The Intercalation Lemma: Canonical Alternating Extension Paths for Truth and Audit

Between any two faithful coarse-grainings that preserve the same invariant class, there isa unique (up to refinement) alternating chain of sheaf glues G and renormalization steps Rthat minimizes cumulative residual. We call this chain the intercalation path. It serves asthe canonical derivation in honest work and as an audit in adversarial contexts: deviationslocalize lies and artifacts. We formalize residual metrics, prove existence and minimality,give a constructive algorithm, and present instruments that expose non-canonical detours inproofs, pipelines, and policies