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 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. It demonstrates that existing categories are capable of preserving records, generating explanations, documenting lineage, and managing policies, yet none were designed to determine whether those preserved materials are constitutionally sufficient to support authoritative replay of the original decision condition. The paper further shows that the gap is not merely operational but categorical, and that it is exacerbated by the passage of time. As the demand for authoritative verification increases, the ability to reconstruct original decision conditions tends to decrease due to model drift, policy change, infrastructure replacement, and institutional turnover. This dynamic—the Legitimacy Reconstruction Paradox—makes the gap both structural and temporal. The paper concludes that Constitutional Replay-Authority is the infrastructure category specifically constituted to address this gap, and that the subsequent papers in this corpus develop the theoretical architecture required to close it.