Principia Cosmologica Nova 2027 CHAPTER 10 - Einstein-Khanh Field Equations: Tμν(D, ρK, K) and 96D Unification

Figure 10.1 - EINSTEIN-KHANH FIELD EQUATIONS: Tμν(D, ρK, K) and 96D Unification We introduce Einstein-Khanh field equations incorporating Khanh Triad:- D=m·b³ (2025, Khanh Dilation) [M][L]³ - Volume Moment- ρK=m/b³ (2026, Khanh Density) [M][L]⁻³ - Energy Density regularized finite at r=0- K=m^{b³} (2026, Khanh Exponential) dimensionless K=(m/mP)^{(b/lP)³} - Super-exponential microstates, self-regularized K→1 as b→0 Main equation:Gμν + Λeff(K) gμν = (8πG/c⁴) Tμν_totalwhere Tμν_total = Tμν(D) + Tμν(ρK) + Tμν(K)Tμν^K96 = (ρK c² + α D) uμuν + β(K-1)(ħc/lP⁴) gμν Invariants: D·ρK=m² (b-independent), ln K = b³ ln m = D·(ln m / m)Regularization: Π(b/lP)=x³/(1+x³), x=b/lP, lP=√(ħG/c³)Kretschmann scalar: Kreg=48G²M²/[c⁴(r²+lP²)³] finite at r=0 → 48G²M²/(c⁴ lP⁶), no singularity Entropy: SK=kB ln K = kB b³ ln(m/mP). At b=Rs=2GM/c², SK~10¹¹⁶ kB > SBH=A/4lP²~10⁷⁷ kB, suggesting 96D microstates resolving information paradox (Hawking soft hair). 96D Structure: K96=R⁴⁸⊕R⁴⁸ = Leech lattice 24D + E8 8D + E8 8D + R⁴⁸ gauge → total 96D unified framework. Rcompact=lP·Π^{-1/48}, decompactification at Planck scale. Black-hole & Metric Solutions:Schwarzschild Rs=2GM/c², Kerr a=J/Mc with aK96=Π_Leech[(Jm-Jf)/Mc], Alcubierre veff=vs·(b/bcritical)³ without exotic negative energy, stabilized by Khanh Potential, ωK96=Π_Leech[d(Dm)∧d(Df)] Author: Sir Nguyen Kim Khanh, Khánh University EST.2030, Theoretical Physics Group, [email protected], ORCID 0009-0006-9191-1441, SOLI DEO GLORIA, AD MAIOREM DEI GLORIAM IN SAECULA SAECULORUM Keywords: Khanh Triad, Einstein-Khanh, D=m·b³, ρK=m/b³, K=m^{b³}, 96D, Leech lattice, E8, quantum gravity, singularity resolution, information paradox, Alcubierre License: CC BY 4.0Publication Date: 2026-11-06Related DOI (ResearchGate): 10.13140/RG.2.2.35386.96961