A Reproducible Covariance-Aware Workflow for Mass-Fractionation Residuals in Multi-Isotope Data

Abstract

Highly fractionated multi-isotope datasets are often distributed as tables containing marginal uncertainties but incomplete covariance, reference-scale, or external-reproducibility metadata. Standard calculations can nevertheless produce apparently standardized residuals, obscuring whether a formal metrological test is supported. This study presents a reproducible computational workflow for transforming isotope ratios to logarithmic delta-prime coordinates, evaluating residuals from a prespecified mass-fractionation relation, propagating reported marginal uncertainty and supplied covariance, and classifying outputs according to metadata completeness. A covariance-weighted residual distance is reported only when a fit-for-purpose residual covariance matrix is available under the declared null model. When covariance is unavailable, the workflow permits a separately labeled zero-covariance sensitivity calculation only after that assumption is explicitly stipulated; otherwise, it reports insufficient metadata for a formal test. Input records capture reference conventions, uncertainty types, fixed or estimated model parameters, and source provenance, ensuring that derived tables retain analytical rigor. Published laboratory-standard-referenced iron-isotope values for CNEOS 2014-01-08 spherules provide an end-to-end demonstration of the workflow. The source table supports coordinate transformation and conditional sensitivity calculations but lacks covariance and calibration metadata needed for formal residual inference or provenance attribution. The workflow therefore makes missing analytical metadata explicit rather than implicitly assuming it away, bridging the gap between rigorous laboratory measurement and secondary data governance. Companion Resources: Interactive Web Application: A live, browser-based implementation of the D_iso admissibility engine is available at: Baird Research & Strategic Sciences (Metric Residue) Open-Source Code & Data: The reference Python implementation, test suites, and reproducibility datasets are hosted in a separate companion Zenodo repository: 10.5281/zenodo.22946923