{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:JABIJHCYYX5ORW3ZLCN5ZENVSR","short_pith_number":"pith:JABIJHCY","schema_version":"1.0","canonical_sha256":"4802849c58c5fae8db79589bdc91b5946bd1021576b0acf6f251fc7b5e11f36b","source":{"kind":"arxiv","id":"1610.01111","version":1},"attestation_state":"computed","paper":{"title":"The Chromatic Number of Ordered Graphs With Constrained Conflict Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Jonathan Rollin, Maria Axenovich, Torsten Ueckerdt","submitted_at":"2016-10-04T18:01:22Z","abstract_excerpt":"An ordered graph $G$ is a graph whose vertex set is a subset of integers. The edges are interpreted as tuples $(u,v)$ with $u < v$. For a positive integer $s$, a matrix $M \\in \\mathbb{Z}^{s \\times 4}$, and a vector $\\mathbf{p} = (p,\\ldots,p) \\in \\mathbb{Z}^s$ we build a conflict graph by saying that edges $(u,v)$ and $(x,y)$ are conflicting if $M(u,v,x,y)^\\top \\geq \\mathbf{p}$ or $M(x,y,u,v)^\\top \\geq \\mathbf{p}$, where the comparison is componentwise. This new framework generalizes many natural concepts of ordered and unordered graphs, such as the page-number, queue-number, band-width, interv"},"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":"1610.01111","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-04T18:01:22Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"3c8781d4f1297685030dd917b6a49b7ea6ae6f6d510c12b0c3fd0c210d734374","abstract_canon_sha256":"f7a9da6b9c32274b09c6b94f230312d583d9440d620bc973e2a6db06999a148f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:12.419331Z","signature_b64":"SGSiqoG82KXG0B2ogjlw4+senw//IUL6Uc4IM8hXHfGOPH9BSkRM2n7nlHT71cXf3LgswsAb+EbWK+M8+fi/Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4802849c58c5fae8db79589bdc91b5946bd1021576b0acf6f251fc7b5e11f36b","last_reissued_at":"2026-05-18T01:03:12.418847Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:12.418847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Chromatic Number of Ordered Graphs With Constrained Conflict Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Jonathan Rollin, Maria Axenovich, Torsten Ueckerdt","submitted_at":"2016-10-04T18:01:22Z","abstract_excerpt":"An ordered graph $G$ is a graph whose vertex set is a subset of integers. The edges are interpreted as tuples $(u,v)$ with $u < v$. For a positive integer $s$, a matrix $M \\in \\mathbb{Z}^{s \\times 4}$, and a vector $\\mathbf{p} = (p,\\ldots,p) \\in \\mathbb{Z}^s$ we build a conflict graph by saying that edges $(u,v)$ and $(x,y)$ are conflicting if $M(u,v,x,y)^\\top \\geq \\mathbf{p}$ or $M(x,y,u,v)^\\top \\geq \\mathbf{p}$, where the comparison is componentwise. This new framework generalizes many natural concepts of ordered and unordered graphs, such as the page-number, queue-number, band-width, interv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01111","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":"1610.01111","created_at":"2026-05-18T01:03:12.418918+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.01111v1","created_at":"2026-05-18T01:03:12.418918+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.01111","created_at":"2026-05-18T01:03:12.418918+00:00"},{"alias_kind":"pith_short_12","alias_value":"JABIJHCYYX5O","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"JABIJHCYYX5ORW3Z","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"JABIJHCY","created_at":"2026-05-18T12:30:22.444734+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/JABIJHCYYX5ORW3ZLCN5ZENVSR","json":"https://pith.science/pith/JABIJHCYYX5ORW3ZLCN5ZENVSR.json","graph_json":"https://pith.science/api/pith-number/JABIJHCYYX5ORW3ZLCN5ZENVSR/graph.json","events_json":"https://pith.science/api/pith-number/JABIJHCYYX5ORW3ZLCN5ZENVSR/events.json","paper":"https://pith.science/paper/JABIJHCY"},"agent_actions":{"view_html":"https://pith.science/pith/JABIJHCYYX5ORW3ZLCN5ZENVSR","download_json":"https://pith.science/pith/JABIJHCYYX5ORW3ZLCN5ZENVSR.json","view_paper":"https://pith.science/paper/JABIJHCY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.01111&json=true","fetch_graph":"https://pith.science/api/pith-number/JABIJHCYYX5ORW3ZLCN5ZENVSR/graph.json","fetch_events":"https://pith.science/api/pith-number/JABIJHCYYX5ORW3ZLCN5ZENVSR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JABIJHCYYX5ORW3ZLCN5ZENVSR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JABIJHCYYX5ORW3ZLCN5ZENVSR/action/storage_attestation","attest_author":"https://pith.science/pith/JABIJHCYYX5ORW3ZLCN5ZENVSR/action/author_attestation","sign_citation":"https://pith.science/pith/JABIJHCYYX5ORW3ZLCN5ZENVSR/action/citation_signature","submit_replication":"https://pith.science/pith/JABIJHCYYX5ORW3ZLCN5ZENVSR/action/replication_record"}},"created_at":"2026-05-18T01:03:12.418918+00:00","updated_at":"2026-05-18T01:03:12.418918+00:00"}