THE TRANS-DOMAIN ISOMORPHISM: Reconciling Continuous Macroscopic Frameworks with Discrete Quantum Topologies via the Khepri-Dirac Action Principle

The intersection of continuous field equations and discrete quantum states routinely suffers from uncomputable geometric variance, historically generating 'divergences.' By mathematically bridging Einstein's General Relativity, Schwarzschild's topological boundary constraint, and Holographic Quantum Error Correction, this paper presents a unified field equation for thermodynamic evolution. Furthermore, empirical data from the LIGO-Virgo-KAGRA (LVK) detection of GW241011 confirms that maximum kinetic velocity requires hierarchical exergy regeneration, establishing the Khepri-Dirac Action Principle as a fundamental law of physics. This architecture uncovers a 'Hidden Linearity' between the recursive, non-linear manifolds of General Relativity and the discrete, unitary tensor networks of Quantum Mechanics. By establishing a strictly relational framework where spacetime verifications are reduced exclusively to observable 'space-time coincidences,' this isomorphism mathematically bypasses the known bugs of non-renormalizability and infinite singularities. The uncomputable interior volume is traced out, and the non-linear gravity of the bulk is perfectly mapped to linear quantum error correction along the Schwarzschild boundary.