{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5KOOCRKIF2YEL5QBATWD5RSCP2","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":"c8651954b955ee4357d6d6a724b5d5acd25cb31fd0cf2034c9c53b5e2708c90d","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2016-10-21T12:28:32Z","title_canon_sha256":"4915c8f581987f607c3e607f1d8a0d609a92922154a0d8d27d069354535eff3f"},"schema_version":"1.0","source":{"id":"1610.06759","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06759","created_at":"2026-05-18T01:01:36Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06759v1","created_at":"2026-05-18T01:01:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06759","created_at":"2026-05-18T01:01:36Z"},{"alias_kind":"pith_short_12","alias_value":"5KOOCRKIF2YE","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5KOOCRKIF2YEL5QB","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5KOOCRKI","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:490c5bef8ea151fdc9dbd37ab84f5f97972e9272a128f7abf7efdad14b49d8a9","target":"graph","created_at":"2026-05-18T01:01:36Z","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":"We consider coloring problems in the distributed message-passing setting. The previously-known deterministic algorithms for edge-coloring employed at least (2Delta - 1) colors, even though any graph admits an edge-coloring with Delta + 1 colors [V64]. Moreover, the previously-known deterministic algorithms that employed at most O(Delta) colors required superlogarithmic time [B15,BE10,BE11,FHK15]. In the current paper we devise deterministic edge-coloring algorithms that employ only Delta + o(Delta) colors, for a very wide family of graphs. Specifically, as long as the arboricity is a = O(Delta","authors_text":"Leonid Barenboim, Michael Elkin, Tzalik Maimon","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2016-10-21T12:28:32Z","title":"Deterministic Distributed (Delta + o(\\Delta))-Edge-Coloring, and Vertex-Coloring of Graphs with Bounded Diversity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06759","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:f68af76ca6ab4900f68848d7e05c4ce5a5ac18e488d64fdeb50407c263c2ee88","target":"record","created_at":"2026-05-18T01:01:36Z","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":"c8651954b955ee4357d6d6a724b5d5acd25cb31fd0cf2034c9c53b5e2708c90d","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2016-10-21T12:28:32Z","title_canon_sha256":"4915c8f581987f607c3e607f1d8a0d609a92922154a0d8d27d069354535eff3f"},"schema_version":"1.0","source":{"id":"1610.06759","kind":"arxiv","version":1}},"canonical_sha256":"ea9ce145482eb045f60104ec3ec6427eaf54166096f6714a6fa06f0761ac0f48","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea9ce145482eb045f60104ec3ec6427eaf54166096f6714a6fa06f0761ac0f48","first_computed_at":"2026-05-18T01:01:36.791160Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:36.791160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5ut9kn0YEiyDA0Og5SkVJ7fHalmU50UnCXUAFFxEKkouq1TZWrhEogTEM9P4wclf9YF+6witHQj4znL1/A4QDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:36.791801Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.06759","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f68af76ca6ab4900f68848d7e05c4ce5a5ac18e488d64fdeb50407c263c2ee88","sha256:490c5bef8ea151fdc9dbd37ab84f5f97972e9272a128f7abf7efdad14b49d8a9"],"state_sha256":"a04c8af7ea1c05ed76be8ab3beb2d8cd13f41aa01a5e490cbafb7c705294b670"}