{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:RQEHQA5MOBXGIQQRTYTN2PZEE4","short_pith_number":"pith:RQEHQA5M","canonical_record":{"source":{"id":"2304.04690","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-04-10T16:11:23Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"5fb61ed95a5e32fe0121fd15c5f7393d6cf45cf03b59cb22a675dd85d97279ce","abstract_canon_sha256":"c345ac5b792440ed072513bf933863ba20b66e174554fe4336bdd94df3f6e021"},"schema_version":"1.0"},"canonical_sha256":"8c087803ac706e6442119e26dd3f24273ab0ebd6a1fbf96057253ba27a7ef4fb","source":{"kind":"arxiv","id":"2304.04690","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.04690","created_at":"2026-07-05T06:50:13Z"},{"alias_kind":"arxiv_version","alias_value":"2304.04690v2","created_at":"2026-07-05T06:50:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.04690","created_at":"2026-07-05T06:50:13Z"},{"alias_kind":"pith_short_12","alias_value":"RQEHQA5MOBXG","created_at":"2026-07-05T06:50:13Z"},{"alias_kind":"pith_short_16","alias_value":"RQEHQA5MOBXGIQQR","created_at":"2026-07-05T06:50:13Z"},{"alias_kind":"pith_short_8","alias_value":"RQEHQA5M","created_at":"2026-07-05T06:50:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:RQEHQA5MOBXGIQQRTYTN2PZEE4","target":"record","payload":{"canonical_record":{"source":{"id":"2304.04690","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-04-10T16:11:23Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"5fb61ed95a5e32fe0121fd15c5f7393d6cf45cf03b59cb22a675dd85d97279ce","abstract_canon_sha256":"c345ac5b792440ed072513bf933863ba20b66e174554fe4336bdd94df3f6e021"},"schema_version":"1.0"},"canonical_sha256":"8c087803ac706e6442119e26dd3f24273ab0ebd6a1fbf96057253ba27a7ef4fb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:50:13.826055Z","signature_b64":"daJzuPPRt9umSPuKtFAIDq+D8hcS/eVVqwnOzWDyUUF3/BlIfgnsPqpDdvhsXb636rSz9SM1kddYlle/1YjZDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8c087803ac706e6442119e26dd3f24273ab0ebd6a1fbf96057253ba27a7ef4fb","last_reissued_at":"2026-07-05T06:50:13.825523Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:50:13.825523Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2304.04690","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:50:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J7UP8djISCLA2f/YRwR40N9uVdFD0Xa/q0bVoJ82w2Nf7fLN1FVdG67Cc3lpqNAINsSc4TNm+d8GziXeVxVGAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T16:14:54.640365Z"},"content_sha256":"19b785239364911593791b365c0eeaa5f1fdc6ea6662a560cdb7a5f14422e5a5","schema_version":"1.0","event_id":"sha256:19b785239364911593791b365c0eeaa5f1fdc6ea6662a560cdb7a5f14422e5a5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:RQEHQA5MOBXGIQQRTYTN2PZEE4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Digraph Colouring and Arc-Connectivity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Guillaume Aubian, Pierre Aboulker, Pierre Charbit","submitted_at":"2023-04-10T16:11:23Z","abstract_excerpt":"The dichromatic number $\\vec\\chi(D)$ of a digraph $D$ is the minimum size of a partition of its vertices into acyclic induced subgraphs. We denote by $\\lambda(D)$ the maximum local edge connectivity of a digraph $D$. Neumann-Lara proved that for every digraph $D$, $\\vec\\chi(D) \\leq \\lambda(D) + 1$. In this paper, we characterize the digraphs $D$ for which $\\vec\\chi(D) = \\lambda(D) + 1$. This generalizes an analogue result for undirected graph proved by Stiebitz and Toft as well as the directed version of Brooks' Theorem proved by Mohar. Along the way, we introduce a generalization of Haj\\'os j"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.04690","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/2304.04690/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:50:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1W8rZ1hyr+5eO5qrByTWEVpUq8ffS8MCciVddZ415WZsHxvbYTtyuSvGkMtbUGQ9i/5pwx0mazt+4t9x2QlyBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T16:14:54.640863Z"},"content_sha256":"eefa608059a18cf5b9e9f9279d91a2405a5dd3d581f68bc33ef2ffa7dd9e0d45","schema_version":"1.0","event_id":"sha256:eefa608059a18cf5b9e9f9279d91a2405a5dd3d581f68bc33ef2ffa7dd9e0d45"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RQEHQA5MOBXGIQQRTYTN2PZEE4/bundle.json","state_url":"https://pith.science/pith/RQEHQA5MOBXGIQQRTYTN2PZEE4