Validation of the Reduced-Jump Spectral Step by Fixed-Count Subsampling

Research Note 2 in the "Geometry of the Critical Line" programme. Paper 25 identified a floor-to-plateau spectral step in the reduced-jump transition matrix |λ₂| across the routing transition in the Newton dynamics of C_α (z) = z − exp (−α/z), but flagged a caveat: the total number of reduced-jump transitions grows 3. 68× across the α sweep, potentially inflating the apparent step via estimation stability. This note resolves the caveat by fixed-count subsampling. At each α, transitions are subsampled to the minimum count (N = 88, 613) and |λ₂| is recomputed 50 times. The subsampled values match the full-data values to within ±0. 001, with a signal-to-noise ratio of 76: 1. The spectral step is real and is not a sample-size artifact.