Policy Fibrations and Theorem U: Policy Fibrations, Monodromy, and the Logical Witness Condition

We establish that any computational system whose operational trace encodes a Pi01-witnessed statement with verification depth exceeding the critical threshold specified by Theorem U necessarily admits a policy fibration with nontrivial monodromy. We provide explicit ZFC encodings of Boolean circuits, categorical semantics, the nerve construction, and the fundamental groupoid. The oracle-relativized verification procedure is formalized via Turing reducibility, and we situate our results within the classical frameworks of Kleene realizability and proof-theoretic ordinal analysis.