{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:2YOEFJUZ5MFD4J22HCRLBCULNR","short_pith_number":"pith:2YOEFJUZ","schema_version":"1.0","canonical_sha256":"d61c42a699eb0a3e275a38a2b08a8b6c4bc649436ab76873646511e09d81273b","source":{"kind":"arxiv","id":"1410.0430","version":1},"attestation_state":"computed","paper":{"title":"Cycles with consecutive odd lengths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jie Ma","submitted_at":"2014-10-02T01:32:19Z","abstract_excerpt":"It is proved that there exists an absolute constant c > 0 such that for every natural number k, every non-bipartite 2-connected graph with average degree at least ck contains k cycles with consecutive odd lengths. This implies the existence of the absolute constant d > 0 that every non-bipartite 2-connected graph with minimum degree at least dk contains cycles of all lengths modulo k, thus providing an answer (in a strong form) to a question of Thomassen. Both results are sharp up to the constant factors."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1410.0430","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-02T01:32:19Z","cross_cats_sorted":[],"title_canon_sha256":"a9e321565c6a118c4ed4e1f1a684a237735b64b04694aa3839d3bbbd7fef2454","abstract_canon_sha256":"31b2acfd12449f5d12800c9cbcae83e5a6ba3d1986d67b96b738f00a614daa2b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:16.443274Z","signature_b64":"YHdjUbcTG+42iavu/0YD95AHsJdjskoHVZILAD3vGY28LmEVt1oSwdYBHO3dMFoFr2UutMbiSW5U1mu5Zb8DBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d61c42a699eb0a3e275a38a2b08a8b6c4bc649436ab76873646511e09d81273b","last_reissued_at":"2026-05-18T02:41:16.442827Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:16.442827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cycles with consecutive odd lengths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jie Ma","submitted_at":"2014-10-02T01:32:19Z","abstract_excerpt":"It is proved that there exists an absolute constant c > 0 such that for every natural number k, every non-bipartite 2-connected graph with average degree at least ck contains k cycles with consecutive odd lengths. This implies the existence of the absolute constant d > 0 that every non-bipartite 2-connected graph with minimum degree at least dk contains cycles of all lengths modulo k, thus providing an answer (in a strong form) to a question of Thomassen. Both results are sharp up to the constant factors."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0430","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1410.0430","created_at":"2026-05-18T02:41:16.442890+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.0430v1","created_at":"2026-05-18T02:41:16.442890+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.0430","created_at":"2026-05-18T02:41:16.442890+00:00"},{"alias_kind":"pith_short_12","alias_value":"2YOEFJUZ5MFD","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_16","alias_value":"2YOEFJUZ5MFD4J22","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_8","alias_value":"2YOEFJUZ","created_at":"2026-05-18T12:28:11.866339+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2YOEFJUZ5MFD4J22HCRLBCULNR","json":"https://pith.science/pith/2YOEFJUZ5MFD4J22HCRLBCULNR.json","graph_json":"https://pith.science/api/pith-number/2YOEFJUZ5MFD4J22HCRLBCULNR/graph.json","events_json":"https://pith.science/api/pith-number/2YOEFJUZ5MFD4J22HCRLBCULNR/events.json","paper":"https://pith.science/paper/2YOEFJUZ"},"agent_actions":{"view_html":"https://pith.science/pith/2YOEFJUZ5MFD4J22HCRLBCULNR","download_json":"https://pith.science/pith/2YOEFJUZ5MFD4J22HCRLBCULNR.json","view_paper":"https://pith.science/paper/2YOEFJUZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.0430&json=true","fetch_graph":"https://pith.science/api/pith-number/2YOEFJUZ5MFD4J22HCRLBCULNR/graph.json","fetch_events":"https://pith.science/api/pith-number/2YOEFJUZ5MFD4J22HCRLBCULNR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2YOEFJUZ5MFD4J22HCRLBCULNR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2YOEFJUZ5MFD4J22HCRLBCULNR/action/storage_attestation","attest_author":"https://pith.science/pith/2YOEFJUZ5MFD4J22HCRLBCULNR/action/author_attestation","sign_citation":"https://pith.science/pith/2YOEFJUZ5MFD4J22HCRLBCULNR/action/citation_signature","submit_replication":"https://pith.science/pith/2YOEFJUZ5MFD4J22HCRLBCULNR/action/replication_record"}},"created_at":"2026-05-18T02:41:16.442890+00:00","updated_at":"2026-05-18T02:41:16.442890+00:00"}