Formalization of N=25 Hyperbubble Stability

We present a rigorous geometric derivation of the ensemble limit N = 25 for the Hyperbottle multiverse, the Hyperbubble.While numerical simulations of the mega snap bifurcation empirically indicate that stability requires an ensemble of approximately 25 coupled manifolds, this addendum establishes the theoretical necessity of this number.We demonstrate that the Hyperbottle manifold M K4 functions as the compactified target space for a Bosonic String vacuum.By explicitly calculating the zero-point energy of the transverse vibrational modes and enforcing the cancellation of the Weyl anomaly, we prove that the critical dimension D = 26 is a mathematical requirement for Lorentz invariance.This result maps directly to an ensemble of 24 active layers plus a global regulator, confirming that N = 25 is not a free parameter but a fundamental condition of the bulk geometry.