{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:7OGCAJ4UG4GPQVNXL4S3OPNYA4","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":"f86cd652b121a83337cc092c72e451aecc46dcee765c4fd344310966df5ba8b8","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2024-07-08T11:14:41Z","title_canon_sha256":"c788dffa6ab0dce886af443cca6c7eccd4f5eea57945f6aa1678f27e14d0d2c9"},"schema_version":"1.0","source":{"id":"2407.05827","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.05827","created_at":"2026-07-05T11:59:52Z"},{"alias_kind":"arxiv_version","alias_value":"2407.05827v3","created_at":"2026-07-05T11:59:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.05827","created_at":"2026-07-05T11:59:52Z"},{"alias_kind":"pith_short_12","alias_value":"7OGCAJ4UG4GP","created_at":"2026-07-05T11:59:52Z"},{"alias_kind":"pith_short_16","alias_value":"7OGCAJ4UG4GPQVNX","created_at":"2026-07-05T11:59:52Z"},{"alias_kind":"pith_short_8","alias_value":"7OGCAJ4U","created_at":"2026-07-05T11:59:52Z"}],"graph_snapshots":[{"event_id":"sha256:e26799308be4ff5a0b95c5602945ecbb73706eafd485eb65bb02eb3b62b5df6b","target":"graph","created_at":"2026-07-05T11:59:52Z","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/2407.05827/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Reed in 1998 conjectured that every graph $G$ satisfies $\\chi(G) \\leq \\lceil \\frac{\\Delta(G)+1+\\omega(G)}{2} \\rceil$. As a partial result, he proved the existence of $\\varepsilon > 0$ for which every graph $G$ satisfies $\\chi(G) \\leq \\lceil (1-\\varepsilon)(\\Delta(G)+1)+\\varepsilon\\omega(G) \\rceil$. We propose an analogue conjecture for digraphs. Given a digraph $D$, we denote by $\\vec{\\chi}(D)$ the dichromatic number of $D$, which is the minimum number of colours needed to partition $D$ into acyclic induced subdigraphs. We let $\\overleftrightarrow{\\omega}(D)$ denote the size of the largest bic","authors_text":"Ken-ichi Kawarabayashi, Lucas Picasarri-Arrieta","cross_cats":["cs.DM"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2024-07-08T11:14:41Z","title":"An analogue of Reed's conjecture for digraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.05827","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":"sha256:8a68c84559954815fa7504049b4ef9721c322ad4f6410a60bfaf3de5c313dffd","target":"record","created_at":"2026-07-05T11:59:52Z","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":"f86cd652b121a83337cc092c72e451aecc46dcee765c4fd344310966df5ba8b8","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2024-07-08T11:14:41Z","title_canon_sha256":"c788dffa6ab0dce886af443cca6c7eccd4f5eea57945f6aa1678f27e14d0d2c9"},"schema_version":"1.0","source":{"id":"2407.05827","kind":"arxiv","version":3}},"canonical_sha256":"fb8c202794370cf855b75f25b73db80738d1fde83139a12631380ccfa1c799ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb8c202794370cf855b75f25b73db80738d1fde83139a12631380ccfa1c799ed","first_computed_at":"2026-07-05T11:59:52.718119Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:59:52.718119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LafrjZFxE4pwlsstvhcOMkj5jB4ghOy+BHAaR9c3/wx5cKI95SQ1ji/Il+Z6fHREDhU7mqqfOG7Wph+d0807BA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:59:52.718592Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.05827","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a68c84559954815fa7504049b4ef9721c322ad4f6410a60bfaf3de5c313dffd","sha256:e26799308be4ff5a0b95c5602945ecbb73706eafd485eb65bb02eb3b62b5df6b"],"state_sha256":"a98b237140323d193dd02ec1640a6cd0e636386cee6525fae82944d67a9e4053"}