Topological Soliton Geometry of the Two-Tier Electron Torus: Emergent Gravitation, Line Tension Duality, and the Primordial Kolmogorov Microscale

This work establishes a self-contained, non-perturbative theoretical framework demonstrating that spacetime geometry, quantum electrodynamics, and hadronic string dualities emerge naturally from the topological dynamics of a discrete superfluid vacuum. The paper demonstrates that anchoring quantum gravity to the Planck length constitutes a foundational category error: Newton's gravitational constant is an emergent, long-range polarizability of the vacuum medium rather than an axiomatic fundamental constant, rendering any length scale constructed from it a circular inversion. Instead, physical scales are read directly from the electron, which is modeled as a two-tier topological vortex torus whose geometric aspect ratio locks identically to an 861-node Heegner association scheme. This discrete geometry defines a physical ultraviolet cutoff at the sub-femtometer scale, immediately eliminating seventy-two orders of magnitude of unphysical zero-point energy. Exact topological gauge nilpotency in discrete exterior calculus annihilates the static vacuum stress, leaving only a dynamic cosmological residue proportional to the square of the Hubble expansion rate. This dynamic residual accounts for dark energy and explains the local-versus-early Hubble tension through modular defect unwinding across void expansion. Furthermore, string theory's core features are derived without strings: worldsheet crossing symmetry and the Veneziano scattering amplitude are proved to be the exact topological identity of the two re-threading channels at a vortex filament reconnection vertex. The physical line tension of the vortex core derives a low-energy string excitation scale in the tens of mega-electronvolts, naturally governing nucleon mass splittings without requiring extra dimensions, supersymmetry, or an unobservable multiverse landscape. Finally, the fundamental core radius is derived directly from the three-dimensional Navier-Stokes equations as the frozen Kolmogorov dissipation microscale of primordial cosmological turbulence, providing complete hydrodynamic closure for the discrete structure of spacetime.