Detecting and Diagnosing Facility Confounding in Empirical Scaling Laws: A Cross-Facility Validation Protocol Applied to Windage Power in Rotor-Stator Systems

A scaling law calibrated on data pooled from several facilities should be validated on a facility it has never seen, and when that test fails, the failure needs its own diagnosis: either the outcome carries a facility-specific effect that the predictors miss, or the predictor set itself cannot be separated from facility identity. We propose a two-stage protocol. The detection stage consists of algebraic-redundancy screening, leave-one-facility-out (LOFO) cross-validation, a facility-cluster bootstrap and a predictor/facility collinearity check; the diagnosis stage consists of a pre-fit identifiability index and a synthetic two-null discriminator. We apply it to 114 windage-power points from four sources (labelled by first author and year: Guo2024, Vrancik1968, Zheng2024, Liu2024) spanning a 900× Reynolds range. The corpus is heterogeneous: only 64 points are physical measurements, 45 are computational fluid dynamics (CFD) outputs for a facility that has not been built (including 8 rows with an inconsistent power basis and 7 with a frozen radial gap), 5 are reconstructed from a fitted constant, and 20 come from a preprint that has not been peer-reviewed. A four-predictor model selected by the Bayesian Information Criterion reaches an in-sample R2=0.870, but a pooled LOFO R2=−0.885, and no held-out facility is predicted better than its own mean. Repeating the structure selection inside each fold selects the same model in every fold. A pre-fit identifiability index shows that one direction of the predictor block, essentially logΠconfinement, is aliased with facility identity (the largest of the K−1=3 canonical correlations 0.996) and has almost no within-facility variation, also on a verified 94-row subset. With K=4 facilities, the two-null discriminator is fragile: under homoscedastic noise, 3 of 4 observed values fall outside both simulated supports; with per-point reported uncertainty, a facility-offset model reaches the observed values of Guo2024, Vrancik1968 and, in its extreme tail, Zheng2024, whereas a collinearity-only model with the same uncertainty does not reach Zheng2024 and reaches Guo2024 only at its 1st percentile, and Liu2024 is reached by neither; we therefore report it as a documented failure mode on small multi-facility corpora rather than as a standalone diagnostic. Twenty-one further attempts, sixteen of them learning methods, also fail the per-facility rule. Only the sign of the Reynolds effect transfers, and only among the physical facilities: within the CFD rows of the unbuilt facility, it is not detectable once 8 misattributed rows are separated.