{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:JFJLOHOIBUXZ6GP6F4VLCTJRM3","short_pith_number":"pith:JFJLOHOI","schema_version":"1.0","canonical_sha256":"4952b71dc80d2f9f19fe2f2ab14d3166f20edbef7800075efbaecb6994bd3720","source":{"kind":"arxiv","id":"1610.01259","version":1},"attestation_state":"computed","paper":{"title":"Iterated Arc Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Claude Tardif, Danny Rorabaugh, David Wehlau, Imed Zaguia","submitted_at":"2016-10-05T02:38:50Z","abstract_excerpt":"The arc graph $\\delta(G)$ of a digraph $G$ is the digraph with the set of arcs of $G$ as vertex-set, where the arcs of $\\delta(G)$ join consecutive arcs of $G$. In 1981, Poljak and R\\\"{o}dl characterised the chromatic number of $\\delta(G)$ in terms of the chromatic number of $G$ when $G$ is symmetric (i.e., undirected). In contrast, directed graphs with equal chromatic numbers can have arc graphs with distinct chromatic numbers. Even though the arc graph of a symmetric graph is not symmetric, we show that the chromatic number of the iterated arc graph $\\delta^k(G)$ still only depends on the ch"},"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":"1610.01259","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-05T02:38:50Z","cross_cats_sorted":[],"title_canon_sha256":"077fe94b15c0cf5ba0526779b189b622967602ec75114b9ca2058f940de7f68e","abstract_canon_sha256":"539952148482c2ad25347ce3f4635c9ada361375c8b496616b27cf0380a23dee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:11.299663Z","signature_b64":"tX6OXo3DNnv1FfWK2dv4l0wAh2C8rL76GghdBLz9Ki7jGiViph1+0NtO657rNUHyxadOD/R0Qh3B5jjn2lsPAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4952b71dc80d2f9f19fe2f2ab14d3166f20edbef7800075efbaecb6994bd3720","last_reissued_at":"2026-05-18T01:03:11.299135Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:11.299135Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Iterated Arc Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Claude Tardif, Danny Rorabaugh, David Wehlau, Imed Zaguia","submitted_at":"2016-10-05T02:38:50Z","abstract_excerpt":"The arc graph $\\delta(G)$ of a digraph $G$ is the digraph with the set of arcs of $G$ as vertex-set, where the arcs of $\\delta(G)$ join consecutive arcs of $G$. In 1981, Poljak and R\\\"{o}dl characterised the chromatic number of $\\delta(G)$ in terms of the chromatic number of $G$ when $G$ is symmetric (i.e., undirected). In contrast, directed graphs with equal chromatic numbers can have arc graphs with distinct chromatic numbers. Even though the arc graph of a symmetric graph is not symmetric, we show that the chromatic number of the iterated arc graph $\\delta^k(G)$ still only depends on the ch"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01259","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":"1610.01259","created_at":"2026-05-18T01:03:11.299223+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.01259v1","created_at":"2026-05-18T01:03:11.299223+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.01259","created_at":"2026-05-18T01:03:11.299223+00:00"},{"alias_kind":"pith_short_12","alias_value":"JFJLOHOIBUXZ","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_16","alias_value":"JFJLOHOIBUXZ6GP6","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_8","alias_value":"JFJLOHOI","created_at":"2026-05-18T12:30:25.849896+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/JFJLOHOIBUXZ6GP6F4VLCTJRM3","json":"https://pith.science/pith/JFJLOHOIBUXZ6GP6F4VLCTJRM3.json","graph_json":"https://pith.science/api/pith-number/JFJLOHOIBUXZ6GP6F4VLCTJRM3/graph.json","events_json":"https://pith.science/api/pith-number/JFJLOHOIBUXZ6GP6F4VLCTJRM3/events.json","paper":"https://pith.science/paper/JFJLOHOI"},"agent_actions":{"view_html":"https://pith.science/pith/JFJLOHOIBUXZ6GP6F4VLCTJRM3","download_json":"https://pith.science/pith/JFJLOHOIBUXZ6GP6F4VLCTJRM3.json","view_paper":"https://pith.science/paper/JFJLOHOI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.01259&json=true","fetch_graph":"https://pith.science/api/pith-number/JFJLOHOIBUXZ6GP6F4VLCTJRM3/graph.json","fetch_events":"https://pith.science/api/pith-number/JFJLOHOIBUXZ6GP6F4VLCTJRM3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JFJLOHOIBUXZ6GP6F4VLCTJRM3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JFJLOHOIBUXZ6GP6F4VLCTJRM3/action/storage_attestation","attest_author":"https://pith.science/pith/JFJLOHOIBUXZ6GP6F4VLCTJRM3/action/author_attestation","sign_citation":"https://pith.science/pith/JFJLOHOIBUXZ6GP6F4VLCTJRM3/action/citation_signature","submit_replication":"https://pith.science/pith/JFJLOHOIBUXZ6GP6F4VLCTJRM3/action/replication_record"}},"created_at":"2026-05-18T01:03:11.299223+00:00","updated_at":"2026-05-18T01:03:11.299223+00:00"}