High-Resolution and Probe-Kernel Falsification Attempt for the N-Stable Single-Cell Regime A via Spike-Quotient Diagnostics (Paper 46 in the Non-Holomorphic Fractal Series)

Paper 46 in the Non-Holomorphic Fractal Series. Paper 45 established a battery of five spike-quotient functionals and proved that any future run returning EAE > 0 or BV-COMP > 0 constitutes numerical evidence against the N-stable single-cell Regime A hypothesis on the boundary subgrid E_bdy ⊂ I_rig = [0.70, 1.10]. Paper 46 applies that battery in two complementary experiments. Path A pushes the resolution from N = 2048 toward N = 4096 on the existing twisted Bird-map Ulam infrastructure (three kernels: WBA, Lorentzian, Alien) to test whether the spike structure survives at higher discretisation. Path B introduces one Series-legal probe kernel—a k-cell uniform cluster explicitly designed to induce BV-COMP > 0 and EAE > 0—and verifies that the Paper 45 inversion formulas k = 1 + 2/BV-COMP = 1 + e^{EAE} recover the planted cluster width exactly. The Regime A baseline (all 60 rows at N = 2048) reproduces VOP = EAE = BV-COMP = 0 identically. The probe-kernel experiments confirm the inversion formulas to machine precision for k = 2, 3, 5, 10, 20. A single-cell probe at (WBA, 0.78) at N = 4096 already returns strictly positive EAE ≈ 5.31 and BV-COMP ≈ 0.823, crossing the falsifiability threshold at this cell. Full N = 4096 coverage is reserved for Paper 47.