{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:3IO5WFKOFGKY4LOJM46WGK4C2M","short_pith_number":"pith:3IO5WFKO","schema_version":"1.0","canonical_sha256":"da1ddb154e29958e2dc9673d632b82d3272cf7d8b6ba281af6fc8815abac045f","source":{"kind":"arxiv","id":"cs/0607008","version":1},"attestation_state":"computed","paper":{"title":"3-facial colouring of plane graphs","license":"","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"F\\'ed\\'eric Havet (INRIA Sophia Antipolis), Jean-S\\'ebastien Sereni (INRIA Sophia Antipolis), Riste Skrekovski","submitted_at":"2006-07-03T06:38:48Z","abstract_excerpt":"A plane graph is l-facially k-colourable if its vertices can be coloured with k colours such that any two distinct vertices on a facial segment of length at most l are coloured differently. We prove that every plane graph is 3-facially 11-colourable. As a consequence, we derive that every 2-connected plane graph with maximum face-size at most 7 is cyclically 11-colourable. These two bounds are for one off from those that are proposed by the (3l+1)-Conjecture and the Cyclic Conjecture."},"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":"cs/0607008","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cs.DM","submitted_at":"2006-07-03T06:38:48Z","cross_cats_sorted":[],"title_canon_sha256":"d7cc01aa072c98fd39ee061eeadd9417ea41dd49dd5660f19cc04d66e712d4e2","abstract_canon_sha256":"a3943048e28e3796cc486bf72b23c6c822cdf2089f3478c9773d2bad1633f585"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:54.600781Z","signature_b64":"CnjxGzIswByyNdfElaUvKFD9I6JLJvB7hInBeqyQ0XNfvfrhXhJQ5QsLXE2BqUCS9g1+FIWDlITguSTdjfdqCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da1ddb154e29958e2dc9673d632b82d3272cf7d8b6ba281af6fc8815abac045f","last_reissued_at":"2026-05-18T01:08:54.600248Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:54.600248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"3-facial colouring of plane graphs","license":"","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"F\\'ed\\'eric Havet (INRIA Sophia Antipolis), Jean-S\\'ebastien Sereni (INRIA Sophia Antipolis), Riste Skrekovski","submitted_at":"2006-07-03T06:38:48Z","abstract_excerpt":"A plane graph is l-facially k-colourable if its vertices can be coloured with k colours such that any two distinct vertices on a facial segment of length at most l are coloured differently. We prove that every plane graph is 3-facially 11-colourable. As a consequence, we derive that every 2-connected plane graph with maximum face-size at most 7 is cyclically 11-colourable. These two bounds are for one off from those that are proposed by the (3l+1)-Conjecture and the Cyclic Conjecture."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0607008","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":"cs/0607008","created_at":"2026-05-18T01:08:54.600327+00:00"},{"alias_kind":"arxiv_version","alias_value":"cs/0607008v1","created_at":"2026-05-18T01:08:54.600327+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0607008","created_at":"2026-05-18T01:08:54.600327+00:00"},{"alias_kind":"pith_short_12","alias_value":"3IO5WFKOFGKY","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_16","alias_value":"3IO5WFKOFGKY4LOJ","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_8","alias_value":"3IO5WFKO","created_at":"2026-05-18T12:25:53.939244+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/3IO5WFKOFGKY4LOJM46WGK4C2M","json":"https://pith.science/pith/3IO5WFKOFGKY4LOJM46WGK4C2M.json","graph_json":"https://pith.science/api/pith-number/3IO5WFKOFGKY4LOJM46WGK4C2M/graph.json","events_json":"https://pith.science/api/pith-number/3IO5WFKOFGKY4LOJM46WGK4C2M/events.json","paper":"https://pith.science/paper/3IO5WFKO"},"agent_actions":{"view_html":"https://pith.science/pith/3IO5WFKOFGKY4LOJM46WGK4C2M","download_json":"https://pith.science/pith/3IO5WFKOFGKY4LOJM46WGK4C2M.json","view_paper":"https://pith.science/paper/3IO5WFKO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=cs/0607008&json=true","fetch_graph":"https://pith.science/api/pith-number/3IO5WFKOFGKY4LOJM46WGK4C2M/graph.json","fetch_events":"https://pith.science/api/pith-number/3IO5WFKOFGKY4LOJM46WGK4C2M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3IO5WFKOFGKY4LOJM46WGK4C2M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3IO5WFKOFGKY4LOJM46WGK4C2M/action/storage_attestation","attest_author":"https://pith.science/pith/3IO5WFKOFGKY4LOJM46WGK4C2M/action/author_attestation","sign_citation":"https://pith.science/pith/3IO5WFKOFGKY4LOJM46WGK4C2M/action/citation_signature","submit_replication":"https://pith.science/pith/3IO5WFKOFGKY4LOJM46WGK4C2M/action/replication_record"}},"created_at":"2026-05-18T01:08:54.600327+00:00","updated_at":"2026-05-18T01:08:54.600327+00:00"}