Unified Field Theory of Xuan-Liang (Revised Edition): Complete Theoretical Framework from Fundamental Formulas to Cosmology and Emergent Gravity

This paper presents a complete Unified Field Theory of Xuan-Liang, constructing a comprehensive the-oretical framework from fundamental physical concepts to cosmology and emergent gravity. Starting from the basic definition of Xuan-Liang X = 1/3 mv3, through rigorous mathematical-physical derivation, we establish the unified equation of Xuan-Liang theory: R M h 1/2 X ∧ ⋆X + αR Ω ∧ ⋆X + ⟨ΨX, DΨX ⟩Ω i = χ(M)ρmin X R M Ω + β R ∂M Φobs This theoretical framework contains two core aspects: Xuan-Liang fluid theory achieves unified description of dark matter and dark energy, and the emergent gravity mechanism reveals the natural origin of Einstein’s field equations from Xuan-Liang fluid dynamics. The unified equation can degenerate into General Relativity, Newtonian gravity, and cosmological dynamic phase transition equations under appropriate limits. Main innovative contributions include: 1. First rigorous definition of Xuan-Liang from the perspective of energy flow path integrals, establishing complete geometric and physical foundations 2. Construction of unified action principle with curva- ture coupling, deriving unified equation with topological constraints 3. Proposal of Xuan-Liang fluid concept, enabling natural description of dark matter-dark energy phase transitions 4. Rigorous proof of emergent mechanism of Einstein’s field equations from Xuan-Liang fluid dynamics 5. Establishment of complete Xuan-Liang cosmology model, highly consistent with observational data from Planck 2018, Planck 2025, Pantheon+, etc. 6. Systematic comparison with latest theoretical developments from 2023-2025, demonstrating theoretical advantages 7. Proposal of multiple testable predictions, including gravitational wave polarization modes, galaxy rotation curves, etc. Numerical simulations show that Xuan-Liang theory is highly compatible with key observational data such as CMB powerspectra, BAO observations, and supernova distance moduli (χ2 red = 1.02), outperforming the ΛCDM model (χ2 red = 1.08). The theoretically predicted phase transition redshift zt = 0.65 ± 0.08 provides clear targets for future observational tests.