{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:H5XAGBIJQYXVRIDYR2FYVR2PL5","short_pith_number":"pith:H5XAGBIJ","schema_version":"1.0","canonical_sha256":"3f6e030509862f58a0788e8b8ac74f5f641758fd6a3e10283e99d6aedd0bd5d0","source":{"kind":"arxiv","id":"1412.0011","version":2},"attestation_state":"computed","paper":{"title":"On the representation of finite distributive lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mark Siggers","submitted_at":"2014-11-28T14:25:12Z","abstract_excerpt":"A simple but elegant result of Rival states that every sublattice $L$ of a finite distributive lattice $\\mathcal{P}$ can be constructed from $\\mathcal{P}$ by removing a particular family $\\mathcal{I}_L$ of its irreducible intervals.\n  Applying this in the case that $\\mathcal{P}$ is a product of a finite set $\\mathcal{C}$ of chains, we get a one-to-one correspondence $L \\mapsto \\mathcal{D}_\\mathcal{P}(L)$ between the sublattices of $\\mathcal{P}$ and the preorders spanned by a canonical sublattice $\\mathcal{C}^\\infty$ of $\\mathcal{P}$.\n  We then show that $L$ is a tight sublattice of the product"},"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":"1412.0011","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-11-28T14:25:12Z","cross_cats_sorted":[],"title_canon_sha256":"cf7b95b95060c356a74ab1d78341c3c56308aabf662970556601d1273a4232d0","abstract_canon_sha256":"f7c65a355c32f3b1117ccf95b4aebe4838ce857ca790337224019a54e07bd032"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:01.102635Z","signature_b64":"V0Dlh2maKc7Etz4QlsLSVYvVS8JfvtGdNrKFoD0y/FBrgOacTh+/DuBKmUNLdHz0IluCew/R+hje+D947LRHAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f6e030509862f58a0788e8b8ac74f5f641758fd6a3e10283e99d6aedd0bd5d0","last_reissued_at":"2026-05-18T01:17:01.102084Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:01.102084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the representation of finite distributive lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mark Siggers","submitted_at":"2014-11-28T14:25:12Z","abstract_excerpt":"A simple but elegant result of Rival states that every sublattice $L$ of a finite distributive lattice $\\mathcal{P}$ can be constructed from $\\mathcal{P}$ by removing a particular family $\\mathcal{I}_L$ of its irreducible intervals.\n  Applying this in the case that $\\mathcal{P}$ is a product of a finite set $\\mathcal{C}$ of chains, we get a one-to-one correspondence $L \\mapsto \\mathcal{D}_\\mathcal{P}(L)$ between the sublattices of $\\mathcal{P}$ and the preorders spanned by a canonical sublattice $\\mathcal{C}^\\infty$ of $\\mathcal{P}$.\n  We then show that $L$ is a tight sublattice of the product"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0011","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":"1412.0011","created_at":"2026-05-18T01:17:01.102169+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.0011v2","created_at":"2026-05-18T01:17:01.102169+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.0011","created_at":"2026-05-18T01:17:01.102169+00:00"},{"alias_kind":"pith_short_12","alias_value":"H5XAGBIJQYXV","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_16","alias_value":"H5XAGBIJQYXVRIDY","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_8","alias_value":"H5XAGBIJ","created_at":"2026-05-18T12:28:30.664211+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/H5XAGBIJQYXVRIDYR2FYVR2PL5","json":"https://pith.science/pith/H5XAGBIJQYXVRIDYR2FYVR2PL5.json","graph_json":"https://pith.science/api/pith-number/H5XAGBIJQYXVRIDYR2FYVR2PL5/graph.json","events_json":"https://pith.science/api/pith-number/H5XAGBIJQYXVRIDYR2FYVR2PL5/events.json","paper":"https://pith.science/paper/H5XAGBIJ"},"agent_actions":{"view_html":"https://pith.science/pith/H5XAGBIJQYXVRIDYR2FYVR2PL5","download_json":"https://pith.science/pith/H5XAGBIJQYXVRIDYR2FYVR2PL5.json","view_paper":"https://pith.science/paper/H5XAGBIJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.0011&json=true","fetch_graph":"https://pith.science/api/pith-number/H5XAGBIJQYXVRIDYR2FYVR2PL5/graph.json","fetch_events":"https://pith.science/api/pith-number/H5XAGBIJQYXVRIDYR2FYVR2PL5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H5XAGBIJQYXVRIDYR2FYVR2PL5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H5XAGBIJQYXVRIDYR2FYVR2PL5/action/storage_attestation","attest_author":"https://pith.science/pith/H5XAGBIJQYXVRIDYR2FYVR2PL5/action/author_attestation","sign_citation":"https://pith.science/pith/H5XAGBIJQYXVRIDYR2FYVR2PL5/action/citation_signature","submit_replication":"https://pith.science/pith/H5XAGBIJQYXVRIDYR2FYVR2PL5/action/replication_record"}},"created_at":"2026-05-18T01:17:01.102169+00:00","updated_at":"2026-05-18T01:17:01.102169+00:00"}