Coarse-Band Dark Matter in the Second Eigenpair: Oscillatory v^(2) Geometry Beneath a Frozen Spike on epsilon in {0.70, 0.71, 0.72, 0.73, 0.74} (Non-Holomorphic Fractal Series — Paper 53)

Oldham Council

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Abstract

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 - |lambda_2| / |lambda_1|…

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Topics & keywords

Keywords
  • Spike (software development)
  • Aliasing
  • Eigenvalues and eigenvectors
  • Dark matter
  • Series (stratigraphy)
  • Sampling (signal processing)
  • Fractal
  • Anisotropy
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