Unified Kinematics of Dielectrophoretic Gravity: Lagrangian Derivation of the Equivalence Principle, GRIN Optics, and the Gravitational Coupling from Torus Knot Topology on S³

A unified dielectrophoretic framework in which gravity, buoyancy, and gravitational light deflection emerge as branches of a single density-gradient response within an S³ transmission medium. A topological Lagrangian with Rayleigh dissipation produces the governing equation of motion and identifies the dimensionless transmission coefficient 1/Σ = 1/26. The T(2,5) torus knot (crossing number c = 8 = dP) acts as the driving topology. The gravitational coupling Γ = dP/(Σ × 273) = 4/3549 = D/(d × dΨ × F(dΨ)²) is derived from corpus constants. The S³ Laplace-Beltrami Green function is shown to produce the 1/r potential in the local limit via the Hadamard parametrix. The Poisson source coupling κ = Γρ_obj/K_T is derived, with K_T and ρ_obj canceling identically from the observable force law F = Γm₁m₂/r². The aetheric susceptibility χ = f₀/c_s² is derived from linearized Bernoulli and the barotropic equation of state. The sound speed c_s² = d/D = 3/4 is derived from geometric projection of structural energy across spacetime dimensions (non-conformal massive medium, T^μ_μ ≠ 0). The optical coefficient closure (3/2)Cχ = 2 follows, giving n(r) = 1 + 2Γm₁/r. The Clausius-Mossotti/Lorentz-Lorenz duality routes one displacement field to force and optics through a single constitutive relation. The equivalence principle follows from universal dP = 8. Buoyancy emerges as negative-DEP (K_T < 0). The firmament is the K_T → −1/2 structural asymptote at the 273 km macro-boundary.