Enterprise artificial intelligence is increasingly embedded in decisions that must remain lawful, explainable, adaptable, and accountable despite personnel turnover, model replacement, regulatory change, and shifting organizational incentives. Existing governance frameworks provide important principles but do not by themselves supply a compact mathematical language for evaluating whether an institution can preserve sound judgment over time. This paper develops a design-science framework for institutional legacy: the durable capacity of a decision system to continue producing beneficial, lawful, explainable, and adaptable outcomes after its original designers have stepped away. The framework contributes: (i) a normalized Legacy Score based on a penalized geometric mean of knowledge retention, governance, human oversight, adaptability, feedback learning, and jurisdictional fidelity; (ii) Decision Confidence and Decision Risk models separating evidentiary confidence from consequence; (iii) authority-aware retrieval and calibrated abstention; (iv) Decision Memory for governed organizational learning; (v) Regulatory Change Velocity mapping change exposure to review intervals; and (vi) a federated regulatory knowledge-graph architecture preserving provenance and legal hierarchy. The paper also proposes eight AI Decision Integrity Rules, an evaluation protocol, and a reproducible computational demonstration. The demonstration combines a deterministic stress test with 200 Monte Carlo replications of 10,000 synthetic decisions each, illustrating Legacy Score non-compensation and comparing consequence- and authority-aware routing with a matched-coverage confidence-only baseline. The contribution remains conceptual rather than field-validated; the simulation tests internal behavior, not production performance, and all parameters require context-specific calibration.

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