A Runtime Specification for Governed Persistence in Persistent AI Systems

This paper is part of an editorial sequence on governed persistence in persistent AI systems. It develops the specification layer of the sequence: a formal-operational reference model that makes the earlier architectural and operational proposals more explicit at the runtime level. Sequence context: A Structural Stability Architecture for Persistent AI Systems (Zenodo DOI: 10.5281/zenodo.19444524) Mathematical Companion to A Structural Stability Architecture for Persistent AI Systems A Minimal Architecture for Gradual Self-Governance in Persistent AI Systems (Zenodo DOI: 10.5281/zenodo.19558537) Learning to Walk the Floor: Operational Policies for Gradual Self-Governance in Persistent AI Systems (Zenodo DOI: 10.5281/zenodo.19558839) A Runtime Specification for Governed Persistence in Persistent AI Systems (this record) Abstract: This document defines a third-layer specification for persistent AI systems operating under governed persistence. Its role is neither to re-argue the existence of drift nor to restate the broader architectural and mathematical background already developed elsewhere. Instead, it provides a formal-operational reference layer that states, with greater precision, what objects the runtime must contain, what variables must be observed, what validity conditions must hold, what transitions are permitted or blocked, how writeback is governed, how recovery is mediated, how learning remains bounded inside the governed regime, and how the main control loop may be executed. The specification is built around six commitments. First, persistent operation is defined relative to preservation of an invariant core rather than unconstrained adaptive continuity. Second, system state is partitioned into typed domains so that persistence, prediction, action, and rules are not collapsed into one adaptive medium. Third, runtime admissibility depends on observable validity variables, including predictive tension, effective memory, coherence, propagation horizon, drive–dissipation balance, integrable error, and stability margin. Fourth, the operational kernel must support the modes Stable, Brake, and Contain, with explicit trigger logic, permission structure, and mediated recovery. Fifth, governed persistence requires a writeback specification with admissibility classes such as admit, defer, restrict, and deny, including special treatment of self-generated structure. Sixth, learning inside the regime must remain staged, policy-class specific, signal-driven, and bounded by progression and regression rules rather than broad self-modification authority. The mathematical layer is intentionally selective. It uses only the forms needed to formalize the operational picture: a tension–memory bound, a regime-balance variable, bounded propagation, a feasibility bound on ordering, and optional energetic or regularization views where they constrain runtime behavior in a practically meaningful way. The pseudocode provided here is therefore not a complete implementation blueprint. It is a reference execution model for a governed persistence loop. The contribution of this document is narrower than a universal safety theory and more concrete than a bridge paper. It specifies the coupling layer between architecture, operational discipline, minimal mathematics, and runtime procedure. This record is the specification-layer endpoint of the present editorial sequence on governed persistence in persistent AI systems. It is also included in the collected editorial unit *Governed Persistence in Persistent AI Systems: Collected Papers (April 2026)* (DOI: 10.5281/zenodo.19559205), which serves as a navigational entry point to the sequence as a whole.