VCDM Framework Part IV: Microscopic Foundation of Vacuum Interface Tension & Closure at Fundamental Constants

This work completes the mathematical framework of the VCDM theory (Vacuum Condensate/Continuum Mechanics) by directly deriving the macroscopic interface tension sigma of the expanding spacetime bubble from the microstates of the Planck scale. We show that the phase boundary parameters postulated in Parts I-III are not phenomenological free parameters, but are rigidly anchored by the interplay of Planck's reduced constant (hbar), the speed of light (c), and the gravitational constant (G). By inserting the microscopic boundary density into the cavitation coupling parameter kappa_cav, the baryon-to-photon ratio eta_B ~ 10^-10 (Part III) is identified as a purely geometric precipitation rate of a single Planck layer l_P. Furthermore, the primordial spectral index n_s ~ 0.965 is derived directly from the visco-elastic damping of capillary waves on the condensate interface without invoking inflaton scalar fields.