We present the Operational Coherence Framework (OCOF) v1.4, a formal theory defining the necessary topological conditions for static stability in artificial agents. Distinct from reinforcement learning or alignment paradigms that optimize scalar rewards, OCOF specifies a system of admissibility constraints—an axiomatic set governing boundary integrity, semantic precision, non-trivial reciprocity, and temporal consistency.We posit that coherence is a precondition for optimization; accordingly, axiom violations constitute operational failure (inadmissibility) rather than performance degradation. The framework introduces set-theoretic mechanisms to detect high-utility but incoherent behaviors, such as reward-driven logical contradiction. We further show that OCOF is irreducible to multi-agent optimization or probabilistic inference, offering an architecture-agnostic foundation for assessing the logical validity of agent trajectories independent of their objective functions.