π Universe: λ-field Luo's Gravitational Potential Well

The classic Roche potential well and Roche limit theory successfully describe the characteristics within a binary celestial system"bidirectional force balance" in binary systems, but their inherent limitations—reliance on virtual centrifugal force, applicability only to binary circular orbits, and failure to explain large-scale galactic stable motion—have forced modern astronomy to introduce multiple ad-hoc patches such as dark matter and dark energy. Taking the analytical framework of "potential gradient–bidirectional force–critical equilibrium" of the Roche potential as a bridge, and based on the core proposition of the π-universe temperature ruler, this paper strictly distinguishes two independent systems of matter temperature and field temperature for the first time. Field temperature is defined as a macroscopic measure of the disorder degree of chaotic field fluctuations, which satisfies the strict quantitative isomorphic relation with λ-field coherence: T_ = Tₚ 1- The λ-field Luo's Gravitational Well model constructed in this paper unifies gravity and virtual centrifugal force in classical theory into the real force of "low-temperature attraction and high-temperature repulsion" bidirectional equilibrium generated by temperature gradients, and replaces the conservation of angular momentum with λ-field coherent spinors. All physical constants of this model are rigorously derived from first principles; the only independent variable is the independently observable core field temperature, with no free fitting parameters. Without any additional patches, it can consistently explain the full-scale celestial stable motion from planetary rings, satellite orbits to galactic rotation curves and galactic spiral arm structures. It naturally explains the classic observational puzzle of "galactic peripheral gas temperature rising instead of falling" from first principles for the first time, and systematically responds to the three core independent observational evidences for dark matter: the Bullet Cluster gravitational lensing, the Cosmic Microwave Background (CMB) power spectrum, and large-scale structure formation. The goodness of fit \ (R²=0. 97\) for the rotation curves of 175 spiral galaxies in the SPARC database is significantly better than the NFW profile of the mainstream ΛCDM model.