{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:CTDNC4DZ4IPKXI4J4DQ7XM2MMS","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":"46c5046cc6d553d5f41f7c74c16bb02901393cacb06e3746cf1fe824d5fe7478","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-04-19T15:09:14Z","title_canon_sha256":"61d6558887e701d7d63de8f9a9007f379e182c294e85928299b64a0658d3563a"},"schema_version":"1.0","source":{"id":"1904.09222","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.09222","created_at":"2026-05-17T23:48:07Z"},{"alias_kind":"arxiv_version","alias_value":"1904.09222v1","created_at":"2026-05-17T23:48:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.09222","created_at":"2026-05-17T23:48:07Z"},{"alias_kind":"pith_short_12","alias_value":"CTDNC4DZ4IPK","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"CTDNC4DZ4IPKXI4J","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"CTDNC4DZ","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:2e46885ff04b9e38def8e7992657f71eb5f6331abda672582994c6eac5852839","target":"graph","created_at":"2026-05-17T23:48:07Z","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":"Vizing's celebrated theorem asserts that any graph of maximum degree $\\Delta$ admits an edge coloring using at most $\\Delta+1$ colors. In contrast, Bar-Noy, Naor and Motwani showed over a quarter century that the trivial greedy algorithm, which uses $2\\Delta-1$ colors, is optimal among online algorithms. Their lower bound has a caveat, however: it only applies to low-degree graphs, with $\\Delta=O(\\log n)$, and they conjectured the existence of online algorithms using $\\Delta(1+o(1))$ colors for $\\Delta=\\omega(\\log n)$. Progress towards resolving this conjecture was only made under stochastic a","authors_text":"Binghui Peng, David Wajc, Ilan Reuven Cohen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-04-19T15:09:14Z","title":"Tight Bounds for Online Edge Coloring"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.09222","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:e8de737ec4034e000d617db3badde8a4d29953fb4b35921d9087272acd303d63","target":"record","created_at":"2026-05-17T23:48:07Z","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":"46c5046cc6d553d5f41f7c74c16bb02901393cacb06e3746cf1fe824d5fe7478","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-04-19T15:09:14Z","title_canon_sha256":"61d6558887e701d7d63de8f9a9007f379e182c294e85928299b64a0658d3563a"},"schema_version":"1.0","source":{"id":"1904.09222","kind":"arxiv","version":1}},"canonical_sha256":"14c6d17079e21eaba389e0e1fbb34c64981a9847bd85b1107df7e40706d5d356","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"14c6d17079e21eaba389e0e1fbb34c64981a9847bd85b1107df7e40706d5d356","first_computed_at":"2026-05-17T23:48:07.992884Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:07.992884Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8HVU7oCCOMmWGG/aIdRAUVHuD1SrGSQGjpAX2Hi+Beb2hF08dz4WHfjifcPrUtnIqKL5MokPN/e5of4gYgtoAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:07.993536Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.09222","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8de737ec4034e000d617db3badde8a4d29953fb4b35921d9087272acd303d63","sha256:2e46885ff04b9e38def8e7992657f71eb5f6331abda672582994c6eac5852839"],"state_sha256":"08c35e15a428fe9073b30a9d12c584860736732de4cbc60948aa6cee40d49953"}