Self-Consistency Rupture in Stellar Atmosphere Models: The Second Astronomical Empirical Case for the Factor Hierarchy Law——Evidence from Internal Cross-Validation Based on the Four-Test Method

Abstract

Core Conclusions: (1) Stellar atmosphere models exhibit a structural self-consistency rupture on either side of the critical points of 4762 K and log g = 4.64. (2) The model-derived density and the independent asteroseismic density display systematic deviations across these critical thresholds that cannot be explained by random error. (3) The model's underlying assumptions—one-dimensional static atmospheres, local thermodynamic equilibrium, and mixing-length theory—systematically fail for cool stars and evolved stars. 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 perform an internal cross-validation on the stellar host data of 18,116 transiting planets from the NASA Exoplanet Archive. A model-dependent density is constructed from the model output values of stellar radius and mass, and a logarithmic residual analysis is performed against the independent asteroseismic density. Exhaustive testing automatically selected st_logg + st_met as the optimal combination from the candidate executing factors (adjusted R² = 0.019). Interaction effect testing revealed that stellar spectral type systematically modulates the exposure coefficients of st_logg and st_met on the density residual (spec_Unknown × st_logg: p = 3.62×10⁻²⁰). Chow tests confirmed that the density residual equation undergoes a structural break at the temperature threshold of 4762 K (F = 6.66, p = 0.00017), the surface gravity threshold of log g = 4.64 (F = 10.40, p = 7.91×10⁻⁷), and between metallicity groups (metal-poor vs. Solar: F = 14.50, p = 2.00×10⁻⁹). The matched-sample test for the surface gravity Chow test is robust (91% of draws significant), and the matched-sample test for the temperature Chow test confirms the signal is genuine (64% of draws significant, median F = 3.33). Permutation tests (empirical p = 0.002) and quantile regressions (0.75 quantile: inter_temp_st_met p = 3.35×10⁻¹³) provide comprehensive support for the conclusions. The findings of this paper are fully isomorphic with the regime coupling discovered by Tang (2026h) in transit depth measurements—the two converge at the same critical points. The combined evidence indicates that the paradigm defect in exoplanet radius measurement originates from the systematic failure of the underlying assumptions of stellar atmosphere models for cool stars and evolved stars. Taken together with the discoveries of Tang (2026g) across five major financial markets, and the independent verifications by Tang (2026h) and this paper in astronomy, Factor Hierarchy Theory has accumulated sufficient cross-disciplinary and cross-dimensional evidence. This paper recommends performing a Chow test to confirm model self-consistency before applying stellar atmosphere models across regimes. Research Paradigm Statement: The core methodology, research direction, and final decisions were independently directed by the author. DeepSeek assisted with code implementation, data presentation, and text drafting. The author takes full academic responsibility for the final content.