{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:VE736PVJ76TECIXMYMNYSKWPU2","short_pith_number":"pith:VE736PVJ","schema_version":"1.0","canonical_sha256":"a93fbf3ea9ffa64122ecc31b892acfa6b3bbe35f11e2aa5ed2a1d114fccd5343","source":{"kind":"arxiv","id":"1806.07511","version":1},"attestation_state":"computed","paper":{"title":"Planar graphs without 4-cycles and close triangles are (2,0,0)-colorable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gexin Yu, Heather Hoskins, Jennifer Vandenbussche, Runrun Liu","submitted_at":"2018-06-20T00:06:07Z","abstract_excerpt":"For a set of nonnegative integers $c_1, \\ldots, c_k$, a $(c_1, c_2,\\ldots, c_k)$-coloring of a graph $G$ is a partition of $V(G)$ into $V_1, \\ldots, V_k$ such that for every $i$, $1\\le i\\le k, G[V_i]$ has maximum degree at most $c_i$. We prove that all planar graphs without 4-cycles and no less than two edges between triangles are $(2,0,0)$-colorable."},"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":"1806.07511","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-20T00:06:07Z","cross_cats_sorted":[],"title_canon_sha256":"90986410ee679684545e676c93dcc83c75a07389f73970ae7761a1db345c6dda","abstract_canon_sha256":"68b17f9b1635421f13a5ccbe4e54ea623e6dbc22a58266360042eb23dd99b9c1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:47.547821Z","signature_b64":"T6ciPloH2vKAB3JVLC9TAOreW0vhRX7DDSVqfde1Du+OhplZIhQ7lZeJTPPJ2ZXy2YrTZFSoBePlIFeOo460DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a93fbf3ea9ffa64122ecc31b892acfa6b3bbe35f11e2aa5ed2a1d114fccd5343","last_reissued_at":"2026-05-18T00:12:47.547079Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:47.547079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Planar graphs without 4-cycles and close triangles are (2,0,0)-colorable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gexin Yu, Heather Hoskins, Jennifer Vandenbussche, Runrun Liu","submitted_at":"2018-06-20T00:06:07Z","abstract_excerpt":"For a set of nonnegative integers $c_1, \\ldots, c_k$, a $(c_1, c_2,\\ldots, c_k)$-coloring of a graph $G$ is a partition of $V(G)$ into $V_1, \\ldots, V_k$ such that for every $i$, $1\\le i\\le k, G[V_i]$ has maximum degree at most $c_i$. We prove that all planar graphs without 4-cycles and no less than two edges between triangles are $(2,0,0)$-colorable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07511","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":"1806.07511","created_at":"2026-05-18T00:12:47.547210+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.07511v1","created_at":"2026-05-18T00:12:47.547210+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.07511","created_at":"2026-05-18T00:12:47.547210+00:00"},{"alias_kind":"pith_short_12","alias_value":"VE736PVJ76TE","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_16","alias_value":"VE736PVJ76TECIXM","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_8","alias_value":"VE736PVJ","created_at":"2026-05-18T12:32:59.047623+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/VE736PVJ76TECIXMYMNYSKWPU2","json":"https://pith.science/pith/VE736PVJ76TECIXMYMNYSKWPU2.json","graph_json":"https://pith.science/api/pith-number/VE736PVJ76TECIXMYMNYSKWPU2/graph.json","events_json":"https://pith.science/api/pith-number/VE736PVJ76TECIXMYMNYSKWPU2/events.json","paper":"https://pith.science/paper/VE736PVJ"},"agent_actions":{"view_html":"https://pith.science/pith/VE736PVJ76TECIXMYMNYSKWPU2","download_json":"https://pith.science/pith/VE736PVJ76TECIXMYMNYSKWPU2.json","view_paper":"https://pith.science/paper/VE736PVJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.07511&json=true","fetch_graph":"https://pith.science/api/pith-number/VE736PVJ76TECIXMYMNYSKWPU2/graph.json","fetch_events":"https://pith.science/api/pith-number/VE736PVJ76TECIXMYMNYSKWPU2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VE736PVJ76TECIXMYMNYSKWPU2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VE736PVJ76TECIXMYMNYSKWPU2/action/storage_attestation","attest_author":"https://pith.science/pith/VE736PVJ76TECIXMYMNYSKWPU2/action/author_attestation","sign_citation":"https://pith.science/pith/VE736PVJ76TECIXMYMNYSKWPU2/action/citation_signature","submit_replication":"https://pith.science/pith/VE736PVJ76TECIXMYMNYSKWPU2/action/replication_record"}},"created_at":"2026-05-18T00:12:47.547210+00:00","updated_at":"2026-05-18T00:12:47.547210+00:00"}