Cathedral OS: A Constrained Control Architecture for AI Alignment, Continuity Reconstruction, and Verifiable Governance

Abstract This paper presents Cathedral OS, a governance, verification, and control architecture for long-horizon AI systems. The framework models alignment as a constrained dynamical system in which unconstrained reasoning is projected into an admissible safety region while continuity reconstruction, contradiction management, and deterministic audit logging are maintained as independent architectural layers. The architecture separates reasoning, safety enforcement, continuity reconstruction, and verification into independently measurable subsystems. We introduce a formal model for alignment-induced distortion, a lineage-aware continuity engine, and a deterministic audit ledger supporting replay-based verification. This decomposition enables quantitative analysis of safety-performance tradeoffs, reconstruction fidelity, governance integrity, and reproducibility. The result is a unified framework for AI governance in which system behavior can be constrained, reconstructed, audited, and independently verified.