{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:OFG7LUUICK27LSQXFOUKGPQLE4","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":"c49c3ae8ce66413ed7b478882963cb90c3046da2e800cd3b5f32c048f2e4a887","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-28T21:07:23Z","title_canon_sha256":"ccb48ec68f4de39835f4fad3b421afc2fbb8926d4ba00be4c15e92d9051c72ef"},"schema_version":"1.0","source":{"id":"1805.11176","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.11176","created_at":"2026-05-18T00:14:43Z"},{"alias_kind":"arxiv_version","alias_value":"1805.11176v1","created_at":"2026-05-18T00:14:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.11176","created_at":"2026-05-18T00:14:43Z"},{"alias_kind":"pith_short_12","alias_value":"OFG7LUUICK27","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OFG7LUUICK27LSQX","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OFG7LUUI","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:887318b622dd3630fb507fe6fc7473876fd0b5d44675d0dc21ed88a948518d6e","target":"graph","created_at":"2026-05-18T00:14:43Z","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 give a simple short proof of Brooks' theorem using only induction and greedy coloring, while avoiding issues of graph connectivity. The argument generalizes easily to some extensions of Brooks' theorem, including its variants for list coloring, signed graphs coloring and correspondence coloring.","authors_text":"Mariusz Zaj\\k{a}c","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-28T21:07:23Z","title":"A short proof of Brooks' theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.11176","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":"sha256:06b1093a324db1d16ea1ea0076f84715b49ea0aad2f188661f043ee999974a9c","target":"record","created_at":"2026-05-18T00:14:43Z","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":"c49c3ae8ce66413ed7b478882963cb90c3046da2e800cd3b5f32c048f2e4a887","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-28T21:07:23Z","title_canon_sha256":"ccb48ec68f4de39835f4fad3b421afc2fbb8926d4ba00be4c15e92d9051c72ef"},"schema_version":"1.0","source":{"id":"1805.11176","kind":"arxiv","version":1}},"canonical_sha256":"714df5d28812b5f5ca172ba8a33e0b2737521c187c5bb9723eb3374ca461dc54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"714df5d28812b5f5ca172ba8a33e0b2737521c187c5bb9723eb3374ca461dc54","first_computed_at":"2026-05-18T00:14:43.662594Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:43.662594Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IsEWtPoXsTzgJf0KiR4OBFlv5utZuD916yO0dduvHZD75eDs36YpWmfbTqx86ZHjb+itRKVyZkQR3Iw3k/OWBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:43.663159Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.11176","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:06b1093a324db1d16ea1ea0076f84715b49ea0aad2f188661f043ee999974a9c","sha256:887318b622dd3630fb507fe6fc7473876fd0b5d44675d0dc21ed88a948518d6e"],"state_sha256":"97eb2294723e7a3287e98cc2e3244067d375eb2e197387e186add0a3fcc1b879"}