{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:7IXJ65ETUU6WWE3KOCZGANIVZA","short_pith_number":"pith:7IXJ65ET","schema_version":"1.0","canonical_sha256":"fa2e9f7493a53d6b136a70b2603515c83f252a142d337d4cc24fce932aa3efed","source":{"kind":"arxiv","id":"1504.06979","version":2},"attestation_state":"computed","paper":{"title":"Obstructions for three-coloring graphs without induced paths on six vertices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Jan Goedgebeur, Maria Chudnovsky, Mingxian Zhong, Oliver Schaudt","submitted_at":"2015-04-27T09:08:24Z","abstract_excerpt":"We prove that there are 24 4-critical $P_6$-free graphs, and give the complete list. We remark that, if $H$ is connected and not a subgraph of $P_6$, there are infinitely many 4-critical $H$-free graphs. Our result answers questions of Golovach et al. and Seymour."},"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":"1504.06979","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-27T09:08:24Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"4d67a82d1dc81e5893a2f7f4aa3c288988a9e4b7ed2edd3a8e0260114e46e2e2","abstract_canon_sha256":"1aaef7728b4d46507eaed2bce861a53f8aad74973f3c1412ab60f6ec6e87fa45"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:09.742694Z","signature_b64":"sqhCGkG2FgdkIoqDXXq4FH72LVerVyrWA/XwQMJWwaI6begFDRk4/5BTPyE4YB4zpTOAuC1YVrlJPIyUS0KSCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa2e9f7493a53d6b136a70b2603515c83f252a142d337d4cc24fce932aa3efed","last_reissued_at":"2026-05-18T00:23:09.742039Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:09.742039Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Obstructions for three-coloring graphs without induced paths on six vertices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Jan Goedgebeur, Maria Chudnovsky, Mingxian Zhong, Oliver Schaudt","submitted_at":"2015-04-27T09:08:24Z","abstract_excerpt":"We prove that there are 24 4-critical $P_6$-free graphs, and give the complete list. We remark that, if $H$ is connected and not a subgraph of $P_6$, there are infinitely many 4-critical $H$-free graphs. Our result answers questions of Golovach et al. and Seymour."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06979","kind":"arxiv","version":2},"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":"1504.06979","created_at":"2026-05-18T00:23:09.742143+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.06979v2","created_at":"2026-05-18T00:23:09.742143+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06979","created_at":"2026-05-18T00:23:09.742143+00:00"},{"alias_kind":"pith_short_12","alias_value":"7IXJ65ETUU6W","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"7IXJ65ETUU6WWE3K","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"7IXJ65ET","created_at":"2026-05-18T12:29:10.953037+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/7IXJ65ETUU6WWE3KOCZGANIVZA","json":"https://pith.science/pith/7IXJ65ETUU6WWE3KOCZGANIVZA.json","graph_json":"https://pith.science/api/pith-number/7IXJ65ETUU6WWE3KOCZGANIVZA/graph.json","events_json":"https://pith.science/api/pith-number/7IXJ65ETUU6WWE3KOCZGANIVZA/events.json","paper":"https://pith.science/paper/7IXJ65ET"},"agent_actions":{"view_html":"https://pith.science/pith/7IXJ65ETUU6WWE3KOCZGANIVZA","download_json":"https://pith.science/pith/7IXJ65ETUU6WWE3KOCZGANIVZA.json","view_paper":"https://pith.science/paper/7IXJ65ET","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.06979&json=true","fetch_graph":"https://pith.science/api/pith-number/7IXJ65ETUU6WWE3KOCZGANIVZA/graph.json","fetch_events":"https://pith.science/api/pith-number/7IXJ65ETUU6WWE3KOCZGANIVZA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7IXJ65ETUU6WWE3KOCZGANIVZA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7IXJ65ETUU6WWE3KOCZGANIVZA/action/storage_attestation","attest_author":"https://pith.science/pith/7IXJ65ETUU6WWE3KOCZGANIVZA/action/author_attestation","sign_citation":"https://pith.science/pith/7IXJ65ETUU6WWE3KOCZGANIVZA/action/citation_signature","submit_replication":"https://pith.science/pith/7IXJ65ETUU6WWE3KOCZGANIVZA/action/replication_record"}},"created_at":"2026-05-18T00:23:09.742143+00:00","updated_at":"2026-05-18T00:23:09.742143+00:00"}