Pseudospectral Instability of Deep Ulam Eigenvalues at the B2 Spray Point for WBA and Lorentzian Kernels (Paper 56 in the Non-Holomorphic Fractal Series)

Paper 56 in the Non-Holomorphic Fractal Series. Building on Papers 51–55, we compare the geometry and pseudospectral conditioning of the ten leading Ulam eigenpairs for WBA and Lorentzian kernels on the twisted Bird-map boundary grid at ε = 0.70 and N ∈ {8192, 16384}. For each kernel and N we compute right and left eigenvectors, match them by eigenvalue, and form a conditioning proxy κ_j = 1/(w_jᵀ v_j). The leading eigenpair has modest conditioning (κ_1 ≈ 10²), but deep tiers attain κ_j ~ 10¹⁶–10¹⁸ for both kernels, despite remaining spike-dominated in their right eigenvectors. A complementary set of θ-partition probes finds no certified multi-packet structure in these extreme tiers at either resolution, indicating that deep Ulam eigenvalues at the B2 spray point (tiers j = 2, …, 10) have extremely large conditioning proxies and are therefore numerically unstable as resonances even when the corresponding right eigenvectors remain spike-dominated.