Dark Matter in the Second Eigenvector: Oscillatory v(2) Geometry Beneath a Frozen Spike in the WBA Micro-Band ϵ∈[0.700,0.710] (Non-Holomorphic Fractal Series — Paper 52)

This paper is Part 52 of the Non-Holomorphic Fractal Series. It probes the twisted Bird-map WBA kernel on the boundary-grid Ulam discretisation across a narrow “micro-band” in the parameter ε, namely ε ∈ {0.700, 0.701, …, 0.710} at N ∈ {8192, 16384}, using the certified Paper 37 builder and a consistent Markov-matrix (P) orientation. For each of the 22 (ε, N) pairs, we compute the two leading eigenpairs of the column-normalised Ulam matrix and record a locked CSV (paper52_microband_scan.csv) with cumulative-mass diagnostics for both eigenvectors and a discrete finite-grid spectral-gap proxy g_{N,ε} = 1 − |λ₂|/|λ₁|. On these grids the leading eigenvector v^{(1)} remains a literal single-cell spike throughout…