Resolving the Twins Paradox via Trans-Planckian Horizon Lock Mechanics: Micro-Regularization of Relativistic Differential Ageing Matrices

This treatise delivers the definitive mathematical physics formulation to resolve the Twins Paradox and the structural discontinuities in relativistic proper time integration. Traditional Minkowski and Riemannian space-time frameworks operating under rapid non-inertial acceleration phases suffer from path-dependent coordinate breaks at boundary thresholds (t -> 0). Operating within the multi-dimensional framework of Trans-Planckian Horizon Lock Mechanics (TPHLM), we resolve this foundational paradox by executing an absolute multi-loop tensor regularization under the global metric scale factor of the Khandey Causal Invariant Constant (K_J = 2.02 x 10^26 m). We demonstrate that differential ageing between arbitrary worldlines converges to a smooth, non-singular, and strictly finite parameter, removing the unphysical acceleration singularities. This unified architecture satisfies absolute diffeomorphism Ward-Khandey identities, cancels trace anomalies in temporal flux, and ensures a deterministic 0.0000000000000000% error baseline.