{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:SZOYDDE7UIYRDYHAJLODQP2K2K","short_pith_number":"pith:SZOYDDE7","schema_version":"1.0","canonical_sha256":"965d818c9fa23111e0e04adc383f4ad2bb5a3e93725093e528c59e9fb19e3d6f","source":{"kind":"arxiv","id":"2405.05222","version":2},"attestation_state":"computed","paper":{"title":"Brooks-type colourings of digraphs in linear time","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"math.CO","authors_text":"Amadeus Reinald, Daniel Gon\\c{c}alves, Lucas Picasarri-Arrieta","submitted_at":"2024-05-08T17:15:01Z","abstract_excerpt":"Brooks' Theorem is a fundamental result on graph colouring, stating that the chromatic number of a graph is almost always upper bounded by its maximal degree. Lov\\'asz showed that such a colouring may then be computed in linear time when it exists. Many analogues are known for variants of (di)graph colouring, notably for list-colouring and partitions into subgraphs with prescribed degeneracy. One of the most general results of this kind is due to Borodin, Kostochka, and Toft, when asking for classes of colours to satisfy \"variable degeneracy\" constraints. An extension of this result to digraph"},"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":"2405.05222","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2024-05-08T17:15:01Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"aed1fa249fc1d21f28af33a5b163f074f63bb4ac5597886860ea5119f86f535b","abstract_canon_sha256":"db13caac1fb12e7f6cb580839e25d3a47c072e894b866642deafd4688cf64e5a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:39:45.537947Z","signature_b64":"EwzkrojNTxLbJMBvHtSWEohjt6ArlAPtjMUuSbAgrCd21IssOvIzXnrh6E2P3Jir3UHOyCg3KoSTQxm7xRs4DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"965d818c9fa23111e0e04adc383f4ad2bb5a3e93725093e528c59e9fb19e3d6f","last_reissued_at":"2026-07-05T10:39:45.537479Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:39:45.537479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Brooks-type colourings of digraphs in linear time","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"math.CO","authors_text":"Amadeus Reinald, Daniel Gon\\c{c}alves, Lucas Picasarri-Arrieta","submitted_at":"2024-05-08T17:15:01Z","abstract_excerpt":"Brooks' Theorem is a fundamental result on graph colouring, stating that the chromatic number of a graph is almost always upper bounded by its maximal degree. Lov\\'asz showed that such a colouring may then be computed in linear time when it exists. Many analogues are known for variants of (di)graph colouring, notably for list-colouring and partitions into subgraphs with prescribed degeneracy. One of the most general results of this kind is due to Borodin, Kostochka, and Toft, when asking for classes of colours to satisfy \"variable degeneracy\" constraints. An extension of this result to digraph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.05222","kind":"arxiv","version":2},"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/2405.05222/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":"2405.05222","created_at":"2026-07-05T10:39:45.537535+00:00"},{"alias_kind":"arxiv_version","alias_value":"2405.05222v2","created_at":"2026-07-05T10:39:45.537535+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.05222","created_at":"2026-07-05T10:39:45.537535+00:00"},{"alias_kind":"pith_short_12","alias_value":"SZOYDDE7UIYR","created_at":"2026-07-05T10:39:45.537535+00:00"},{"alias_kind":"pith_short_16","alias_value":"SZOYDDE7UIYRDYHA","created_at":"2026-07-05T10:39:45.537535+00:00"},{"alias_kind":"pith_short_8","alias_value":"SZOYDDE7","created_at":"2026-07-05T10:39:45.537535+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.06928","citing_title":"Coloring digraphs with $\\Delta-b$ colors","ref_index":15,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SZOYDDE7UIYRDYHAJLODQP2K2K","json":"https://pith.science/pith/SZOYDDE7UIYRDYHAJLODQP2K2K.json","graph_json":"https://pith.science/api/pith-number/SZOYDDE7UIYRDYHAJLODQP2K2K/graph.json","events_json":"https://pith.science/api/pith-number/SZOYDDE7UIYRDYHAJLODQP2K2K/events.json","paper":"https://pith.science/paper/SZOYDDE7"},"agent_actions":{"view_html":"https://pith.science/pith/SZOYDDE7UIYRDYHAJLODQP2K2K","download_json":"https://pith.science/pith/SZOYDDE7UIYRDYHAJLODQP2K2K.json","view_paper":"https://pith.science/paper/SZOYDDE7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2405.05222&json=true","fetch_graph":"https://pith.science/api/pith-number/SZOYDDE7UIYRDYHAJLODQP2K2K/graph.json","fetch_events":"https://pith.science/api/pith-number/SZOYDDE7UIYRDYHAJLODQP2K2K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SZOYDDE7UIYRDYHAJLODQP2K2K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SZOYDDE7UIYRDYHAJLODQP2K2K/action/storage_attestation","attest_author":"https://pith.science/pith/SZOYDDE7UIYRDYHAJLODQP2K2K/action/author_attestation","sign_citation":"https://pith.science/pith/SZOYDDE7UIYRDYHAJLODQP2K2K/action/citation_signature","submit_replication":"https://pith.science/pith/SZOYDDE7UIYRDYHAJLODQP2K2K/action/replication_record"}},"created_at":"2026-07-05T10:39:45.537535+00:00","updated_at":"2026-07-05T10:39:45.537535+00:00"}