Paper 48 in the Non-Holomorphic Fractal Series. Paper 47 established that numerical Regime A is fully falsified across the entire boundary grid Ebdy at N = 4096. Paper 48 asks how the inferred cluster-width proxies kEAE and kBV 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 kEAE and kBV remain single- to few-digit and the divergence D is bounded and non-monotone, and a spray class B2 where kBV stays bounded but kEAE 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 kEAE = 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.
Michael Bird (Thu,) studied this question.