Execution Integrity Protocol (EIP) introduces deterministic admissibility continuity as a primitive infrastructure requirement for adaptive execution systems. The paper formalizes invariant identity continuity across admissibility-critical stages including evaluation, authorization, verification, execution, and audit reconstruction. EIP establishes a continuity-bound execution model in which authorization artifacts remain admissible only while reference continuity, canonical representation stability, and artifact validity are jointly preserved at the execution boundary. The work defines formal continuity predicates, theorem-based admissibility properties, fail-closed mismatch handling, deterministic reconstruction semantics, and execution-boundary verification requirements for distributed, autonomous, and continuously evolving systems. Comparative analysis against RBAC, ABAC, OAuth, zero-trust architectures, and capability systems positions deterministic reference continuity as a systems dimension absent from existing authorization infrastructures. Related Resources Website:https://unifiedagencyarchitecture.org/ Repository:https://github.com/ORYNTH-systems Related Publications:Unified Agency Architecture (UAA)Deterministic Execution Integrity for Autonomous Financial InfrastructureAdaptive Orchestration Management System (AOMS)