{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:4WB54MNBQE5NOWTUBL6XXJMXRF","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":"2c4295d42ffc761511a0e7f76712274dc7133316aa2374866ffa2fe54b542525","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-09-26T20:04:33Z","title_canon_sha256":"52dc94cc175c73536ff55d913cedddb0cd5bec22325d7a8611c01c4039d43093"},"schema_version":"1.0","source":{"id":"1109.5705","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5705","created_at":"2026-05-18T03:19:57Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5705v2","created_at":"2026-05-18T03:19:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5705","created_at":"2026-05-18T03:19:57Z"},{"alias_kind":"pith_short_12","alias_value":"4WB54MNBQE5N","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4WB54MNBQE5NOWTU","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4WB54MNB","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:3974a03e10671d52391e930c8c2d385252e844402433c4474c79acc52a5346bc","target":"graph","created_at":"2026-05-18T03:19:57Z","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":"Rival and Zaguia showed that the antichain cutsets of a finite Boolean lattice are exactly the level sets. We show that a similar characterization of antichain cutsets holds for any strongly connected poset of locally finite height. As a corollary, we get such a characterization for semimodular lattices, supersolvable lattices, Bruhat orders, locally shellable lattices, and many more. We also consider a generalization to strongly connected hypergraphs having finite edges.","authors_text":"Russ Woodroofe, Stephan Foldes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-09-26T20:04:33Z","title":"Antichain cutsets of strongly connected posets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5705","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":"sha256:49fba451013b9c373b3c6be6c18cc5e78fee6ad4da3d340cd25501968d5e9e34","target":"record","created_at":"2026-05-18T03:19:57Z","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":"2c4295d42ffc761511a0e7f76712274dc7133316aa2374866ffa2fe54b542525","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-09-26T20:04:33Z","title_canon_sha256":"52dc94cc175c73536ff55d913cedddb0cd5bec22325d7a8611c01c4039d43093"},"schema_version":"1.0","source":{"id":"1109.5705","kind":"arxiv","version":2}},"canonical_sha256":"e583de31a1813ad75a740afd7ba597894253520a45710c4b6c3d367e24544fa6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e583de31a1813ad75a740afd7ba597894253520a45710c4b6c3d367e24544fa6","first_computed_at":"2026-05-18T03:19:57.094669Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:57.094669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MRRHuR8lRMzPeVVA445BnbdP30N+kJB4DvuOxTa4jmlJJqoKskRKdn1gmd+6gCpyZrfsPwP595uPjiFhPURJAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:57.095306Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.5705","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49fba451013b9c373b3c6be6c18cc5e78fee6ad4da3d340cd25501968d5e9e34","sha256:3974a03e10671d52391e930c8c2d385252e844402433c4474c79acc52a5346bc"],"state_sha256":"d6b8a1a7cb22bc9795afef23aa2160659c4c461631f775ee7f21694c638854e3"}