Learning the Lab, Not the Law: An Audit Framework for Structure-Level Domain Confounding in Symbolic Scientific Discovery

When symbolic regression (SR) is run on data pooled from several facilities, a compact expression can fit well and still describe where the measurements happen to lie rather than a physical relationship. We present an audit framework for this structure-level domain confounding. A design-identifiability screen (Stage 0) checks, from design metadata alone, which dimensionless groups the experiments can separate; honesty tests, discriminant tests, few-cluster inference and normalized conformal prediction then assign separate verdicts to the fitted law and to any structure selected by model selection. On 14,400 simulated designs the rank/condition-number screen is correct for 79% against 66% for a pairwise-correlation screen applied to the same design. On a factorial benchmark of 2880 simulated corpora in nine regimes, the discriminant tests recognized a genuine transition at the reference threshold in 100% of the main regime (320/320) and flagged a structure in 1.4% of the 1600 corpora without one; after the conformal check, 74% of the genuine transitions of the main regime (37.5% across the four genuine-transition regimes) and 0.06% of the others were reported as physics. A genuine transition on sparse support was never recovered (0/320), because the minority-side rule that withholds attribution from the artefact rejects it too, and model selection alone presented a structure as physical for up to 100% of the support-induced pseudo-transitions. As an illustration we audit a public corpus of 114 windage measurements from four facilities spanning 70× in scale. Bayesian model selection retains a two-regime law with a nominal Bayes factor of 5.8×105; the discriminant tests classify it as statistically supported but physically unattributed, and the fitted law does not transport to a withheld facility.