{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5LBAKT2ZTHXXUKZ4NCVRO5CV54","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"26c1e48b91fee31b62f9b4f83f82d52e7381b6288cb4086e3517289cd87550a3","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-09-14T22:10:21Z","title_canon_sha256":"642e0b9981692d650b9dad78df03e1692f570de866de9d30e7cf6b59d61e150c"},"schema_version":"1.0","source":{"id":"1109.3218","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.3218","created_at":"2026-05-18T03:20:57Z"},{"alias_kind":"arxiv_version","alias_value":"1109.3218v2","created_at":"2026-05-18T03:20:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.3218","created_at":"2026-05-18T03:20:57Z"},{"alias_kind":"pith_short_12","alias_value":"5LBAKT2ZTHXX","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5LBAKT2ZTHXXUKZ4","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5LBAKT2Z","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:9e5b2b25da23642ce88ad8009a9227d93fe6460021509ab599d37f8702fb8959","target":"graph","created_at":"2026-05-18T03:20:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let P be a set of n points in general position in the plane. We study the chromatic number of the intersection graph of the open triangles determined by P. It is known that this chromatic number is at least n^3/27+O(n^2), and if P is in convex position, the answer is n^3/24+O(n^2). We prove that for arbitrary P, the chromatic number is at most n^3/19.259+O(n^2).","authors_text":"David R. Wood, Ruy Fabila-Monroy","cross_cats":["cs.CG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-09-14T22:10:21Z","title":"Colouring the Triangles Determined by a Point Set"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.3218","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a4f0beeaa1f8a77a821f262d4760078991553ee6fe719e5f1a1908a4e4742f3c","target":"record","created_at":"2026-05-18T03:20:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"26c1e48b91fee31b62f9b4f83f82d52e7381b6288cb4086e3517289cd87550a3","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-09-14T22:10:21Z","title_canon_sha256":"642e0b9981692d650b9dad78df03e1692f570de866de9d30e7cf6b59d61e150c"},"schema_version":"1.0","source":{"id":"1109.3218","kind":"arxiv","version":2}},"canonical_sha256":"eac2054f5999ef7a2b3c68ab177455ef10c1f0bac67114561214f07ddbe3938f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eac2054f5999ef7a2b3c68ab177455ef10c1f0bac67114561214f07ddbe3938f","first_computed_at":"2026-05-18T03:20:57.080255Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:20:57.080255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vdpdRo6iqq69GvEK4OmQDJ4R7Z2x8X4W+ReLqy7XxANEXcAMqp2620eDuhHiKs6ZVnUvT7te+js3Zfz/Nb2hBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:20:57.080915Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.3218","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4f0beeaa1f8a77a821f262d4760078991553ee6fe719e5f1a1908a4e4742f3c","sha256:9e5b2b25da23642ce88ad8009a9227d93fe6460021509ab599d37f8702fb8959"],"state_sha256":"85ff2a81e96c857e67b7d615fd929fba17d31557f0d4593c3ae6eabb6077de56"}