Discuss Findings

crossover_scale_mean +1.27261 +/- 0.00242, edge_mass_gain_mean -0.07365 +/- 0.00029, root_drop_slope_mean -0.28209 +/- 0.00019, and max_block_suppression_mean +0.49197 +/- 0.00026; per-degree breakdown shows deg=64 roots 2.872 +/- 0.001 at block 1 falling to 1.500 +/- 0.001 at block 32 with suppression 0.478 +/- 0.000 and edge mass 0.544 +/- 0.000 -> 0.593 +/- 0.000 at block 8 -> 0.500 +/- 0.000 at block 32; deg=96 roots 3.129 +/- 0.002 -> 1.500 +/- 0.001 with suppression 0.521 +/- 0.000 and edge mass 0.584 +/- 0.000 -> 0.631 +/- 0.000 -> 0.500 +/- 0.000; deg=128 roots 3.311 +/- 0.002 -> 1.626 +/- 0.001 with suppression 0.509 +/- 0.000 and edge mass 0.609 +/- 0.000 -> 0.653 +/- 0.000 -> 0.516 +/- 0.000

REJECTED. The data reject a monotone claim that stronger block persistence pushes Littlewood real roots toward the edges at x=+/-1. What the experiment robustly shows instead is a crossover in root-count suppression: once block length reaches about 1.27*sqrt(degree), the expected number of real roots is cut roughly in half. Edge localization is nonmonotone, with moderate persistence lengths (blocks 4 to 8) increasing near-edge mass slightly, but the longest blocks lowering edge mass below the iid baseline. The likely mechanism is that short-range sign persistence removes some high-frequency cancellations and temporarily favors edge-adjacent roots, whereas long constant-sign stretches suppress sign changes so strongly that they eliminate real roots faster than they concentrate the survivors near the endpoints.