{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QWX5HHW34Z5PKRUBTA3USYT5PT","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":"6bcd0292f52db683e9b932884b518a8e05c6f4de02e03c3513d3d83ad2cafe03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-02-12T22:44:57Z","title_canon_sha256":"7e2f8fc37d96bb6fd561a7672f00d2627240ffd05d0db0374689c5313ea886a1"},"schema_version":"1.0","source":{"id":"1202.2581","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2581","created_at":"2026-05-18T04:02:26Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2581v1","created_at":"2026-05-18T04:02:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2581","created_at":"2026-05-18T04:02:26Z"},{"alias_kind":"pith_short_12","alias_value":"QWX5HHW34Z5P","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"QWX5HHW34Z5PKRUB","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"QWX5HHW3","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:346df3572ab3bcdf366f118ec17bfc2911cd30803449269782e9777df421ba91","target":"graph","created_at":"2026-05-18T04:02:26Z","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":"An equation is called graph-regular if it always has monochromatic solutions under edge-colorings of the complete graph on the naturals. We present two Rado-like conditions which are respectively necessary and sufficient for an equation to be graph-regular.","authors_text":"Andy Parrish","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-02-12T22:44:57Z","title":"Toward a graph version of Rado's theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2581","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:b5140eeaed05c68c6646dfd519111d205e72ad3d59bda5add468416ede646d2a","target":"record","created_at":"2026-05-18T04:02:26Z","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":"6bcd0292f52db683e9b932884b518a8e05c6f4de02e03c3513d3d83ad2cafe03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-02-12T22:44:57Z","title_canon_sha256":"7e2f8fc37d96bb6fd561a7672f00d2627240ffd05d0db0374689c5313ea886a1"},"schema_version":"1.0","source":{"id":"1202.2581","kind":"arxiv","version":1}},"canonical_sha256":"85afd39edbe67af54681983749627d7cedad9967e00292193914ba16f7d7eab5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85afd39edbe67af54681983749627d7cedad9967e00292193914ba16f7d7eab5","first_computed_at":"2026-05-18T04:02:26.155165Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:26.155165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vosRJfV5OyIftmMxwszrOuWxwlIAuKyi0MCUqlwBLXJvY5vaUwyO/KX+M2rI6H6+aIMD2RltAm4dCAEVk22lCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:26.155819Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.2581","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5140eeaed05c68c6646dfd519111d205e72ad3d59bda5add468416ede646d2a","sha256:346df3572ab3bcdf366f118ec17bfc2911cd30803449269782e9777df421ba91"],"state_sha256":"69ae90f82637b994c7282a7c13c9db64eb84db8272d70e8b92786a98c7c0a1a5"}