The Computational Legitimacy Gap: Why Existing AI Infrastructure Categories Cannot Authoritatively Verify Computational Decisions

The proliferation of artificial intelligence in high-stakes domains has driven the development of a sophisticated computational trust ecosystem, encompassing cybersecurity, observability, explainability, provenance, governance, auditability, and compliance systems. Yet these established categories, while indispensable, were designed to address fundamentally different questions than the one increasingly demanded by regulators, courts, auditors, and the public: Can a computational decision be authoritatively verified under the precise conditions (information, policies, model state, and system environment) that existed at the moment it was made? This paper builds directly on Constitutional Replay-Authority (Otto, 2026), which defined the proposed infrastructure category dedicated to computational legitimacy and replay verification. The present paper identifies and analyzes the specific infrastructure deficiency—the Computational Legitimacy Gap—that necessitates that category. Drawing on a category-theoretic analysis and recent developments in AI regulation and verifiable systems (2025–2026), the paper demonstrates that existing categories are categorically misaligned with long-term legitimacy requirements. As model evolution, policy drift, and extended accountability horizons intensify, Constitutional Replay-Authority is positioned as the dedicated categorical response to this previously under-recognized structural challenge.