Unified Quantum Gravitational Field Equation in KUTW From Weyl- Cartan Action:- Black Holes, Neutron Stars, and Axion Dark Matter

We present a comprehensive derivation of three interconnected quantum-gravitational field equations from a fundamental Weyl-Cartan action principle, rigorously grounded in heterotic string theory and the Kaundinya Unified Theory of Everything (KUTE) framework. The KUTE axioms form the cornerstone of this work, resolving longstanding problems including the cosmological constant problem, singularity resolution, hierarchy problem, and mass gap through a novel approach without a traditional cosmological constant, instead featuring cosmological parameters $\Lambda$ tied to density scales. The unified framework yields: (i) \textbf{Dillip's Equation} (10D, $\Lambda=9$) describing black hole interior dynamics, (ii) \textbf{Weyl-Cartan-Penrose (WCP) Equation} (6D, $\Lambda=6$) governing neutron star core physics, and (iii) \textbf{Weyl-Einstein-Bose (WEB) Equation} (4D, $\Lambda=3$) for axion dark matter phenomenology. The parameters $\Lambda$ emerge naturally from KUTE Axiom 1 (nested radical dynamics) through systematic dimensional reduction from heterotic $E_8 \times E_8$ on Narain lattices $\Gamma^{16+d,d}$. Each equation incorporates essential features including torsion, CP violation, and entanglement projection, providing singularity resolution and predicting testable phenomena such as neutron star mass limits ($2.5$--$3.0 M_\odot$), axion masses ($m_a = 6.2 \pm 0.4 \mu$eV), and chiral gravitational wave signatures. The framework establishes a complete bridge from fundamental quantum gravity to observable astrophysics