The Topological Fluid Vacuum: A Unification of Spacetime, Matter, and Cosmological Evolution

We present a framework modeling the physical vacuum as a topological superfluid governed by Bogoliubov-de Gennes dynamics, from which gravity, electromagnetism, and matter emerge as limiting descriptions. We derive four results. First, Newton's constant is shown to be consistent to 1.3% between two independent derivations — the Sciama-Mach environmental relation and the spectral ladder relation for the electron mass — constituting a self-consistency theorem (Section 3B-III). Second, the Israel-Stewart phonon relaxation time τ₀ is derived via Son-Wingate general coordinate invariance, reducing the dark energy sector from four free parameters to effectively one phenomenological parameter ε (Section 5C-I). Third, the determinant of the T(2,21) torus knot equals 21 is proved analytically via Alexander polynomial, providing a topological origin for the exponent in the electron-Planck mass relation (Section 3B-II). Fourth, the Eckart viscosity used in previous viscous cosmology models is shown to be acausal and replaced by the Israel-Stewart formulation, resolving a structural failure in the dark energy equation of state. The framework predicts w(z=2) > −1.05, distinguishable from CPL parametrization at 3–5σ by Euclid, and n = 21 in the spectral ladder relation falsifiable by JILA/BIPM precision G measurements by 2028. Thirteen open problems are identified as explicit targets for future work, including the 38-node K-theory proof, the T(2,21) stability under gradient flow, and the microscopic derivation of ε.