{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:CXZGH5KNYQ5LMS2CXWKBOQOQEW","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":"ea2edb530796ef1a31096eff8509bf8213f586dca672fbcbb7f733b392a22f85","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-06-30T03:36:31Z","title_canon_sha256":"2db577c7820df19a24127e3922ff1ed7267b52bbed60aed10ce1572692bc7017"},"schema_version":"1.0","source":{"id":"2306.17388","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.17388","created_at":"2026-06-05T01:14:23Z"},{"alias_kind":"arxiv_version","alias_value":"2306.17388v2","created_at":"2026-06-05T01:14:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.17388","created_at":"2026-06-05T01:14:23Z"},{"alias_kind":"pith_short_12","alias_value":"CXZGH5KNYQ5L","created_at":"2026-06-05T01:14:23Z"},{"alias_kind":"pith_short_16","alias_value":"CXZGH5KNYQ5LMS2C","created_at":"2026-06-05T01:14:23Z"},{"alias_kind":"pith_short_8","alias_value":"CXZGH5KN","created_at":"2026-06-05T01:14:23Z"}],"graph_snapshots":[{"event_id":"sha256:27c6b2908afa499ea27d2da49be3e517efa179a07de5009814ee1274168254fb","target":"graph","created_at":"2026-06-05T01:14:23Z","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/2306.17388/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Ramsey multiplicity problem asks for the minimum asymptotic density of monochromatic labelled copies of a graph $H$ in a red/blue colouring of the edges of $K_n$. We introduce an off-diagonal generalization in which the goal is to minimize a certain weighted sum of the densities of red copies of one graph and blue copies of another. We build up various properties of this new notion, including a useful \"dual formulation,\" and use these results to solve the problem for several pairs of graphs.","authors_text":"Elena Moss, Jonathan A. Noel","cross_cats":["cs.DM"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-06-30T03:36:31Z","title":"Off-Diagonal Ramsey Multiplicity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.17388","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":"sha256:24082235ede4bd7ab0e5a3d72d46db09c51a1413156c1103320ccf9deba5b93c","target":"record","created_at":"2026-06-05T01:14:23Z","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":"ea2edb530796ef1a31096eff8509bf8213f586dca672fbcbb7f733b392a22f85","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-06-30T03:36:31Z","title_canon_sha256":"2db577c7820df19a24127e3922ff1ed7267b52bbed60aed10ce1572692bc7017"},"schema_version":"1.0","source":{"id":"2306.17388","kind":"arxiv","version":2}},"canonical_sha256":"15f263f54dc43ab64b42bd941741d02597724e9156e714002f4308d8b9141380","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"15f263f54dc43ab64b42bd941741d02597724e9156e714002f4308d8b9141380","first_computed_at":"2026-06-05T01:14:23.721106Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-05T01:14:23.721106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9Dw8EcoxrLLdS2x/yh96hBu/516oL2holSaElKAjfq5NwH3A1cRE+E8+lcYB9tp+Rc/G8hdSQdFoTe7PLEidBA==","signature_status":"signed_v1","signed_at":"2026-06-05T01:14:23.721865Z","signed_message":"canonical_sha256_bytes"},"source_id":"2306.17388","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:24082235ede4bd7ab0e5a3d72d46db09c51a1413156c1103320ccf9deba5b93c","sha256:27c6b2908afa499ea27d2da49be3e517efa179a07de5009814ee1274168254fb"],"state_sha256":"00069bc4f85b8814947109a7f8c4e729989530614a85c3157586096cd022b15c"}