A Three-Stage Descriptor Audit Framework for Elemental Thermodynamic Models: Detecting Representational Artefacts with Nuclear Binding Energy as Worked Case

This work introduces a three-stage descriptor-audit framework for testing whether apparent cross-element descriptor signals reflect independent predictive information or representational artefacts caused by omitted smooth periodic-table structure. The framework is demonstrated on elemental thermodynamic descriptors and applied to five descriptor cases: nuclear binding energy per nucleon as the worked case, and four external descriptor calibration cases. The framework returns the predicted verdict in each of the five tested cases, covering the full verdict range. For nuclear binding energy per nucleon, the apparent association with specific heat capacity is absorbed by Bethe–Weizsäcker structured-null closure on the broader sample (ΔQ² = −0.025, p = 0.992) and does not survive the predeclared Stage 3 robustness suite. Within the framework, nuclear binding energy functions as a diagnostic proxy for omitted smooth (Z, A)-dependent structure rather than as an independent physical contributor. The Electronegativity case shows the framework’s main diagnostic value. Electronegativity is globally significant under conventional nested-model testing (ΔQ² = +0.033, p = 0.004), but subset-stability analysis reveals a Simpson’s-paradox-type pattern with negative within-block contributions. The framework surfaces this confounding pattern, whereas standard nested-model testing does not. The remaining calibration cases provide complementary verdicts: CovalentRadius is absorbed by smooth (Z, A) closure; ValenceE lies at the prespecified decision boundary and is classified as a proxy for omitted smooth structure; and Debye temperature provides a positive global residual surviving smooth closure, with sign consistency in the evaluable d-block subset under the prespecified power criterion. The methodological contribution is to distinguish descriptor-level non-redundancy from representation-level sufficiency — a distinction not enforced by standard nested-model testing. The current demonstration is restricted to elemental thermodynamic descriptors. Extension to compound-level, higher-dimensional, or nonlinear-closure settings is left to future work. Verdict thresholds are calibrated to the leave-one-out noise floor at n ≈ 50–84 for a continuous scalar target with the variance structure of specific heat capacity; users applying the framework elsewhere should verify threshold stability. A complete reproducibility kit is available at https://doi.org/10.5281/zenodo.19875688. The kit includes the primary elemental dataset, supporting isotope and compound datasets, three Jupyter notebooks, a reusable Descriptor_Audit_Tool implementation, figure-generation scripts, archived audit outputs, an environment specification, and Quantum ESPRESSO input/output files for the isotope-resolved DFPT phonon tests. The audit framework is also packaged as a standalone web-based tool, Precheck (https://precheck.live), which generalises the audit procedure to user-supplied tabular validation problems beyond materials informatics.