{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:J43FGZ65N4E75GYXBXB7IJIULU","short_pith_number":"pith:J43FGZ65","schema_version":"1.0","canonical_sha256":"4f365367dd6f09fe9b170dc3f425145d399967b323604fee8b415fb4bb5afda9","source":{"kind":"arxiv","id":"1810.07332","version":1},"attestation_state":"computed","paper":{"title":"A class of non-matchable distributive lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Haiyuan Yao, Xu Wang, Xuxu Zhao","submitted_at":"2018-10-17T00:35:57Z","abstract_excerpt":"The set of all perfect matchings of a plane (weakly) elementary bipartite graph equipped with a partial order is a poset, moreover the poset is a finite distributive lattice and its Hasse diagram is isomorphic to $Z$-transformation directed graph of the graph. A finite distributive lattice is matchable if its Hasse diagram is isomorphic to a $Z$-transformation directed graph of a plane weakly elementary bipartite graph, otherwise non-matchable. We introduce the meet-irreducible cell with respect to a perfect matching of a plane (weakly) elementary bipartite graph and give its equivalent charac"},"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":"1810.07332","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-17T00:35:57Z","cross_cats_sorted":[],"title_canon_sha256":"273a6234381c76f42c90077a2eded6df151c4115564feee35f24ddde4ab8308e","abstract_canon_sha256":"a74904b3c86ad224eda5a03be97d4c59fec7611cb56cad4b5512d5e8f9988b21"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:58.811869Z","signature_b64":"qC+/JmqjdOhU2bMqmDEkWkNTHt4cKRQoyTnlVFoeOcgdcfRrl7ZtUuCvBbdOBDPcOSRIZ3cUdnXXfICeprpBBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f365367dd6f09fe9b170dc3f425145d399967b323604fee8b415fb4bb5afda9","last_reissued_at":"2026-05-18T00:02:58.811220Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:58.811220Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A class of non-matchable distributive lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Haiyuan Yao, Xu Wang, Xuxu Zhao","submitted_at":"2018-10-17T00:35:57Z","abstract_excerpt":"The set of all perfect matchings of a plane (weakly) elementary bipartite graph equipped with a partial order is a poset, moreover the poset is a finite distributive lattice and its Hasse diagram is isomorphic to $Z$-transformation directed graph of the graph. A finite distributive lattice is matchable if its Hasse diagram is isomorphic to a $Z$-transformation directed graph of a plane weakly elementary bipartite graph, otherwise non-matchable. We introduce the meet-irreducible cell with respect to a perfect matching of a plane (weakly) elementary bipartite graph and give its equivalent charac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.07332","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":"1810.07332","created_at":"2026-05-18T00:02:58.811331+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.07332v1","created_at":"2026-05-18T00:02:58.811331+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.07332","created_at":"2026-05-18T00:02:58.811331+00:00"},{"alias_kind":"pith_short_12","alias_value":"J43FGZ65N4E7","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_16","alias_value":"J43FGZ65N4E75GYX","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_8","alias_value":"J43FGZ65","created_at":"2026-05-18T12:32:31.084164+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/J43FGZ65N4E75GYXBXB7IJIULU","json":"https://pith.science/pith/J43FGZ65N4E75GYXBXB7IJIULU.json","graph_json":"https://pith.science/api/pith-number/J43FGZ65N4E75GYXBXB7IJIULU/graph.json","events_json":"https://pith.science/api/pith-number/J43FGZ65N4E75GYXBXB7IJIULU/events.json","paper":"https://pith.science/paper/J43FGZ65"},"agent_actions":{"view_html":"https://pith.science/pith/J43FGZ65N4E75GYXBXB7IJIULU","download_json":"https://pith.science/pith/J43FGZ65N4E75GYXBXB7IJIULU.json","view_paper":"https://pith.science/paper/J43FGZ65","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.07332&json=true","fetch_graph":"https://pith.science/api/pith-number/J43FGZ65N4E75GYXBXB7IJIULU/graph.json","fetch_events":"https://pith.science/api/pith-number/J43FGZ65N4E75GYXBXB7IJIULU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J43FGZ65N4E75GYXBXB7IJIULU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J43FGZ65N4E75GYXBXB7IJIULU/action/storage_attestation","attest_author":"https://pith.science/pith/J43FGZ65N4E75GYXBXB7IJIULU/action/author_attestation","sign_citation":"https://pith.science/pith/J43FGZ65N4E75GYXBXB7IJIULU/action/citation_signature","submit_replication":"https://pith.science/pith/J43FGZ65N4E75GYXBXB7IJIULU/action/replication_record"}},"created_at":"2026-05-18T00:02:58.811331+00:00","updated_at":"2026-05-18T00:02:58.811331+00:00"}