Topological Impedance Matching in Structured Vacua: Non-BCS Coherent Transport and Catalyzed Nuclear Transitions

This work establishes a unified theoretical framework demonstrating that room-temperature superconductivity and low-energy nuclear reactions emerge as dual physical manifestations of topological impedance matching between engineered solid-state systems and the discrete spectral manifold of the physical vacuum. Electrical resistance is identified as topological representational friction caused by a non-commutative spectral obstruction between continuous wave mechanics and the discrete vacuum substrate. In impedance-matched flat-band heterostructures, this obstruction vanishes identically, enabling non-BCS lossless transport governed by the flat-band quantum metric under resonant optical drive without requiring thermal Cooper pairing. Concurrently, the proton charge radius and the neutron-proton mass splitting are derived as the vacuum saturation resolution limit and the topological isospin activation threshold of a three-vorton Borromean knot. At hydrodynamic velocity stagnation points, divergent electronic screening collapses the electrostatic Coulomb barrier into a sub-picometer Yukawa potential, dramatically increasing tunneling probability and driving thermal power generation under dual acoustic resonance. Topological helicity conservation strictly suppresses fragmentation into neutron channels, collapsing the nuclear reaction onto exclusive helium-4 production, while the nuclear mass defect partitions downward across the discrete vacuum nodes directly into lattice phonons without emitting high-energy gamma radiation.