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A Coq mechanisation accompanies the paper (34 complete proofs; zero admits for the two central results). (I) Trace types. FinTrace(s0,sn) is an inductive family of typed execution traces. FinTrace and Star(Step) are isomorphic as path types but not judgementally equal; TraceElim exposes the event label e:Event explicitly, giving a more ergonomic interface for event-driven induction. We prove the Trace-Reachability Correspondence, Deterministic Replay, and a canonicity framework via reducibility candidates with a Transport Lemma (RC-elim deferred; all other Core results are Coq-verified). (II) Sheaf semantics. Trace-indexed propositions are contravariant sheaves over the free trace partial-order category Tf. 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We prove the Trace-Reachability Correspondence, Deterministic Replay, and a canonicity framework via reducibility candidates with a Transport Lemma (RC-elim deferred; all other Core results are Coq-verified). (II) Sheaf semantics. Trace-indexed propositions are contravariant sheaves over the free trace partial-order category Tf. 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