{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:OIUAZODLWW7YW6FTBLSBCE6KBR","short_pith_number":"pith:OIUAZODL","schema_version":"1.0","canonical_sha256":"72280cb86bb5bf8b78b30ae41113ca0c7085688cb898756b25935058162c720d","source":{"kind":"arxiv","id":"1708.02580","version":5},"attestation_state":"computed","paper":{"title":"The canonical join complex for biclosed sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexander Clifton, Alexander Garver, Peter Dillery","submitted_at":"2017-08-08T17:56:04Z","abstract_excerpt":"The canonical join complex of a semidistributive lattice is a simplicial complex whose faces are canonical join representations of elements of the semidistributive lattice. We give a combinatorial classification of the faces of the canonical join complex of the lattice of biclosed sets of segments supported by a tree, as introduced by the third author and McConville. We also use our classification to describe the elements of the shard intersection order of the lattice of biclosed sets. As a consequence, we prove that this shard intersection order is a lattice."},"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":"1708.02580","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-08T17:56:04Z","cross_cats_sorted":[],"title_canon_sha256":"d838519d06d7ada796f6b4b33c97e9cb67f3c16f71d556cfbb8cd9c4f1b5d36d","abstract_canon_sha256":"078077f2cd7943b364ff3ff75c8564e3d26bc6d2c652b182a9cfb5cb9d3d7407"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:04.529157Z","signature_b64":"XGj+Yh2JPCVml0phobW4vabl46R4NE6JqxxPd8AUuEfd6ql4hNAhvGa3yQcI9wSo4mjEfpn+HmJa451dWFfkAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72280cb86bb5bf8b78b30ae41113ca0c7085688cb898756b25935058162c720d","last_reissued_at":"2026-05-18T00:34:04.528541Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:04.528541Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The canonical join complex for biclosed sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexander Clifton, Alexander Garver, Peter Dillery","submitted_at":"2017-08-08T17:56:04Z","abstract_excerpt":"The canonical join complex of a semidistributive lattice is a simplicial complex whose faces are canonical join representations of elements of the semidistributive lattice. We give a combinatorial classification of the faces of the canonical join complex of the lattice of biclosed sets of segments supported by a tree, as introduced by the third author and McConville. We also use our classification to describe the elements of the shard intersection order of the lattice of biclosed sets. As a consequence, we prove that this shard intersection order is a lattice."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02580","kind":"arxiv","version":5},"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":"1708.02580","created_at":"2026-05-18T00:34:04.528627+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.02580v5","created_at":"2026-05-18T00:34:04.528627+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.02580","created_at":"2026-05-18T00:34:04.528627+00:00"},{"alias_kind":"pith_short_12","alias_value":"OIUAZODLWW7Y","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_16","alias_value":"OIUAZODLWW7YW6FT","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_8","alias_value":"OIUAZODL","created_at":"2026-05-18T12:31:34.259226+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/OIUAZODLWW7YW6FTBLSBCE6KBR","json":"https://pith.science/pith/OIUAZODLWW7YW6FTBLSBCE6KBR.json","graph_json":"https://pith.science/api/pith-number/OIUAZODLWW7YW6FTBLSBCE6KBR/graph.json","events_json":"https://pith.science/api/pith-number/OIUAZODLWW7YW6FTBLSBCE6KBR/events.json","paper":"https://pith.science/paper/OIUAZODL"},"agent_actions":{"view_html":"https://pith.science/pith/OIUAZODLWW7YW6FTBLSBCE6KBR","download_json":"https://pith.science/pith/OIUAZODLWW7YW6FTBLSBCE6KBR.json","view_paper":"https://pith.science/paper/OIUAZODL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.02580&json=true","fetch_graph":"https://pith.science/api/pith-number/OIUAZODLWW7YW6FTBLSBCE6KBR/graph.json","fetch_events":"https://pith.science/api/pith-number/OIUAZODLWW7YW6FTBLSBCE6KBR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OIUAZODLWW7YW6FTBLSBCE6KBR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OIUAZODLWW7YW6FTBLSBCE6KBR/action/storage_attestation","attest_author":"https://pith.science/pith/OIUAZODLWW7YW6FTBLSBCE6KBR/action/author_attestation","sign_citation":"https://pith.science/pith/OIUAZODLWW7YW6FTBLSBCE6KBR/action/citation_signature","submit_replication":"https://pith.science/pith/OIUAZODLWW7YW6FTBLSBCE6KBR/action/replication_record"}},"created_at":"2026-05-18T00:34:04.528627+00:00","updated_at":"2026-05-18T00:34:04.528627+00:00"}