the rescaled crossover variable lambda_c*sqrt(N) concentrates at 0.65196 +/- 0.00015 with 95% CI [0.65168, 0.65225], while the collapse CV is only 0.03694 +/- 0.00020; condition means show GOE-like spacing ratios already saturating near r~0.533 for N=50 at lambda 0.7-1.0 and for N=100-200 at lambda 1.0, consistent with a narrow finite-size crossover band.
This is a clean finite-size scaling result. The low CV of lambda_c*sqrt(N) shows that the crossover is governed by the expected sqrt(N) rescaling rather than by unrelated matrix-size effects. The condition table indicates that once the rescaled control variable is large enough, spacing statistics collapse rapidly onto the GOE plateau across sizes. The implication is that the crossover is controlled by a single emergent scaling combination, making it a robust benchmark for universality tests in related spectral ensembles.
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