Execution Admissibility Theory for Autonomous Agents — Part III: Non-Bypass and Conformance Closure Theorem

This record contains Part III of the Execution Admissibility Theory for Autonomous Agents series. It is a formal theoretical closure specification intended for audit, regulatory, and insurability evaluation contexts. Title: Execution Admissibility Theory for Autonomous Agents — Part III: Non-Bypass and Conformance Closure Theorem Author: Aslanbek Yurievich KhamikoevIndependent Researcher, AI Systems Governance and Execution Safety Position in Series Part III establishes the structural necessity condition that completes the sufficiency result of Part I and the control-surface model of Part II. Part I (bounded-loss theorem anchor) establishes formal deployability and insurability conditions under invariant-mediated execution-admissibility constraints. Part II introduces: Control-surface formalization Policy-cone relationship Execution regime separation Control-surface integrity criteria Insurability condition as regime property Audit and regulator interpretation layer Explicit non-implementation scope boundary Part III introduces: Surface–effect coupling formalization Non-bypass invariance property Bypass destabilization lemma Structural closure theorem Conformance corollary Applicability bounds Part III proves that bounded-loss sufficiency (Part I) structurally requires a gate-complete, non-bypassable execution surface (Part II). The result is a structural necessity theorem, not a protocol specification and not an implementation claim. Scope Classification Document role: Theoretical Closure / Structural Necessity Theorem Status: Non-Implementation Theoretical Specification Applicability: Effectful execution channels only Statements in this document are property-level and structural. It does not define protocol formats, cryptographic constructions, machine state machines, routing mechanisms, credential schemas, verifier frameworks, or enforcement topologies. Relation to Series Supplement to: Execution Admissibility Theory for Autonomous Agents — Part II: Control Surface and Regime Separation (DOI: 10. 5281/zenodo. 18685758) Indirectly grounded in: Execution Admissibility Theory for Autonomous Agents — Part I: Deployable and Insurable AGI Requires Verifiable Execution Admissibility (DOI: 10. 5281/zenodo. 18663653) Series structure: Part I — Sufficiency (bounded-loss theorem) Part II — Structural mediation model (execution surface) Part III — Necessity of non-bypass closure This establishes the sufficiency–structure–necessity separation of the Execution Admissibility Theory corpus. Files Included in This Record ExecutionAdmissibilityTheoryPartIII. pdfCanonical formatted publication version ExecutionAdmissibilityTheoryPartIII. texLaTeX source (Overleaf-ready) ExecutionAdmissibilityTheoryPartIII. txtPlain-text archival version File order reflects canonical publication hierarchy: (1) formatted publication record (2) source document (3) archival plain-text reference. This series forms a structured DOI-linked theoretical corpus on execution admissibility as a deployability and insurability condition for high-capability autonomous systems.