Nested Tests of Non-Keplerian Scaling in Exoplanet Systems: Solar-System Calibration and Population-Level Upper Limits

We revisit Kepler’s third law in an instrument-aware, catalog-wide setting by casting the Keplerian scaling as a nested null model. The alternative augments log P with a minimal logistic term. Using the Solar System as a calibrated positive control, we recover a modest yet detectable effect localized near a trajectory-dependent encounter scale. Applying the same pipeline to public exoplanet catalogs (PSCompPars and KOI), the logistic extension is disfavored by information criteria (AICc/BIC) with negative likelihood-ratio statistics; the maximum-likelihood amplitude is â = 0. We therefore report a 95% profile-likelihood upper bound α ₉₅ , providing a falsifiable benchmark for future, physically motivated multivariate corrections. Using the Solar System as a calibrated positive control, we find a modest yet detectable improvement: ∆AICc = −1.6, ∆BIC = −0.5, LRT = 3.1 (p = 0.078), and a 4.2% reduction in cross-validated residual scale. By contrast, the exoplanet ensembles are disfavored, with ∆AICc = +2.8 and ∆BIC = +5.3 (> 0), â = 0, and α95 = 0.07.