{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:XLLJSQGX5PADUIE26G6KI2JIRL","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":"0accae9a6794653d2647f63e480efd7d60832544afc51f28926e1a079e308252","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-02-15T20:51:56Z","title_canon_sha256":"57a74c9ca0bc59f571f0440bbe6de7a152c1c6f79894e27fdd541448bd7198eb"},"schema_version":"1.0","source":{"id":"2502.10903","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.10903","created_at":"2026-06-11T01:10:25Z"},{"alias_kind":"arxiv_version","alias_value":"2502.10903v2","created_at":"2026-06-11T01:10:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.10903","created_at":"2026-06-11T01:10:25Z"},{"alias_kind":"pith_short_12","alias_value":"XLLJSQGX5PAD","created_at":"2026-06-11T01:10:25Z"},{"alias_kind":"pith_short_16","alias_value":"XLLJSQGX5PADUIE2","created_at":"2026-06-11T01:10:25Z"},{"alias_kind":"pith_short_8","alias_value":"XLLJSQGX","created_at":"2026-06-11T01:10:25Z"}],"graph_snapshots":[{"event_id":"sha256:12f98d847d22ad8f972f57c4b50768c4bffaaa796e72179452b2e87c00db41a7","target":"graph","created_at":"2026-06-11T01:10:25Z","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/2502.10903/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The super-neighborhood of a vertex set $A$ in a graph $G$, denoted by $\\Lambda^2(A)$, is the set of vertices adjacent to at least two vertices in $A$. We say that a bipartite graph $G=(X, Y)$ with $|X| \\geq 2$ satisfies the double Hall property (with respect to $X$) if $|\\Lambda^2(A)| \\geq |A|$ for any subset $A \\subseteq X$ with $|A| \\geq 2$. Kostochka et al. first conjectured that if a bipartite graph $G=(X, Y)$ satisfies a slightly weaker version of the double Hall property, then $G$ contains a cycle that covers all vertices of $X$. They verified their conjecture for $|X| \\leq 6$. In this p","authors_text":"Guantao Chen, Jennifer Vandenbussche, Mikhail Lavrov, Yimo Su, Yuying Ma","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-02-15T20:51:56Z","title":"Bipartite graphs with the double Hall property"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.10903","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":"sha256:36107b1a9df0d73c5aa598e9e8f69029682c40b02783516851a6ad261a1b4084","target":"record","created_at":"2026-06-11T01:10:25Z","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":"0accae9a6794653d2647f63e480efd7d60832544afc51f28926e1a079e308252","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-02-15T20:51:56Z","title_canon_sha256":"57a74c9ca0bc59f571f0440bbe6de7a152c1c6f79894e27fdd541448bd7198eb"},"schema_version":"1.0","source":{"id":"2502.10903","kind":"arxiv","version":2}},"canonical_sha256":"bad69940d7ebc03a209af1bca469288afc0a345a5729228e3a1b49553171e386","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bad69940d7ebc03a209af1bca469288afc0a345a5729228e3a1b49553171e386","first_computed_at":"2026-06-11T01:10:25.391055Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-11T01:10:25.391055Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"89CWHC3wBMt0OIfqpERVbTEgqcfCunIMDrfTzSmfRYggDOpDQ16wVqvlGvD5tYpItcQPiCVz/TtaSNO1X67QAw==","signature_status":"signed_v1","signed_at":"2026-06-11T01:10:25.391960Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.10903","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36107b1a9df0d73c5aa598e9e8f69029682c40b02783516851a6ad261a1b4084","sha256:12f98d847d22ad8f972f57c4b50768c4bffaaa796e72179452b2e87c00db41a7"],"state_sha256":"4082e2877f304796832e76928b3c91226bb6cfe5c45e5424dfc1deb687bd5721"}