Grid-Phase Trap: Spatial Aliasing of the Lorentzian Deep Spectrum under Sub-Cell Partition Shifts on the Twisted Boundary Grid at ε = 0.70 (Paper 55 in the Non-Holomorphic Fractal Series)

Paper 55 in the Non-Holomorphic Fractal Series. Papers 52–53 documented a parameter-axis Nyquist trap: at the twisted Bird-map boundary grid with WBA kernel, tiny changes in ε produce large swings in the sub-dominant spectral geometry. Paper 54 extended this to the kernel axis, establishing kernel-independence of the dark-matter phenomenon at ε = 0.70. Paper 55 probes the partition axis: keeping ε, kernel, and N fixed, we slide the Ulam grid by a fraction of a cell and measure whether the spike location and deep-tier cumulative-mass diagnostics remain stable. We scan five equally spaced sub-cell grid-phase shifts δ ∈ {0, 0.2, 0.4, 0.6, 0.8} · Δx at N ∈ {8192, 16384} with the Lorentzian kernel at ε = 0.70. The spike location in v(1) is grid-phase-locked: it jumps by one cell index for each δ increment at both N, tracking the shift to sub-cell precision. The deep-tier cumulative-mass diagnostics (k50, k75, k90, top1pct) are invariant across all five phases: k90 ∈ {1, 2, 6} and top1pct = 1.000000 for every (j, N, δ) triple. The spike-dominated geometry is a grid-phase trap: it is locked to the partition and insensitive to sub-cell shifts on the executed grids.