A Topological Vortex Framework for Unified Physics: Mathematical Correspondences with Nature

We present a minimal phenomenological framework in which classical electromagnetism, weak-field gravity, and key quantum kinematics emerge on a three-dimensional physical slice from the projection of circulation, defects, and flows in a higher-dimensional vortex sheet. A small-parameter expansion in thinness and geometric flatness controls all approximations, enabling closed-form mappings from 4D structure to 3D observables. In this picture: (i) electric fields arise from projected “slope” (potential gradients) while magnetic fields are projected eddies; (ii) weak-field gravitoelectric and gravitomagnetic responses follow from charge-blind “intake” and induced circulation; and (iii) quantum kinematics is recovered via a phase–circulation construction that yields the standard minimal couplings on the slice. Topological charge is identified with an oriented puncture count of core strands through the transition slab, explaining charge quantization and naturally accommodating drag-only (electromagnetically neutral) excitations. We derive a generic mass template for slender, closed defects that combines core and compressibility contributions with logarithmic renormalization in the loop radius. The framework makes concrete, testable predictions across sectors (e.g., GEM frame-drag relations, charge/counting rules, and vortex-mass scalings) and is accompanied by an open, programmatic verification suite that checks dimensional consistency and canonical identities (e.g., Poisson laws and GEM relations) across all derivations. Together these results suggest a unified, falsifiable route from a single hydrodynamic substrate to the observed electromagnetic, gravitational, and quantum structures on our slice.