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RQEHQA5MOBXGIQQRTYTN2PZEE4/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-23T16:14:54Z","links":{"resolver":"https://pith.science/pith/RQEHQA5MOBXGIQQRTYTN2PZEE4","bundle":"https://pith.science/pith/RQEHQA5MOBXGIQQRTYTN2PZEE4/bundle.json","state":"https://pith.science/pith/RQEHQA5MOBXGIQQRTYTN2PZEE4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RQEHQA5MOBXGIQQRTYTN2PZEE4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:RQEHQA5MOBXGIQQRTYTN2PZEE4","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":"c345ac5b792440ed072513bf933863ba20b66e174554fe4336bdd94df3f6e021","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-04-10T16:11:23Z","title_canon_sha256":"5fb61ed95a5e32fe0121fd15c5f7393d6cf45cf03b59cb22a675dd85d97279ce"},"schema_version":"1.0","source":{"id":"2304.04690","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.04690","created_at":"2026-07-05T06:50:13Z"},{"alias_kind":"arxiv_version","alias_value":"2304.04690v2","created_at":"2026-07-05T06:50:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.04690","created_at":"2026-07-05T06:50:13Z"},{"alias_kind":"pith_short_12","alias_value":"RQEHQA5MOBXG","created_at":"2026-07-05T06:50:13Z"},{"alias_kind":"pith_short_16","alias_value":"RQEHQA5MOBXGIQQR","created_at":"2026-07-05T06:50:13Z"},{"alias_kind":"pith_short_8","alias_value":"RQEHQA5M","created_at":"2026-07-05T06:50:13Z"}],"graph_snapshots":[{"event_id":"sha256:eefa608059a18cf5b9e9f9279d91a2405a5dd3d581f68bc33ef2ffa7dd9e0d45","target":"graph","created_at":"2026-07-05T06:50:13Z","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/2304.04690/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The dichromatic number $\\vec\\chi(D)$ of a digraph $D$ is the minimum size of a partition of its vertices into acyclic induced subgraphs. We denote by $\\lambda(D)$ the maximum local edge connectivity of a digraph $D$. Neumann-Lara proved that for every digraph $D$, $\\vec\\chi(D) \\leq \\lambda(D) + 1$. In this paper, we characterize the digraphs $D$ for which $\\vec\\chi(D) = \\lambda(D) + 1$. This generalizes an analogue result for undirected graph proved by Stiebitz and Toft as well as the directed version of Brooks' Theorem proved by Mohar. Along the way, we introduce a generalization of Haj\\'os j","authors_text":"Guillaume Aubian, Pierre Aboulker, Pierre Charbit","cross_cats":["cs.DM"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-04-10T16:11:23Z","title":"Digraph Colouring and Arc-Connectivity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.04690","kind":"arxiv","version":2},"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":"sha256:19b785239364911593791b365c0eeaa5f1fdc6ea6662a560cdb7a5f14422e5a5","target":"record","created_at":"2026-07-05T06:50:13Z","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":"c345ac5b792440ed072513bf933863ba20b66e174554fe4336bdd94df3f6e021","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-04-10T16:11:23Z","title_canon_sha256":"5fb61ed95a5e32fe0121fd15c5f7393d6cf45cf03b59cb22a675dd85d97279ce"},"schema_version":"1.0","source":{"id":"2304.04690","kind":"arxiv","version":2}},"canonical_sha256":"8c087803ac706e6442119e26dd3f24273ab0ebd6a1fbf96057253ba27a7ef4fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8c087803ac706e6442119e26dd3f24273ab0ebd6a1fbf96057253ba27a7ef4fb","first_computed_at":"2026-07-05T06:50:13.825523Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:50:13.825523Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"daJzuPPRt9umSPuKtFAIDq+D8hcS/eVVqwnOzWDyUUF3/BlIfgnsPqpDdvhsXb636rSz9SM1kddYlle/1YjZDw==","signature_status":"signed_v1","signed_at":"2026-07-05T06:50:13.826055Z","signed_message":"canonical_sha256_bytes"},"source_id":"2304.04690","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19b785239364911593791b365c0eeaa5f1fdc6ea6662a560cdb7a5f14422e5a5","sha256:eefa608059a18cf5b9e9f9279d91a2405a5dd3d581f68bc33ef2ffa7dd9e0d45"],"state_sha256":"7c2c5275e4c02e498594e6e0bb66bc238eda3ef05483cb302d53310e7b28fbac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Popr6DtrmTfrZO6KIlcFhAw6Nrqwu2XyLuRmODx47I4wWleRZaCPYZdSO6eu1khJD5+HCGX/sQWRrKKSG1yzDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-23T16:14:54.644535Z","bundle_sha256":"1c6251da2c7ec685f274396c7902d7289b3d2a0892623d4e077110c7241782ad"}}