Theoretical and computational research increasingly depends on derivation chains whose complexity exceeds the practical audit capacity of individual researchers. Across disciplines — from theoretical physics and computational biology to economics and climate modeling — approximations become hidden, normalization conventions drift, numerical pipelines disconnect from the claims they instantiate, and predictions become unverifiable without access to unpublished code. This paper introduces Executable Scientific Provenance (ESP): a formal architecture in which every scientific claim is embedded in a dependency directed acyclic graph (DAG) carrying explicit provenance metadata. The framework defines six provenance classes (A–F) describing the epistemic origin of derived objects, and seven certification tags — CERTIFIED, CONDITIONAL, BOUNDED, SYMBOLIC, COMPARISON_ONLY, AGGREGATION_UNDER_REVIEW, DEPRECATED — describing their operational status within a living derivation graph. Lean 4 serves as an executable audit layer enforcing a zero-sorry policy, synchronizing theorem metadata, and stabilizing dependency topology. Normalization epochs and branch locking prevent silent numerical drift across large repositories. As a large-scale stress test, the framework is applied to the muon anomalous magnetic moment a_mu = (g-2)/2, tracing a discrepancy trajectory from +38σ to −0.09σ through three sequentially identified and corrected provenance failures — an ontology assignment error, stale running-coupling propagation, and a leading-logarithmic approximation leak — while leaving certified sectors intact throughout. The audit sequence demonstrates that provenance-aware derivation graphs localize failures coherently under ppm-level precision pressure. The framework is domain-agnostic. The same failure modes — opaque derivation chains, hidden approximations, disconnected numerics, silent normalization drift — appear across quantitative disciplines, and the ESP architecture provides a common vocabulary for diagnosing and containing them. The paper introduces the concept of epistemic topology: the global structure of a derivation graph viewed as a stratified space whose regions are distinguished by provenance class and certification status. Companion paper: T.M. Nguyen, The Physics of the Self-Field Theory: A Unified Framework from One Lagrangian (2026). DOI: 10.5281/zenodo.20019179