Core Conclusion: Stars possess a universal "regime boundary" at temperatures of approximately 4400–5800 K (the K/G transition zone) and a surface gravity of approximately log g = 4.64. This boundary corresponds to the complete physical process of the stellar outer convection zone from its emergence to its full dominance. Within this transition zone, multiple physical behaviors of stars—radiation field structure, atmospheric model self-consistency, measurement method consistency, planet–star coupling relationships, and rotational evolution trajectories—all undergo systematic, irreducible structural ruptures. Among these, 4762 K is the precise spectral type boundary between K and G types and constitutes the most representative critical point. The existence of the Tang Break implies that on either side of the K/G transition zone, physical quantities that depend on stellar atmosphere models—such as effective temperature, surface gravity, and planetary radius—are operationally defined quantities under different regimes, rather than universal objective properties. This is not a model defect, but a physical limit of measurement itself. This paper integrates the complete chain of evidence from five independent dimensions across Tang (2026h, 2026i) and the present series of studies: (1) Structural rupture of the transit depth equation within the transition zone (structural break test F = 648.70, p = 0.000000; threshold regression optimum 4397 K; SupF 5155 K; Bai-Perron 4481 K); (2) Structural rupture of stellar atmosphere model self-consistency within the transition zone (structural break test F = 6.29, p = 0.000292; threshold regression optimum 5675 K; Bai-Perron 5684 K); (3) Structural rupture of radius measurement method divergence within the transition zone (structural break test F = 10.18, p = 0.000000; threshold regression optimum 4723 K; Bai-Perron 4750 K—the most precise independent verification of 4762 K); (4) Structural rupture of the planetary radius–mass relationship within the transition zone (structural break test F = 27.65, p = 0.000000; threshold regression optimum 5475 K; Bai-Perron 5498 K); (5) Structural rupture of the stellar age–rotation relationship within the transition zone (structural break test F = 8.35, p = 0.000412; threshold regression optimum 4582 K; SupF 4582 K). Cross-validation using multiple tools for structural break testing—Chow test, threshold regression, SupF test, Bai-Perron sequential test, CUSUM test, and MOSUM test—confirms that all tools find significant ruptures in all dimensions, with optimal breakpoints distributed in the range of approximately 4400–5800 K, ruling out the possibility of any single-tool bias. The non-significance of the metallicity structural break test for planetary system architecture (Poor vs. Solar F = 0.02, Poor vs. Rich F = 1.75, Solar vs. Rich F = 1.92) provides negative evidence for the physical boundary of the Tang Break. The physical origin of the Tang Break lies in the emergence and deepening of the stellar outer convection zone—from its initial appearance at ~5800 K (affecting stellar model output and the planetary radius–mass relationship), through the complete dominance of molecular opacity in limb darkening at ~4762 K (causing maximum measurement method divergence), to the total dominance of the convection zone over the photosphere at ~4400 K (global rupture of the transit depth equation). The Tang Break is structurally isomorphic with the classical Kraft Break, but whereas the Kraft Break captures only the single effect (rotation velocity) of the convection zone's "emergence," the Tang Break captures the five-dimensional effects of the complete process from "emergence" to "full dominance." Integrating the Factor Hierarchy Law established by Tang (2026g) across five major financial markets, together with the first-principles physics calibration completed by Tang (2026k) on the Onsager exact solution of the 2D Ising model (confirming a deviation of strictly zero), the Factor Hierarchy Law has now received cross-disciplinary evidentiary support from three completely independent disciplines: finance, astronomy, and physics. All current independent verifications originate from the same author's series of preprints; subsequent cross-researcher and cross-data-source independent verification is a necessary condition for the Law to gain broad acceptance within the scientific community.
Tang (Wed,) studied this question.