{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:GVS3JIECHQXPOUUV2CRHEBLN5Z","short_pith_number":"pith:GVS3JIEC","schema_version":"1.0","canonical_sha256":"3565b4a0823c2ef75295d0a272056dee6e8db7d4f9b2a103521031988ec549a4","source":{"kind":"arxiv","id":"1604.03115","version":2},"attestation_state":"computed","paper":{"title":"A broad class of shellable lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Jay Schweig, Russ Woodroofe","submitted_at":"2016-04-11T20:00:04Z","abstract_excerpt":"We introduce a new class of lattices, the modernistic lattices, and their duals, the comodernistic lattices. We show that every modernistic or comodernistic lattice has shellable order complex. We go on to exhibit a large number of examples of (co)modernistic lattices. We show comodernism for two main families of lattices that were not previously known to be shellable: the order congruence lattices of finite posets, and a weighted generalization of the k-equal partition lattices.\n  We also exhibit many examples of (co)modernistic lattices that were already known to be shellable. To start with,"},"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":"1604.03115","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-04-11T20:00:04Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"09da7c4ac44aff5fa7af1d6d77ba7a913b366e43e14f0061995225a3720db545","abstract_canon_sha256":"cfbd37e8cc7e952c4c2868731738d705d302b1b64f575afc660582f9f116929c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:24.786936Z","signature_b64":"d53NSk0U0u6P2le3UBycrLWOeDJbB1N6lG8K5fwVJHclZqxl6Jvdz+hH/YKJZNlidtw6HZxar3TbKFgC4OCZDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3565b4a0823c2ef75295d0a272056dee6e8db7d4f9b2a103521031988ec549a4","last_reissued_at":"2026-05-18T00:44:24.786413Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:24.786413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A broad class of shellable lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Jay Schweig, Russ Woodroofe","submitted_at":"2016-04-11T20:00:04Z","abstract_excerpt":"We introduce a new class of lattices, the modernistic lattices, and their duals, the comodernistic lattices. We show that every modernistic or comodernistic lattice has shellable order complex. We go on to exhibit a large number of examples of (co)modernistic lattices. We show comodernism for two main families of lattices that were not previously known to be shellable: the order congruence lattices of finite posets, and a weighted generalization of the k-equal partition lattices.\n  We also exhibit many examples of (co)modernistic lattices that were already known to be shellable. To start with,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03115","kind":"arxiv","version":2},"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":"1604.03115","created_at":"2026-05-18T00:44:24.786496+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.03115v2","created_at":"2026-05-18T00:44:24.786496+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.03115","created_at":"2026-05-18T00:44:24.786496+00:00"},{"alias_kind":"pith_short_12","alias_value":"GVS3JIECHQXP","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_16","alias_value":"GVS3JIECHQXPOUUV","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_8","alias_value":"GVS3JIEC","created_at":"2026-05-18T12:30:19.053100+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/GVS3JIECHQXPOUUV2CRHEBLN5Z","json":"https://pith.science/pith/GVS3JIECHQXPOUUV2CRHEBLN5Z.json","graph_json":"https://pith.science/api/pith-number/GVS3JIECHQXPOUUV2CRHEBLN5Z/graph.json","events_json":"https://pith.science/api/pith-number/GVS3JIECHQXPOUUV2CRHEBLN5Z/events.json","paper":"https://pith.science/paper/GVS3JIEC"},"agent_actions":{"view_html":"https://pith.science/pith/GVS3JIECHQXPOUUV2CRHEBLN5Z","download_json":"https://pith.science/pith/GVS3JIECHQXPOUUV2CRHEBLN5Z.json","view_paper":"https://pith.science/paper/GVS3JIEC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.03115&json=true","fetch_graph":"https://pith.science/api/pith-number/GVS3JIECHQXPOUUV2CRHEBLN5Z/graph.json","fetch_events":"https://pith.science/api/pith-number/GVS3JIECHQXPOUUV2CRHEBLN5Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GVS3JIECHQXPOUUV2CRHEBLN5Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GVS3JIECHQXPOUUV2CRHEBLN5Z/action/storage_attestation","attest_author":"https://pith.science/pith/GVS3JIECHQXPOUUV2CRHEBLN5Z/action/author_attestation","sign_citation":"https://pith.science/pith/GVS3JIECHQXPOUUV2CRHEBLN5Z/action/citation_signature","submit_replication":"https://pith.science/pith/GVS3JIECHQXPOUUV2CRHEBLN5Z/action/replication_record"}},"created_at":"2026-05-18T00:44:24.786496+00:00","updated_at":"2026-05-18T00:44:24.786496+00:00"}