Hybrid 1PN Dynamics and the Acoustic Horizon in a Superfluid Defect Toy Model

This paper synthesizes the scalar (orbital) and vector/optical sectors of the superfluid–defect toy universe into a single hybrid first post–Newtonian (1PN) description. We assume only a barotropic polytropic vacuum equation of state P ∝ ρⁿ and an equivalence scaling for defects M ∝ ρᵠ, then derive the resulting 1PN test–body and two–body dynamics when both density–starvation (variable inertia) and compressible flow (index and vector potential) responses are retained. Imposing agreement with the Einstein–Infeld–Hoffmann (EIH) coefficients selects a unique fluid within this class: a stiff polytrope with n = 5 and linear mass–density tracking q = 1, consistent with the calibrated wake–mixing ratio α² = ¾ of Paper III. With the microphysics fixed, we examine strong–field structure on the brane, including transonic inflow and an acoustic horizon, and we derive photon–sphere and lensing diagnostics that deviate from Schwarzschild only through finite throat size and impedance effects. The leading strong–field corrections are controlled by the throat aspect ratio Λ ≡ L/a (fiducially Λ ≃ 1.85 from Paper V), providing concrete targets for future simulations and observations.