{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:3DHCOFLVYKPLEAM6BSWBOPE4AB","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":"f6200cbb7bad9f7f9e50272fc5103feec08591ed20fdcaec4988d56b0456e513","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2020-12-03T16:41:18Z","title_canon_sha256":"4894beb3413d5f2fb76e5dc9def8f1c64c01bc7f9ea6f26a54dba7deafa37817"},"schema_version":"1.0","source":{"id":"2012.02057","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.02057","created_at":"2026-07-05T04:18:13Z"},{"alias_kind":"arxiv_version","alias_value":"2012.02057v2","created_at":"2026-07-05T04:18:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.02057","created_at":"2026-07-05T04:18:13Z"},{"alias_kind":"pith_short_12","alias_value":"3DHCOFLVYKPL","created_at":"2026-07-05T04:18:13Z"},{"alias_kind":"pith_short_16","alias_value":"3DHCOFLVYKPLEAM6","created_at":"2026-07-05T04:18:13Z"},{"alias_kind":"pith_short_8","alias_value":"3DHCOFLV","created_at":"2026-07-05T04:18:13Z"}],"graph_snapshots":[{"event_id":"sha256:c84d6dcc72a135a7b34db29e7a020d19af5bdcd9926b0d14484faf4d851405eb","target":"graph","created_at":"2026-07-05T04:18:13Z","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/2012.02057/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A graph H is common if the number of monochromatic copies of H in a 2-edge-colouring of the complete graph is minimised by the random colouring. Burr and Rosta, extending a famous conjecture by Erdos, conjectured that every graph is common. The conjectures by Erdos and by Burr and Rosta were disproved by Thomason and by Sidorenko, respectively, in the late 1980s. Collecting new examples for common graphs had not seen much progress since then, although very recently, a few more graphs are verified to be common by the flag algebra method or the recent progress on Sidorenko's conjecture.\n  Our co","authors_text":"Andrzej Grzesik, Bernard Lidick\\'y, Jan Volec, Joonkyung Lee","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2020-12-03T16:41:18Z","title":"On tripartite common graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.02057","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:cfdf324aa557f7676edc01b5d1350f9350989e9de64f05fe794029a38340f21b","target":"record","created_at":"2026-07-05T04:18:13Z","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":"f6200cbb7bad9f7f9e50272fc5103feec08591ed20fdcaec4988d56b0456e513","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2020-12-03T16:41:18Z","title_canon_sha256":"4894beb3413d5f2fb76e5dc9def8f1c64c01bc7f9ea6f26a54dba7deafa37817"},"schema_version":"1.0","source":{"id":"2012.02057","kind":"arxiv","version":2}},"canonical_sha256":"d8ce271575c29eb2019e0cac173c9c00663e586854c0ca553936b96563fe5899","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8ce271575c29eb2019e0cac173c9c00663e586854c0ca553936b96563fe5899","first_computed_at":"2026-07-05T04:18:13.897096Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:18:13.897096Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H6hMHtsiNWR7KJujF2p/ipVpsmQB4EZTcAcP2+Oo9yHX86o+U98xl6tnu3PhAWssL2iXILT2ryTbLqzcI+P3AA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:18:13.897528Z","signed_message":"canonical_sha256_bytes"},"source_id":"2012.02057","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfdf324aa557f7676edc01b5d1350f9350989e9de64f05fe794029a38340f21b","sha256:c84d6dcc72a135a7b34db29e7a020d19af5bdcd9926b0d14484faf4d851405eb"],"state_sha256":"d38e3e07265ebc9a0fa90b10339b3ad1a2768675d3b7f004f8575d441a048ca0"}