{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:YI3HZZJ3JBW2TK6HHRHPMLJM2G","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":"bf1158013ead033e7e1f880f1d8504edaa2c6068714c21258514f2267ab91513","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-06T11:56:01Z","title_canon_sha256":"c712578fb13f892fa6a2db49846835b1a3cc94c6e990b8ba97d12bceae530320"},"schema_version":"1.0","source":{"id":"1212.1300","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.1300","created_at":"2026-05-18T03:15:18Z"},{"alias_kind":"arxiv_version","alias_value":"1212.1300v2","created_at":"2026-05-18T03:15:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1300","created_at":"2026-05-18T03:15:18Z"},{"alias_kind":"pith_short_12","alias_value":"YI3HZZJ3JBW2","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"YI3HZZJ3JBW2TK6H","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"YI3HZZJ3","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:6a9ec6aef37328658b488f9da6b63f4820dc1a504244132ff1b3c286da56c8e4","target":"graph","created_at":"2026-05-18T03:15:18Z","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 prove several results from different areas of extremal combinatorics, giving complete or partial solutions to a number of open problems. These results, coming from areas such as extremal graph theory, Ramsey theory and additive combinatorics, have been collected together because in each case the relevant proofs are quite short.","authors_text":"Benny Sudakov, David Conlon, Jacob Fox","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-06T11:56:01Z","title":"Short proofs of some extremal results"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1300","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":"sha256:5e06a878a5cace6f4bee449ca758e25b995e8b30326433c1a05bfc4954b85aa6","target":"record","created_at":"2026-05-18T03:15:18Z","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":"bf1158013ead033e7e1f880f1d8504edaa2c6068714c21258514f2267ab91513","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-06T11:56:01Z","title_canon_sha256":"c712578fb13f892fa6a2db49846835b1a3cc94c6e990b8ba97d12bceae530320"},"schema_version":"1.0","source":{"id":"1212.1300","kind":"arxiv","version":2}},"canonical_sha256":"c2367ce53b486da9abc73c4ef62d2cd1992d0c0f4b5a17b2e0aa63a478448339","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2367ce53b486da9abc73c4ef62d2cd1992d0c0f4b5a17b2e0aa63a478448339","first_computed_at":"2026-05-18T03:15:18.549834Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:18.549834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e8cRQoIIColvbicQAA0BMomos+R55Ma5T/tVVWsej2V7AoVJIngWRMyP0Z1x78xS4Ex/h7Qobw1wAdo1pl5CAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:18.550689Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.1300","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e06a878a5cace6f4bee449ca758e25b995e8b30326433c1a05bfc4954b85aa6","sha256:6a9ec6aef37328658b488f9da6b63f4820dc1a504244132ff1b3c286da56c8e4"],"state_sha256":"21345b7b21ceadbd14970bf468abc76ee1b0e412f55a3d62f1612fadfcbe3d94"}