Evolutive Consensus for Agentic AI: OEE Incompleteness of External Guardrails and the Execution Calculus for Safe Evolutive Agents

Le résumé fourni par la source

Guardrail architectures implement a one-dimensional execution model: a fixed verification criterion applied to a projection of the execution context. Three structural limitations follow — context blindness, fragmentation bypass, and non-replayability — that cannot be resolved by refining the criterion or its projection. They are properties of one-dimensional execution, not engineering deficiencies. This paper analyses these limitations from the position of the complete OEE execution model, derived from the binary relation R ⊆ X×X, and proves that every external guardrail architecture is geometrically incomplete for evolutive agents. OEE (Ontological–Eschatological–Epistemic) denotes the three constitutively separated levels present in every execution model: the admissibility criterion τ, the domain specification ωτ, and the execution context C. Any verifier that applies a fixed external τ to a projection of C is one-dimensional and, by Theorem 1, cannot be OEE-complete. No refinement of τ_V or π_V can close the gap: the gap is geometric, not parametric. In the OEE execution model, every admission is simultaneously execution, verification, and an immutable causal record: τ is constitutive in C, evaluated over the complete causal history before every action. For agentic systems, the OEE execution substrate is extended with evolutive consensus — the terminal condition in which all constituent abstractions have completed their τ-evaluation over the shared C. Protection, security, and forensics are structural consequences of this single design choice. Guardrail bypass is a τ-specification gap, not a runtime failure. The incompleteness is provable from the rank structure of binary relations in ZF set theory, without new axioms. The OEE execution model also provides the formal basis for the open problem of the dichotomy between discrete execution and its continuous execution spectrum — a representation in which the spectral signatures of individual abstractions and the results of their interactions are formally separable — formalised as OP8.

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