{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:Z4NQRDAJQ6REJF2YBUI5F5CDIB","short_pith_number":"pith:Z4NQRDAJ","schema_version":"1.0","canonical_sha256":"cf1b088c0987a24497580d11d2f4434071bd10aa555155692d646698776542c2","source":{"kind":"arxiv","id":"1905.00782","version":3},"attestation_state":"computed","paper":{"title":"Uncountable dichromatic number without short directed cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.CO","authors_text":"Attila Jo\\'o","submitted_at":"2019-05-02T14:46:37Z","abstract_excerpt":"A. Hajnal and P. Erd\\H{o}s proved that a graph with uncountable chromatic number cannot avoid short cycles, it must contain for example $ C_4 $ (among other obligatory subgraphs). It was shown recently by D. T. Soukup that, in contrast of the undirected case, it is consistent that for any $ n<\\omega $ there exists an uncountably dichromatic digraph without directed cycles shorter than $ n $. He asked if it is provable already in ZFC. We answer his question positively by constructing for every infinite cardinal $ \\kappa $ and $ n<\\omega $ a digraph of size $ 2^{\\kappa} $ with dichromatic number"},"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":"1905.00782","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-02T14:46:37Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"e86f8b4416a6cd6d90b64845ec33195195e42e1a1c89ff45e98bc52c86389021","abstract_canon_sha256":"071db961c122def514cdf19a37d449544b9ee32f4a35759da18788cd9983894a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:20:32.351273Z","signature_b64":"8/ZcKp/NzL4fFdRCh0G1+Kfg+lBxR8MJ6LtGX1RVW4R55C3jJOxY+Z7YsAehZJxcGWoLl/XuCximMSfpdKCsBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf1b088c0987a24497580d11d2f4434071bd10aa555155692d646698776542c2","last_reissued_at":"2026-07-05T06:20:32.350833Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:20:32.350833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uncountable dichromatic number without short directed cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.CO","authors_text":"Attila Jo\\'o","submitted_at":"2019-05-02T14:46:37Z","abstract_excerpt":"A. Hajnal and P. Erd\\H{o}s proved that a graph with uncountable chromatic number cannot avoid short cycles, it must contain for example $ C_4 $ (among other obligatory subgraphs). It was shown recently by D. T. Soukup that, in contrast of the undirected case, it is consistent that for any $ n<\\omega $ there exists an uncountably dichromatic digraph without directed cycles shorter than $ n $. He asked if it is provable already in ZFC. We answer his question positively by constructing for every infinite cardinal $ \\kappa $ and $ n<\\omega $ a digraph of size $ 2^{\\kappa} $ with dichromatic number"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.00782","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1905.00782/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1905.00782","created_at":"2026-07-05T06:20:32.350889+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.00782v3","created_at":"2026-07-05T06:20:32.350889+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.00782","created_at":"2026-07-05T06:20:32.350889+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z4NQRDAJQ6RE","created_at":"2026-07-05T06:20:32.350889+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z4NQRDAJQ6REJF2Y","created_at":"2026-07-05T06:20:32.350889+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z4NQRDAJ","created_at":"2026-07-05T06:20:32.350889+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.07264","citing_title":"On the growth rate of dichromatic numbers of finite subdigraphs","ref_index":5,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Z4NQRDAJQ6REJF2YBUI5F5CDIB","json":"https://pith.science/pith/Z4NQRDAJQ6REJF2YBUI5F5CDIB.json","graph_json":"https://pith.science/api/pith-number/Z4NQRDAJQ6REJF2YBUI5F5CDIB/graph.json","events_json":"https://pith.science/api/pith-number/Z4NQRDAJQ6REJF2YBUI5F5CDIB/events.json","paper":"https://pith.science/paper/Z4NQRDAJ"},"agent_actions":{"view_html":"https://pith.science/pith/Z4NQRDAJQ6REJF2YBUI5F5CDIB","download_json":"https://pith.science/pith/Z4NQRDAJQ6REJF2YBUI5F5CDIB.json","view_paper":"https://pith.science/paper/Z4NQRDAJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.00782&json=true","fetch_graph":"https://pith.science/api/pith-number/Z4NQRDAJQ6REJF2YBUI5F5CDIB/graph.json","fetch_events":"https://pith.science/api/pith-number/Z4NQRDAJQ6REJF2YBUI5F5CDIB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z4NQRDAJQ6REJF2YBUI5F5CDIB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z4NQRDAJQ6REJF2YBUI5F5CDIB/action/storage_attestation","attest_author":"https://pith.science/pith/Z4NQRDAJQ6REJF2YBUI5F5CDIB/action/author_attestation","sign_citation":"https://pith.science/pith/Z4NQRDAJQ6REJF2YBUI5F5CDIB/action/citation_signature","submit_replication":"https://pith.science/pith/Z4NQRDAJQ6REJF2YBUI5F5CDIB/action/replication_record"}},"created_at":"2026-07-05T06:20:32.350889+00:00","updated_at":"2026-07-05T06:20:32.350889+00:00"}