to recursive transmissibility systems with persistent downstream state and graph-dependent rollback requirements. It is not presented as theology, cosmology, or universal governance theory, but as an operational vocabulary for provenance-aware recoverability governance in recursive AI systems.
Thomas Mitchell (Tue,) studied this question.