We extend the WBA boundary-grid eigenpair scan from the micro-band (Paper 52, step 0. 001) to the coarse band epsilon in 0. 70, 0. 71, 0. 72, 0. 73, 0. 74 at N in 8192, 16384. The leading eigenvector remains a literal single-cell delta spike (k50 = k75 = k90 = 1, top1pct = 1. 000000) at all ten coarse-band points, confirming the Paper 51 sharpened null across the full band and both grid sizes. The second eigenvector forms a highly compressed, ultra-high-frequency wavepacket: its signed version carries sign-change counts near 3800 (approximately 0. 23N at N = 16384), yet its absolute mass collapses to k90^ (2) = 2 cells near the spike centre. The finite-grid gap proxy g (N, epsilon) = 1 - |lambda₂| / |lambda₁| remains strongly non-monotone across the coarse band, ranging from 0. 253 at epsilon = 0. 72 to 0. 984 at epsilon = 0. 73 at N = 16384. Combining coarse-band and micro-band data reveals a Nyquist-style aliasing trap: coarse sampling at step 0. 01 can give the impression of smooth parameter dependence while interstitial micro-band sampling at step 0. 001 exposes violent finite-grid oscillations in the sub-dominant spectrum. A k = 3 micro-band probe records six epsilon-N-dependent conjugate-pair configurations, confirming that the real versus complex-conjugate classification of the sub-dominant spectrum remains unstable under grid refinement near the B2 band. All statements are strictly finite-grid, scoped to the executed epsilon-mesh and N in 8192, 16384. Data locked in paper53coarsebandₛcan. csv and paper53ₖ3ₘicroband. csv (both checkers passed). No new kernels, Banach spaces, certified gaps, or universal constants are introduced.
Michael Bird (Sun,) studied this question.