{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:3SEQBYLK6DQA7HZLXC6YWUZIRS","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"20fea1c464a26134f980e3a35bbd3b962e59d66133f981166cfc98678ac36e39","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-09-02T21:26:43Z","title_canon_sha256":"7bde5c98ac61a856b8812ce2c91dd7c43c061563fa0851e0312f9d65edaf9aa3"},"schema_version":"1.0","source":{"id":"1109.0562","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.0562","created_at":"2026-05-18T04:14:07Z"},{"alias_kind":"arxiv_version","alias_value":"1109.0562v1","created_at":"2026-05-18T04:14:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.0562","created_at":"2026-05-18T04:14:07Z"},{"alias_kind":"pith_short_12","alias_value":"3SEQBYLK6DQA","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"3SEQBYLK6DQA7HZL","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"3SEQBYLK","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:284d8cb459d3ce4d59fd4979ad9b1311097954ef4931bff21a41cc8cadd0223d","target":"graph","created_at":"2026-05-18T04:14:07Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"A binary matrix has the consecutive ones property (C1P) if it is possible to order the columns so that all 1s are consecutive in every row. In [McConnell, SODA 2004 768-777] the notion of incompatibility graph of a binary matrix was introduced and it was shown that odd cycles of this graph provide a certificate that a matrix does not have the consecutive ones property. A bound of (k+2) was claimed for the smallest odd cycle of a non-C1P matrix with k columns. In this note we show that this result can be obtained simply and directly via Tucker patterns, and that the correct bound is (k+2) when ","authors_text":"Cedric Chauve, Mehrnoush Malekesmaeili, Tamon Stephen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-09-02T21:26:43Z","title":"A tight bound on the length of odd cycles in the incompatibility graph of a non-C1P matrix"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0562","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:aeaabc3c8389f5b2841c4165e02a8bcba38f977fc451b33a381757c699db4f0e","target":"record","created_at":"2026-05-18T04:14:07Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"20fea1c464a26134f980e3a35bbd3b962e59d66133f981166cfc98678ac36e39","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-09-02T21:26:43Z","title_canon_sha256":"7bde5c98ac61a856b8812ce2c91dd7c43c061563fa0851e0312f9d65edaf9aa3"},"schema_version":"1.0","source":{"id":"1109.0562","kind":"arxiv","version":1}},"canonical_sha256":"dc8900e16af0e00f9f2bb8bd8b53288c9dd89f75f42d04fcdf9f7ea330abff1b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc8900e16af0e00f9f2bb8bd8b53288c9dd89f75f42d04fcdf9f7ea330abff1b","first_computed_at":"2026-05-18T04:14:07.320772Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:07.320772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j3AO9MumYSn91Xpg81Js5nYLyxvegpQIe7G/MDnOvalGt5kusQuBE7G+f+Dso9VkpWQQUiUHA4OfmLpw5KrvDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:07.321222Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.0562","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aeaabc3c8389f5b2841c4165e02a8bcba38f977fc451b33a381757c699db4f0e","sha256:284d8cb459d3ce4d59fd4979ad9b1311097954ef4931bff21a41cc8cadd0223d"],"state_sha256":"433353829f9cec92d68d515a93ca3c871c38341ab7a4bd50ab8c252cf75bdf2a"}