N-Scaling and Entropic Divergence of Regime-B Breakout Clusters on the Twisted Bird-Map Boundary Grid (Paper 48 in the Non-Holomorphic Fractal Series)

Paper 48 in the Non-Holomorphic Fractal Series. Paper 47 established that numerical Regime A is fully falsified across the entire boundary grid E_bdy at N = 4096. Paper 48 asks how the inferred cluster-width proxies k_EAE and k_BV behave when the Ulam resolution is doubled across selected high-signal cells. We rerun the spike-quotient battery from Papers 45–47 on six boundary cells for N ∈ {2048, 4096, 8192} and add N = 16384 on three of them, obtaining a 21-row battery table. The resulting N-scan supports a discrete two-class taxonomy within numerical Regime B: a coherent class B1 where k_EAE and k_BV remain single- to few-digit and the divergence D is bounded and non-monotone, and a spray class B2 where k_BV stays bounded but k_EAE and D grow strictly across three successive doublings (four N-grids). In particular, the WBA kernel at ε = 0.70 exhibits a four-N sequence k_EAE = 165, 360, 529, 863 with D = 1.704, 2.065, 2.199, 2.426 and no sign of saturation, while Lorentzian corners and the Alien cell at ε = 0.76 remain in B1 on all computed grids.