{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:6BS2XKPS42B2XQ4TPHS5B4OCVE","short_pith_number":"pith:6BS2XKPS","schema_version":"1.0","canonical_sha256":"f065aba9f2e683abc39379e5d0f1c2a90ee1acc350968fe3d6e8cc6c7b3c3e49","source":{"kind":"arxiv","id":"1904.03818","version":1},"attestation_state":"computed","paper":{"title":"Minimum degree conditions for the existence of cycles of all lengths modulo $k$ in graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Shuya Chiba, Tomoki Yamashita","submitted_at":"2019-04-08T03:22:36Z","abstract_excerpt":"Thomassen, in 1983, conjectured that for a positive integer $k$, every $2$-connected non-bipartite graph of minimum degree at least $k + 1$ contains cycles of all lengths modulo $k$. In this paper, we settle this conjecture affirmatively."},"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":"1904.03818","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-04-08T03:22:36Z","cross_cats_sorted":[],"title_canon_sha256":"26bbf4afbf1741a771313c1a3e6617bfb7e58e38b86285601f87610785d19124","abstract_canon_sha256":"3bd8f09d2a4e0ffccbb4e19300874385d2ae5a9d6f7e18e5a980a809fa3f9b09"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:08.054487Z","signature_b64":"6ucZiET4mntRFiKBxoRFzwOU9RUwFUQkGnNhNqymzGnvSLuuUbnKf+Fbk2hcUX1Qn6Gd9lU/W3Zt6R3e5RThBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f065aba9f2e683abc39379e5d0f1c2a90ee1acc350968fe3d6e8cc6c7b3c3e49","last_reissued_at":"2026-05-17T23:49:08.053816Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:08.053816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimum degree conditions for the existence of cycles of all lengths modulo $k$ in graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Shuya Chiba, Tomoki Yamashita","submitted_at":"2019-04-08T03:22:36Z","abstract_excerpt":"Thomassen, in 1983, conjectured that for a positive integer $k$, every $2$-connected non-bipartite graph of minimum degree at least $k + 1$ contains cycles of all lengths modulo $k$. In this paper, we settle this conjecture affirmatively."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.03818","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":"1904.03818","created_at":"2026-05-17T23:49:08.053906+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.03818v1","created_at":"2026-05-17T23:49:08.053906+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.03818","created_at":"2026-05-17T23:49:08.053906+00:00"},{"alias_kind":"pith_short_12","alias_value":"6BS2XKPS42B2","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_16","alias_value":"6BS2XKPS42B2XQ4T","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_8","alias_value":"6BS2XKPS","created_at":"2026-05-18T12:33:10.108867+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/6BS2XKPS42B2XQ4TPHS5B4OCVE","json":"https://pith.science/pith/6BS2XKPS42B2XQ4TPHS5B4OCVE.json","graph_json":"https://pith.science/api/pith-number/6BS2XKPS42B2XQ4TPHS5B4OCVE/graph.json","events_json":"https://pith.science/api/pith-number/6BS2XKPS42B2XQ4TPHS5B4OCVE/events.json","paper":"https://pith.science/paper/6BS2XKPS"},"agent_actions":{"view_html":"https://pith.science/pith/6BS2XKPS42B2XQ4TPHS5B4OCVE","download_json":"https://pith.science/pith/6BS2XKPS42B2XQ4TPHS5B4OCVE.json","view_paper":"https://pith.science/paper/6BS2XKPS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.03818&json=true","fetch_graph":"https://pith.science/api/pith-number/6BS2XKPS42B2XQ4TPHS5B4OCVE/graph.json","fetch_events":"https://pith.science/api/pith-number/6BS2XKPS42B2XQ4TPHS5B4OCVE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6BS2XKPS42B2XQ4TPHS5B4OCVE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6BS2XKPS42B2XQ4TPHS5B4OCVE/action/storage_attestation","attest_author":"https://pith.science/pith/6BS2XKPS42B2XQ4TPHS5B4OCVE/action/author_attestation","sign_citation":"https://pith.science/pith/6BS2XKPS42B2XQ4TPHS5B4OCVE/action/citation_signature","submit_replication":"https://pith.science/pith/6BS2XKPS42B2XQ4TPHS5B4OCVE/action/replication_record"}},"created_at":"2026-05-17T23:49:08.053906+00:00","updated_at":"2026-05-17T23:49:08.053906+00:00"}