{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:Z4NQRDAJQ6REJF2YBUI5F5CDIB","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":"071db961c122def514cdf19a37d449544b9ee32f4a35759da18788cd9983894a","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-02T14:46:37Z","title_canon_sha256":"e86f8b4416a6cd6d90b64845ec33195195e42e1a1c89ff45e98bc52c86389021"},"schema_version":"1.0","source":{"id":"1905.00782","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.00782","created_at":"2026-07-05T06:20:32Z"},{"alias_kind":"arxiv_version","alias_value":"1905.00782v3","created_at":"2026-07-05T06:20:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.00782","created_at":"2026-07-05T06:20:32Z"},{"alias_kind":"pith_short_12","alias_value":"Z4NQRDAJQ6RE","created_at":"2026-07-05T06:20:32Z"},{"alias_kind":"pith_short_16","alias_value":"Z4NQRDAJQ6REJF2Y","created_at":"2026-07-05T06:20:32Z"},{"alias_kind":"pith_short_8","alias_value":"Z4NQRDAJ","created_at":"2026-07-05T06:20:32Z"}],"graph_snapshots":[{"event_id":"sha256:0f0a207a21da4918703652d06129741f152a1a8551c01bbcd3072d351c39de54","target":"graph","created_at":"2026-07-05T06:20:32Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1905.00782/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Attila Jo\\'o","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-02T14:46:37Z","title":"Uncountable dichromatic number without short directed cycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.00782","kind":"arxiv","version":3},"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:e4d9081932af21c924e98367afbe09525824a33201ba367777833355c622c9bb","target":"record","created_at":"2026-07-05T06:20:32Z","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":"071db961c122def514cdf19a37d449544b9ee32f4a35759da18788cd9983894a","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-02T14:46:37Z","title_canon_sha256":"e86f8b4416a6cd6d90b64845ec33195195e42e1a1c89ff45e98bc52c86389021"},"schema_version":"1.0","source":{"id":"1905.00782","kind":"arxiv","version":3}},"canonical_sha256":"cf1b088c0987a24497580d11d2f4434071bd10aa555155692d646698776542c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf1b088c0987a24497580d11d2f4434071bd10aa555155692d646698776542c2","first_computed_at":"2026-07-05T06:20:32.350833Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:20:32.350833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8/ZcKp/NzL4fFdRCh0G1+Kfg+lBxR8MJ6LtGX1RVW4R55C3jJOxY+Z7YsAehZJxcGWoLl/XuCximMSfpdKCsBg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:20:32.351273Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.00782","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4d9081932af21c924e98367afbe09525824a33201ba367777833355c622c9bb","sha256:0f0a207a21da4918703652d06129741f152a1a8551c01bbcd3072d351c39de54"],"state_sha256":"0db0353d72b8058205f5c90c688affc668feba5799dc54a34439242c221f82c7"}