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 kEAE and kBV remain single- to few-digit, and a spray class B2 where kBV stays bounded while kEAE grows monotonically across three successive Ulam-grid doublings (four N-grids), with WBA ε = 0. 70 as the sole confirmed B2 cell 12. Paper 49 asks: what discrete numerical process produces the B2 spray? We pursue two complementary approaches on the locked grids N ∈ 2048, 4096, 8192, 16384. First, we fit an empirical power law to the four-grid B2 sequence and obtain kEAE (N) ≈ 0. 5072·N⁰. 7715 with no visible saturation on the four computed grids, while kBV remains bounded in 3. 10, 3. 35 (Proposition 2. 1, grid-scoped). Second, a direct comparison of off-diagonal transition-mass structure between WBA and Lorentzian Ulam matrices at N = 1024 using column Shannon entropy and a bandwidth of 51 cells (5% of N) yields nearly identical tail fractions (0. 9111 vs. 0. 9011) and relative entropies, a difference of approximately one percentage point that is not statistically meaningful. This null result demonstrates that the B2 spray is not driven by a simple, global inflation of off-diagonal mass in the Ulam matrix. It localises the B2 spray on the executed grids to eigenvector concentration rather than gross off-diagonal transition structure.
Michael Bird (Fri,) studied this question.