{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:HP26OO7PJ3BVGBFKSIBCUNWI3V","short_pith_number":"pith:HP26OO7P","schema_version":"1.0","canonical_sha256":"3bf5e73bef4ec35304aa92022a36c8dd7f1439f2fa525f2b2fbe0378ed2d50cb","source":{"kind":"arxiv","id":"1007.1430","version":2},"attestation_state":"computed","paper":{"title":"Sub-exponentially many 3-colorings of triangle-free planar graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Arash Asadi, Luke Postle, Robin Thomas, Zdenek Dvorak","submitted_at":"2010-07-08T18:08:39Z","abstract_excerpt":"Thomassen conjectured that every triangle-free planar graph on n vertices has exponentially many 3-colorings, and proved that it has at least 2^[n^(1/12)/20000] distinct 3-colorings. We show that it has at least 2^sqrt(n/362) distinct 3-colorings."},"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":"1007.1430","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-07-08T18:08:39Z","cross_cats_sorted":[],"title_canon_sha256":"5f7cb03d59004e2897a69080b922eaf0a2c73800afbd9ea9968a728f964be593","abstract_canon_sha256":"b6684c64e04b87eea3a84d43a55af6defecf2b8c78602f80f6ba8254f9eaf1f5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:25:28.255384Z","signature_b64":"x4IA3zv5MBAnjdltiGJRCak38KhAOIja/3FZlWgpEGPuwkHWx5+GyhEmE9/bgZoiUt39Li7qjDNVv3r6shioBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3bf5e73bef4ec35304aa92022a36c8dd7f1439f2fa525f2b2fbe0378ed2d50cb","last_reissued_at":"2026-05-18T04:25:28.254822Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:25:28.254822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sub-exponentially many 3-colorings of triangle-free planar graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Arash Asadi, Luke Postle, Robin Thomas, Zdenek Dvorak","submitted_at":"2010-07-08T18:08:39Z","abstract_excerpt":"Thomassen conjectured that every triangle-free planar graph on n vertices has exponentially many 3-colorings, and proved that it has at least 2^[n^(1/12)/20000] distinct 3-colorings. We show that it has at least 2^sqrt(n/362) distinct 3-colorings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.1430","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":"1007.1430","created_at":"2026-05-18T04:25:28.254899+00:00"},{"alias_kind":"arxiv_version","alias_value":"1007.1430v2","created_at":"2026-05-18T04:25:28.254899+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.1430","created_at":"2026-05-18T04:25:28.254899+00:00"},{"alias_kind":"pith_short_12","alias_value":"HP26OO7PJ3BV","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_16","alias_value":"HP26OO7PJ3BVGBFK","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_8","alias_value":"HP26OO7P","created_at":"2026-05-18T12:26:07.630475+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/HP26OO7PJ3BVGBFKSIBCUNWI3V","json":"https://pith.science/pith/HP26OO7PJ3BVGBFKSIBCUNWI3V.json","graph_json":"https://pith.science/api/pith-number/HP26OO7PJ3BVGBFKSIBCUNWI3V/graph.json","events_json":"https://pith.science/api/pith-number/HP26OO7PJ3BVGBFKSIBCUNWI3V/events.json","paper":"https://pith.science/paper/HP26OO7P"},"agent_actions":{"view_html":"https://pith.science/pith/HP26OO7PJ3BVGBFKSIBCUNWI3V","download_json":"https://pith.science/pith/HP26OO7PJ3BVGBFKSIBCUNWI3V.json","view_paper":"https://pith.science/paper/HP26OO7P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1007.1430&json=true","fetch_graph":"https://pith.science/api/pith-number/HP26OO7PJ3BVGBFKSIBCUNWI3V/graph.json","fetch_events":"https://pith.science/api/pith-number/HP26OO7PJ3BVGBFKSIBCUNWI3V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HP26OO7PJ3BVGBFKSIBCUNWI3V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HP26OO7PJ3BVGBFKSIBCUNWI3V/action/storage_attestation","attest_author":"https://pith.science/pith/HP26OO7PJ3BVGBFKSIBCUNWI3V/action/author_attestation","sign_citation":"https://pith.science/pith/HP26OO7PJ3BVGBFKSIBCUNWI3V/action/citation_signature","submit_replication":"https://pith.science/pith/HP26OO7PJ3BVGBFKSIBCUNWI3V/action/replication_record"}},"created_at":"2026-05-18T04:25:28.254899+00:00","updated_at":"2026-05-18T04:25:28.254899+00:00"}