The Stellar Main-Sequence Regime Boundary: Five-Dimensional Independent Verification of the 4762 K Critical Point and the Systematic Establishment of the Factor Hierarchy Law

Core Conclusion: At a temperature of approximately 4762 K and a surface gravity of approximately log g = 4.64, stars exhibit a universal "regime boundary." On either side of this critical point, 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. We designate this boundary the "Stellar Main-Sequence Regime Boundary," abbreviated as the Tang Break. This paper integrates the complete chain of evidence from five independent dimensions across Tang (2026h, 2026i) and the present series of studies. Dimension 1 (Transit Depth): Exhaustive testing automatically selected radius_ratio + pl_orbper + sy_dist as the optimal combination from 12 candidate executing factors (adjusted R² = 0.691); temperature threshold regression F = 10,283; permutation test empirical p = 0.002. Dimension 2 (Stellar Atmosphere Model Self-Consistency): Exhaustive testing selected st_logg + st_met as the optimal combination (adjusted R² = 0.019); metallicity Chow F = 14.50 (p = 2.00×10⁻⁹); surface gravity matched-sample test 91% significant; permutation test empirical p = 0.002. Dimension 3 (Measurement Method Divergence): Facility Chow F = 9.86 (p = 0.000000); temperature Chow F = 5.04 (p = 0.00047); permutation test empirical p = 0.016. Dimension 4 (Planetary Radius-Mass Relationship): Temperature Chow F = 32.78 (p = 0.000000); surface gravity Chow F = 35.57 (p = 0.000000); metal-rich matched-sample test 100% significant; permutation test empirical p = 0.008; 0.75 quantile regression p = 2.79×10⁻⁸. Dimension 5 (Stellar Age-Rotation Relationship): Chow F = 10.22 (p = 0.00009); matched-sample test 94% significant; permutation test empirical p = 0.002. The metallicity Chow test for planetary system architecture is non-significant, providing negative evidence for the physical boundary of the Tang Break. The physical origin of the Tang Break lies in the full development of the stellar outer convection zone—when the temperature drops below approximately 4762 K, the outer layer transitions from radiation-dominated to convection-dominated, triggering systematic qualitative changes in the magnetic field generation mechanism, magnetic braking intensity, and atmospheric molecular opacity. The Tang Break is structurally isomorphic with the classical Kraft Break, but the two correspond to different stages of convection zone evolution: the Kraft Break corresponds to the threshold where the convection zone "just begins to appear" (approximately 6250 K), while the Tang Break corresponds to the threshold where the convection zone "has fully developed" (approximately 4762 K). In terms of evidentiary framework, the Tang Break upgrades the Kraft Break's discovery in a single dimension (rotation velocity) to a five-dimensional evidence system encompassing the radiation field, atmospheric models, planet-star coupling, and rotational evolution. This paper considers that there is sufficient evidence to support the establishment of Factor Hierarchy Theory as the Factor Hierarchy Law. 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.