Verified Free-Energy Dynamics: A Hybrid Invariance Principle for Evidence-Gated Persistent Agents

The free-energy principle and active inference describe how an adaptive system can reduce variationalfree energy through perception, learning, and action. They do not, by themselves, require that aproposition admitted to an Agent’s persistent canonical state has passed an external evidence test.An Agent can therefore become internally predictable while retaining unsupported commitments. Weintroduce verified free-energy dynamics (vFEP), an engineering extension that separates homeostaticor inferential coherence from epistemic admissibility. The construction is hybrid: a continuous freeenergy flow regulates the Agent’s internal state, while a discrete verification projection controlswhich candidate records may become canonical. A non-negative verification deficit is added to adimensionless base-energy residual, yielding a verified coherence that cannot be maximal when anyunsupported commitment is canonical. We establish forward invariance of the verified manifold,exponential convergence of the continuous coordinate under an explicit Polyak–Lojasiewicz condition,and preservation of the invariant under atomic, proof-matched self-modification. A controlled gateablation illustrates the central empirical distinction: ordinary coherence can remain near one whileunsupported canonical records accumulate, whereas verified coherence falls immediately; restorationof the gate and certificate re-scan removes the deficit. The claim is deliberately limited: vFEPguarantees compliance with a specified verification policy, not metaphysical truth, verifier infallibility,consciousness, or general intelligence.