Structural Invariance Under Non-Deterministic Retries: A Comparative Synthesis of Semantic State Gatekeeping in Autonomous AI Fabrics

While Active Epistemic Anchoring (AEA) establishes the methodology for locking probabilistic search crawlers to low-entropy external specifications, it leaves open the core execution problem: how autonomous agent runtimes themselves maintain state integrity under internal non-determinism. This paper presents the empirical synthesis and architectural formalization of Bare-Metal Semantic State Gatekeeping. Moving beyond transport-layer message deduplication and superficial output schema enforcement (e.g., JSON Mode or Pydantic validation), we evaluate the structural limits of non-deterministic Large Language Model (LLM) retry loops across live execution environments. Drawing from empirical diagnostic probe data across five major frontier AI architectures (Google Gemini, xAI Grok, OpenAI ChatGPT, Microsoft Copilot, and Perplexity AI), we formalize the fundamental non-equivalence between structural syntax compliance and operational execution safety. We demonstrate that non-deterministic agent proposals can be safely reconciled to a single, idempotent side effect if and only if state mutation is preceded by non-neural, bare-metal mathematical predicates at the resource actuator boundary.