{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:XQKLKYGOFOXCSJ7CU6DUZOZWT4","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":"061d0a85034ffc74837070529c4be5c94c70dea1c32739c22b399bb153a0b20a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-07-27T01:48:38Z","title_canon_sha256":"d2f7b66d313d9df5e745e3bd405b8e82489e037e5860db984346c6370e3c997a"},"schema_version":"1.0","source":{"id":"2607.23928","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.23928","created_at":"2026-07-28T01:23:18Z"},{"alias_kind":"arxiv_version","alias_value":"2607.23928v1","created_at":"2026-07-28T01:23:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.23928","created_at":"2026-07-28T01:23:18Z"},{"alias_kind":"pith_short_12","alias_value":"XQKLKYGOFOXC","created_at":"2026-07-28T01:23:18Z"},{"alias_kind":"pith_short_16","alias_value":"XQKLKYGOFOXCSJ7C","created_at":"2026-07-28T01:23:18Z"},{"alias_kind":"pith_short_8","alias_value":"XQKLKYGO","created_at":"2026-07-28T01:23:18Z"}],"graph_snapshots":[{"event_id":"sha256:8f7143f02eec5aa3d39c71fd5711d7043f59a2835f0ebbe39e76a5078d61487f","target":"graph","created_at":"2026-07-28T01:23:18Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.23928/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A class of bipartite graphs is said to have the strong Erd\\H{o}s-Hajnal property if there exists $\\varepsilon > 0$ such that every graph $((A, B), E)$ in the class contains a complete or empty induced subgraph with parts $X \\subseteq A$, $Y \\subseteq B$ where $|X| \\ge \\varepsilon|A|$ and $|Y| \\ge \\varepsilon|B|$. Scott, Seymour and Spirkl \\cite{scott2023} proved that it is enough to forbid a forest and the bipartite complement of a forest. In this paper, we provide quantitative bounds on $\\varepsilon$ when we restrict to matchings.","authors_text":"Sida Li","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-07-27T01:48:38Z","title":"A note on matchings and co-matchings in bipartite graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.23928","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:d530ac0377f9c8bafa55afd573baa273a8ab6ce996671264a453b5ecdc715f80","target":"record","created_at":"2026-07-28T01:23:18Z","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":"061d0a85034ffc74837070529c4be5c94c70dea1c32739c22b399bb153a0b20a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-07-27T01:48:38Z","title_canon_sha256":"d2f7b66d313d9df5e745e3bd405b8e82489e037e5860db984346c6370e3c997a"},"schema_version":"1.0","source":{"id":"2607.23928","kind":"arxiv","version":1}},"canonical_sha256":"bc14b560ce2bae2927e2a7874cbb369f3cc41062b8b1e7ee6f4bfd84c18221c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc14b560ce2bae2927e2a7874cbb369f3cc41062b8b1e7ee6f4bfd84c18221c2","first_computed_at":"2026-07-28T01:23:18.136858Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-28T01:23:18.136858Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A23BOCQf8zGM40aEGJnjLMvb+ocvwnWdjrSDl6ScMHWfYpDMhK4UVEg0/ATpqr+IsHnBrJo2lwL99JF5wcmhAg==","signature_status":"signed_v1","signed_at":"2026-07-28T01:23:18.137718Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.23928","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d530ac0377f9c8bafa55afd573baa273a8ab6ce996671264a453b5ecdc715f80","sha256:8f7143f02eec5aa3d39c71fd5711d7043f59a2835f0ebbe39e76a5078d61487f"],"state_sha256":"7da7b6a2cec797f414b13866922117a58416737ec04b0ea5d392d95b9739762f"}