Projective Pole Duality and Superfluid Hydrodynamics: A Unified Geometric and Fluid-Dynamic Framework for Gravity, Mass, and Cosmic Acceleration

We present a unified theoretical framework that combines the pure geometric topology of Projective Pole Duality (PPD) with the empirical success of Dynamic Vacuum Theory (DVT). Standard Model cosmology and General Relativity (Lambda-CDM) postulate unobserved dark sector entities (Dark Matter, Dark Energy) and rely on a mathematically singular spacetime continuum. In contrast, we demonstrate that zero (0) and infinity (infinity) are not disconnected limits, but the two poles of a single Riemann Sphere (r * r* = l_0 * R_infinity). Time is not a distinct 4th dimension, but the internal rotation rate of a 4D fiber within an 8D Octonionic Hopf Fibration (S^3 -> S^7 -> S^4), yielding the universal relativistic invariant v_ext^2 + v_int^2 = c^2. Gravitational acceleration is derived as the quantum interference pattern between the local zero-pole and cosmic infinity-pole: a(r) = |psi_0 + e^(i*theta) * psi_infinity|^2 = GM/r^2 + 2*cos(theta)*sqrt(GM*a_infinity/r^2) + a_infinity. In the macroscopic fluid limit, this geometric interference manifests as the compressible superfluid vacuum of DVT, governed by the non-linear equation a_DVT = a_N / tanh(sqrt(a_N / a_0)). This framework topologically resolves the r -> 0 singularity into cavitation horizons, analytically predicts the 6*pi^5 proton-to-electron mass ratio, and accurately reproduces flat galactic rotation curves and cluster dynamics with zero free parameters.