Planetary Radius as a Regime-Dependent Relational Quantity: Evidence for a Paradigm Defect in Exoplanet Radius Measurement——A Cross-Disciplinary Empirical Test in Astronomy Based on Factor Hierarchy Theory and the Four-Test Method

Core Conclusions: (1) Transit depth is not an intrinsic property of a planet, but a “relational quantity” arising from the coupling of the planet, the stellar radiation field, and the detector response. (2) The discovery facility is a proxy regime factor for the stellar radiation field—the true regime factors are stellar spectral type, metallicity, and surface gravity. (3) The concept of “planetary radius” as used in astronomy for four decades lacks physical universality in cross-regime comparisons. This study applies the Principle of Testability and the Four-Test Method proposed by Tang (2026g), augmented by the 5W2H and PDCA completeness frameworks, to a presupposition-free exhaustive analysis of 39,913 raw records from the NASA Exoplanet Archive. Exhaustive testing automatically selected radius_ratio + pl_orbper + sy_dist as the optimal combination from 12 candidate executing factors (adjusted R² = 0.691, VIF < 5). Interaction effect testing revealed that the discovery facility systematically modulates the exposure coefficient of radius_ratio on transit depth (ΔR² = 0.048, p = 6.59×10⁻⁷); however, this effect completely vanishes when controlling for stellar spectral type—G-type: F = 0.05, p = 0.99; K-type: F = 1.01, p = 0.39. This finding reveals a new structural form within Factor Hierarchy Theory: the proxy regime factor. Stellar spectral type, metallicity, and surface gravity were all tested and confirmed as significant regime factors. The regime coupling is strongest in the metal-poor group (ΔR² = 0.0313, p = 1.21×10⁻¹⁵) and disappears in the metal-rich group (p = 0.428). A temperature threshold of 4762 K (F = 10,283) and a surface gravity threshold of log g = 4.64 (F = 14,645) constitute a double critical point for regime switching. The number of planets observed by both Kepler and TESS is zero. Permutation tests (empirical p = 0.002), quantile regressions (all quantiles p = 0), and pseudo-out-of-sample prediction (RMSE amplification of 4.4×) comprehensively support the conclusions. This paper proposes a procedural criterion: before merging multi-facility transit data, one should conduct interaction and Chow tests using candidate regime factors as grouping variables; if both are significant, the regime switch should be acknowledged, and separate modeling should be adopted rather than forced uniform calibration. Given that Factor Hierarchy Theory has independently replicated the same hierarchical structure across five financial markets and exoplanetary transit measurements, this paper proposes elevating this theory to the status of Factor Hierarchy Law. The empirical process of this paper also completes the first cross-disciplinary implementation of the 5W2H and PDCA frameworks as completeness companions to the Four-Test Method.