{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:4QM4O6VXWBQMPGGWCG5M5RSNWD","short_pith_number":"pith:4QM4O6VX","schema_version":"1.0","canonical_sha256":"e419c77ab7b060c798d611bacec64db0efcfd8ba56bfa8ac57654a75887792ee","source":{"kind":"arxiv","id":"1409.6269","version":1},"attestation_state":"computed","paper":{"title":"Crosscut-simplicial Lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Thomas McConville","submitted_at":"2014-09-22T18:28:40Z","abstract_excerpt":"We call a lattice crosscut-simplicial if the crosscut complex of every atomic interval is equal to the boundary of a simplex. Every interval of such a lattice is either contractible or homotopy equivalent to a sphere. Recently, Hersh and Meszaros introduced SB-labellings and proved that if a lattice has an SB-labelling then it is crosscut-simplicial. Some known examples of lattices with a natural SB-labelling include the join-distributive lattices, the weak order of a Coxeter group, and the Tamari lattice. Generalizing these three examples, we prove that every meet-semidistributive lattice is "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1409.6269","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-09-22T18:28:40Z","cross_cats_sorted":[],"title_canon_sha256":"b4082f5c7dbb22b1d415c161207ce4a9208c99521cc192c98b83dbb79c604346","abstract_canon_sha256":"004e36975b551a0cf8ad3f8dbb724234df721d1ed78afb8d1d132f5b31462695"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:16.299900Z","signature_b64":"a0bBgjj9Xnu3EgyDJw++0Hv2nUEYhG9TDT/VEkOb2iMC7fMXUYzNzxX94vzEVoWFCkUnTifAbEWVICtN9XqpDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e419c77ab7b060c798d611bacec64db0efcfd8ba56bfa8ac57654a75887792ee","last_reissued_at":"2026-05-18T00:34:16.299160Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:16.299160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Crosscut-simplicial Lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Thomas McConville","submitted_at":"2014-09-22T18:28:40Z","abstract_excerpt":"We call a lattice crosscut-simplicial if the crosscut complex of every atomic interval is equal to the boundary of a simplex. Every interval of such a lattice is either contractible or homotopy equivalent to a sphere. Recently, Hersh and Meszaros introduced SB-labellings and proved that if a lattice has an SB-labelling then it is crosscut-simplicial. Some known examples of lattices with a natural SB-labelling include the join-distributive lattices, the weak order of a Coxeter group, and the Tamari lattice. Generalizing these three examples, we prove that every meet-semidistributive lattice is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6269","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1409.6269","created_at":"2026-05-18T00:34:16.299266+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.6269v1","created_at":"2026-05-18T00:34:16.299266+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.6269","created_at":"2026-05-18T00:34:16.299266+00:00"},{"alias_kind":"pith_short_12","alias_value":"4QM4O6VXWBQM","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_16","alias_value":"4QM4O6VXWBQMPGGW","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_8","alias_value":"4QM4O6VX","created_at":"2026-05-18T12:28:14.216126+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4QM4O6VXWBQMPGGWCG5M5RSNWD","json":"https://pith.science/pith/4QM4O6VXWBQMPGGWCG5M5RSNWD.json","graph_json":"https://pith.science/api/pith-number/4QM4O6VXWBQMPGGWCG5M5RSNWD/graph.json","events_json":"https://pith.science/api/pith-number/4QM4O6VXWBQMPGGWCG5M5RSNWD/events.json","paper":"https://pith.science/paper/4QM4O6VX"},"agent_actions":{"view_html":"https://pith.science/pith/4QM4O6VXWBQMPGGWCG5M5RSNWD","download_json":"https://pith.science/pith/4QM4O6VXWBQMPGGWCG5M5RSNWD.json","view_paper":"https://pith.science/paper/4QM4O6VX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.6269&json=true","fetch_graph":"https://pith.science/api/pith-number/4QM4O6VXWBQMPGGWCG5M5RSNWD/graph.json","fetch_events":"https://pith.science/api/pith-number/4QM4O6VXWBQMPGGWCG5M5RSNWD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4QM4O6VXWBQMPGGWCG5M5RSNWD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4QM4O6VXWBQMPGGWCG5M5RSNWD/action/storage_attestation","attest_author":"https://pith.science/pith/4QM4O6VXWBQMPGGWCG5M5RSNWD/action/author_attestation","sign_citation":"https://pith.science/pith/4QM4O6VXWBQMPGGWCG5M5RSNWD/action/citation_signature","submit_replication":"https://pith.science/pith/4QM4O6VXWBQMPGGWCG5M5RSNWD/action/replication_record"}},"created_at":"2026-05-18T00:34:16.299266+00:00","updated_at":"2026-05-18T00:34:16.299266+00:00"}