{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:AYDIILWBW7ZUIIYRWO6FCUINGI","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":"6de723a1c10ca16c6dbcb5fbbb124968feccb49c192a91fe207b0e0bb883504c","cross_cats_sorted":["quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2021-02-14T07:27:10Z","title_canon_sha256":"100b33df1deb0284a8c41ce08913b37c189350e95cfe9f412d426946b5c7eb1b"},"schema_version":"1.0","source":{"id":"2102.07089","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.07089","created_at":"2026-07-05T02:15:01Z"},{"alias_kind":"arxiv_version","alias_value":"2102.07089v1","created_at":"2026-07-05T02:15:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.07089","created_at":"2026-07-05T02:15:01Z"},{"alias_kind":"pith_short_12","alias_value":"AYDIILWBW7ZU","created_at":"2026-07-05T02:15:01Z"},{"alias_kind":"pith_short_16","alias_value":"AYDIILWBW7ZUIIYR","created_at":"2026-07-05T02:15:01Z"},{"alias_kind":"pith_short_8","alias_value":"AYDIILWB","created_at":"2026-07-05T02:15:01Z"}],"graph_snapshots":[{"event_id":"sha256:d37b00398d82188f878d551f78b8ca37210dd19e9ade8d6092bca57ced38b7a5","target":"graph","created_at":"2026-07-05T02:15:01Z","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/2102.07089/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given a graph $G$ with $n$ vertices and maximum degree $\\Delta$, it is known that $G$ admits a vertex coloring with $\\Delta + 1$ colors such that no edge of $G$ is monochromatic. This can be seen constructively by a simple greedy algorithm, which runs in time $O(n\\Delta)$.\n  Very recently, a sequence of results (e.g., [Assadi et. al. SODA'19, Bera et. al. ICALP'20, Alon Assadi Approx/Random'20]) show randomized algorithms for $(\\epsilon + 1)\\Delta$-coloring in the query model making $\\tilde{O}(n\\sqrt{n})$ queries, improving over the greedy strategy on dense graphs. In addition, a lower bound o","authors_text":"Fang Song, Jackson Morris","cross_cats":["quant-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2021-02-14T07:27:10Z","title":"Simple vertex coloring algorithms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.07089","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":"sha256:752114d31916b66aac1b364744c6579d0e99d3a1a99b222b64b1a5f7d9ceb2c5","target":"record","created_at":"2026-07-05T02:15:01Z","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":"6de723a1c10ca16c6dbcb5fbbb124968feccb49c192a91fe207b0e0bb883504c","cross_cats_sorted":["quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2021-02-14T07:27:10Z","title_canon_sha256":"100b33df1deb0284a8c41ce08913b37c189350e95cfe9f412d426946b5c7eb1b"},"schema_version":"1.0","source":{"id":"2102.07089","kind":"arxiv","version":1}},"canonical_sha256":"0606842ec1b7f3442311b3bc51510d320231273320f8371b987b66cc03e1cf8a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0606842ec1b7f3442311b3bc51510d320231273320f8371b987b66cc03e1cf8a","first_computed_at":"2026-07-05T02:15:01.174366Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:15:01.174366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W1UjyYBJ32jlQMFo9rAJsaEV0UX7+n1hibuGZIJ8jBje7qTyfv0Y+Qix7OOwCC5wW45UK3k8yPr/HuhsrBHiAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:15:01.174837Z","signed_message":"canonical_sha256_bytes"},"source_id":"2102.07089","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:752114d31916b66aac1b364744c6579d0e99d3a1a99b222b64b1a5f7d9ceb2c5","sha256:d37b00398d82188f878d551f78b8ca37210dd19e9ade8d6092bca57ced38b7a5"],"state_sha256":"3f089d52cbe3e69d8662263dcd658dd3ad9035e4544e97f7973c9c6b0035823c"}