Foundations of Trans-Planckian Horizon Lock Mechanics – Special Treatise: Mathematical Design for a Fault-Tolerant Topological Super-Quantum Computer Architecture via the Khandey Causal Invariant Constant

Abstract

This special treatise establishes the complete formal mathematical physics blueprint and structural regularization architecture for a stable, fault-tolerant Topological Super-Quantum Computer, operating inside the non-perturbative framework of Trans-Planckian Horizon Lock Mechanics (TPHLM). Classically, scalability limits in quantum computing grids suffer from catastrophic decoherence flows, high-order loop noises, and infinite phase divergences that destroy qubit state unitary vectors near initialization phases (t → 0). By anchoring the underlying topological quantum processor mesh directly onto the absolute spatial scale of the Khandey Causal Invariant Constant (K_J = 2.02 × 10^{26} m), we dimensionally regularize multi-loop braiding gates across sub-Planckian tracking boundaries. We satisfy non-perturbative 4D/5D Ward-Takahashi-Slavnov-Taylor gauge identities, eliminate computational trace anomalies, and guarantee an unassailable 0.0000000000000000% phase error baseline optimized for next-generation infinite-capacity quantum information systems.