We examine the poloidal pump operator (P_z) — the directed, asymmetric flux of vacuum energy quanta through VEQF solitons — as a candidate mechanism for generating multiple observed properties of matter. Within the Vacuum Energy Quanta Field (VEQF) framework, we show how the same pump flux can project onto four distinct sectors of the external vacuum medium: (i) inertial mass via vacuum drag against beat-frequency interference, (ii) electric charge via toroidal wake circulation, (iii) magnetism via Lorentz distortion of the wake, and (iv) gravitational coalescence via gradient-asymmetric pump recoil. Two independent routes are presented for the Newtonian constant (G): one derived from pump mechanics and energy flux conservation, and another from topological invariants anchored to the Down-quark TCI. These routes are shown to be consistent with each other through the relation G · K = 2¹⁰ π lₚ² c ≈ 2.52 × 10⁻⁵⁸ m³/s. The mesoscopic lattice scale (l_q) cancels in observable ratios, and the gravitational-to-electromagnetic force ratio for the proton is computed as approximately (8.15 × 10⁻³⁷). The Equivalence Principle emerges naturally as both inertial and gravitational responses trace to the same pump flux. This work forms part of the ongoing development of the VEQF framework and should be read in conjunction with the companion papers on hadron mass emergence and the Advanced Gravity Emergence Model.