Verification as a Condition for Semantic Integrity in Statistical Systems

This paper introduces a behavioral instrumentation framework for evaluating semantic termination and verification integrity in generative AI systems. Building on the Taxicab Condition and the tau(x)-operator developed in prior work, the paper presents a prompt-level orchestration prototype designed to approximate invariant-governed inference behavior and expose structural divergence between locally coherent and globally admissible outputs. The core of the research is the Taxicab Diagnostic—a four-phase replication protocol designed to test for silent adaptation, shallow termination, and invariant decay. Through this diagnostic, the paper documents the Judicial Ceiling, an empirical finding demonstrating that self-evaluation (Verification) remains structurally distinct from execution within probabilistic dependency systems. This yields the formal architectural condition: V(c) ≠ E(c). By distinguishing between formal necessity, behavioral evidence, and architectural implementation, the paper positions the Semantic AI Reactor (SAIR) framework as a proposed architectural response to limitations inherent in probabilistic dependency expansion rather than as an optimization of existing generative systems. The work serves as a falsifiable behavioral bridge between modal-dependence theory and observable inference dynamics.