Nuclear Spectral Approach to Field Theory Dualities and Geometric Mirror Symmetry

A nuclear spectral framework is developed to unify topological invariants in noncommutative geometry into a universal invariant that encodes dual field theories and geometric mirror symmetry. It is shown that duality and mirror symmetry are characterized by stable equivalence of these universal invariants, and explicit constructions demonstrate Seiberg duality, mirror symmetry, and bulk–boundary correspondence. Edge cases are analyzed to delineate the model's limits, thereby providing a rigorous categorical foundation for nonperturbative dualities.