Hidden Numerical Foundations in Physics: A Provenance Audit for Laboratory Timing, Normalization, and Model-Dependent Constants

Physics routinely demands derivations and physical justification for explicitly stated constants, yet equally consequential numerical choices may remain hidden inside laboratory timing conventions, normalization rules, fitted delays, weighting windows, cutoffs, limiting procedures, and data-processing pipelines. This paper introduces a Numerical Provenance Audit, together with a focused Timing Foundation Audit, for identifying numerical selectors that materially affect physical conclusions. The framework traces each selector’s source and classifies it as derived, measured, calibrated, fitted, selected, or unresolved. It then evaluates how uncertainty or arbitrariness in that selector propagates into the reported result. The paper distinguishes operational reproducibility from foundational physical validity. A calculation may be mathematically correct and reproducible under a declared laboratory-time or analysis construction while its stronger physical interpretation remains conditional on an upstream numerical choice. Formal contributions include the Hidden-Number Extraction Theorem, the Equal Numerical Provenance Theorem, the Earliest-Free-Choice Principle, the Foundation Dependence Index, and a foundational uncertainty term that can be incorporated into a conventional error budget. A detailed case study applies the audit to an entropy-relaxation experiment involving plastically deformed amorphous solids. The audit identifies a quarter-cycle analysis window, an empirically optimized shear-relaxation lag, a fitted relaxation-to-structure delay near 0.3 times the relaxation time, a numerical entropy cutoff, and final sample-specific scaling slopes. The original observations and fits remain supported within the declared analysis pipeline, while the strongest physical interpretation remains conditioned on the temporal-pairing procedure. The framework is intended as a constructive tool for authors, reviewers, and experimental researchers. It does not argue that laboratory time, fitted parameters, or numerical conventions are inherently invalid. Instead, it proposes that physically decisive numerical quantities receive equivalent provenance, sensitivity, and uncertainty review regardless of whether they appear explicitly or remain hidden inside an analysis pipeline.