Sorting the Spray: Cumulative Mass Diagnostics and Eigenvector Concentration on Twisted Ulam Grids

Paper 48 established a discrete two-class taxonomy within numerical Regime B on the twisted Bird-map boundary grid: a coherent class B1 where both k_EAE and k_BV remain single- to few-digit, and a spray class B2 where k_BV stays bounded while k_EAE grows monotonically across three successive Ulam-grid doublings (four N-grids), with WBA ε = 0.70 as the sole confirmed B2 cell. The B2 sequence admits an empirical power-law fit k_EAE(N) ≈ 0.5072·N^0.7715 on N ∈ {2048, 4096, 8192, 16384}, with k_BV remaining in [3.10, 3.35] across the same grids. A complementary off-diagonal probe at N = 1024 shows that WBA ε = 0.70 and Lorentzian ε = 1.02 have nearly identical column entropies and tail fractions (0.9111 vs.…