Field Topology Theory: A Geometric Derivation of the Exclusion Principle and Quantum Statistics

We derive the Pauli Exclusion Principle as a geometric impossibility rather than an algebraic postulate. Working within a framework where particles are stable topological configurations of a continuous spacetime field, we show that two identical spin-½ vortices of the same handedness cannot simultaneously satisfy three independent geometric constraints—the spinorial half-winding condition, the dual handedness condition, and the precession space-time lock—required for spatial overlap. The admissible configuration set for co-location is proven empty (the Nopert Theorem). Integer-spin configurations, lacking the spinorial sign flip, do not encounter this obstruction and admit coherent overlap, recovering Bose-Einstein statistics. The framework generates four quantitative predictions distinguishing it from standard quantum mechanics: a field-dependent correction to the electron g-factor near the Schwinger limit, a topological pathway to the fine-structure constant, environment-dependent softening of degeneracy pressure at extreme curvature, and handedness-dependent scattering asymmetries. Experimental tests in high-field QED, neutron star observations, and spin-resolved interferometry are identified.