A Structural Stability Architecture for Persistent AI Systems with Mathematical Companion

This record opens a publication sequence on governed persistence in persistent AI systems and contains two companion documents at its foundational layer. The main paper, A Structural Stability Architecture for Persistent AI Systems, proposes a conservative architectural framework for long-horizon adaptive systems centered on identity preservation, constrained transitions between memory, prediction and action, explicit validity thresholds, observability, braking, and fail-closed containment. The companion note, Mathematical Companion to A Structural Stability Architecture for Persistent AI Systems, provides a compact mathematical background for the principal supporting laws used selectively by the architecture, without restating the full broader corpus. Together, the two documents establish the architectural layer and the minimal mathematical companion layer of the sequence. This foundational record is followed by the subsequent documents in the same editorial sequence: A Minimal Architecture for Gradual Self-Governance in Persistent AI Systems (DOI: 10.5281/zenodo.19558537), Learning to Walk the Floor: Operational Policies for Gradual Self-Governance in Persistent AI Systems (DOI: 10.5281/zenodo.19558839), and A Runtime Specification for Governed Persistence in Persistent AI Systems (DOI: 10.5281/zenodo.19558986). This record 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.