{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:VJCLJWGWEMKSK4H2A5UDUJSAZK","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":"629a2ce0c1e9b6381fef30675d552ea13a965990ca2de0b38442fd068f0562b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-31T18:55:52Z","title_canon_sha256":"e9997993285c16a6143e270cceeab5bc098e61f0ce16a9ccb7dc65a2aa4b14d4"},"schema_version":"1.0","source":{"id":"1403.8127","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.8127","created_at":"2026-05-18T02:55:11Z"},{"alias_kind":"arxiv_version","alias_value":"1403.8127v1","created_at":"2026-05-18T02:55:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.8127","created_at":"2026-05-18T02:55:11Z"},{"alias_kind":"pith_short_12","alias_value":"VJCLJWGWEMKS","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"VJCLJWGWEMKSK4H2","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"VJCLJWGW","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:3c880edd1460fc8e4db3d67f71bcfa3ccc4e9f0ce5823250255760e1efd449e6","target":"graph","created_at":"2026-05-18T02:55:11Z","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"},"paper":{"abstract_excerpt":"Let $k$ and $r$ be two integers with $k \\ge 2$ and $k\\ge r \\ge 1$. In this paper we show that (1) if a strongly connected digraph $D$ contains no directed cycle of length $1$ modulo $k$, then $D$ is $k$-colorable; and (2) if a digraph $D$ contains no directed cycle of length $r$ modulo $k$, then $D$ can be vertex-colored with $k$ colors so that each color class induces an acyclic subdigraph in $D$. The first result gives an affirmative answer to a question posed by Tuza in 1992, and the second implies the following strong form of a conjecture of Diwan, Kenkre and Vishwanathan: If an undirected","authors_text":"Jie Ma, Wenan Zang, Zhibin Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-31T18:55:52Z","title":"Coloring Digraphs with Forbidden Cycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.8127","kind":"arxiv","version":1},"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:b3a59d03b2007ceca768121fafa826ccba99bdc5831c406e50d32c710fd5c305","target":"record","created_at":"2026-05-18T02:55:11Z","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":"629a2ce0c1e9b6381fef30675d552ea13a965990ca2de0b38442fd068f0562b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-31T18:55:52Z","title_canon_sha256":"e9997993285c16a6143e270cceeab5bc098e61f0ce16a9ccb7dc65a2aa4b14d4"},"schema_version":"1.0","source":{"id":"1403.8127","kind":"arxiv","version":1}},"canonical_sha256":"aa44b4d8d623152570fa07683a2640ca87d00bad4078b770ba145f51be12df3b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa44b4d8d623152570fa07683a2640ca87d00bad4078b770ba145f51be12df3b","first_computed_at":"2026-05-18T02:55:11.778934Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:11.778934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TzGLW2vyX8VxDis/dh8mififj5eOT/T/0nhWpjz1Vy/9tc2IyeaK537ksEtb9z8rW6BAFKrJpmIyQLOybQ12Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:11.779375Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.8127","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3a59d03b2007ceca768121fafa826ccba99bdc5831c406e50d32c710fd5c305","sha256:3c880edd1460fc8e4db3d67f71bcfa3ccc4e9f0ce5823250255760e1efd449e6"],"state_sha256":"4c68c79844d1c86851923713bea1491f93d4918f4029d9ac3dd49c597e5e00ba"}