{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:PLVV7GEV6KT3H3KNRVYY2NDOS7","short_pith_number":"pith:PLVV7GEV","schema_version":"1.0","canonical_sha256":"7aeb5f9895f2a7b3ed4d8d718d346e97ceafba81d421084cb65cf4327d02af6f","source":{"kind":"arxiv","id":"1312.6263","version":1},"attestation_state":"computed","paper":{"title":"Representing distributive lattices with Galois connections in terms of rough sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.RA","authors_text":"Jouni J\\\"arvinen, Michiro Kondo, Wojciech Dzik","submitted_at":"2013-12-21T15:16:34Z","abstract_excerpt":"This paper studies expansions of bounded distributive lattices equipped with a Galois connection. We introduce GC-frames and canonical frames for these algebras. The complex algebras of GC-frames are defined in terms of rough set approximation operators. We prove that each bounded distributive lattice with a Galois connection can be embedded into the complex algebra of its canonical frame. We show that for every spatial Heyting algebra $L$ equipped with a Galois connection, there exists a GC-frame such that $L$ is isomorphic to the complex algebra of this frame, and an analogous result holds f"},"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":"1312.6263","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-12-21T15:16:34Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"b1b3e71f4850b2e9ff7333cc4005c996a1e37d1f516bcf7f52f5ca01af4a7e0a","abstract_canon_sha256":"0384c651841dc2a5a10e28b74f255c2e44f459059dcd82666a0e450b3d3b87cf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:05.690415Z","signature_b64":"x2cUFNW4rwYa9dCZRZ6s8rOY7c1ayv+hcPS/Xxwsnp42AWlcG8aDiDn5qR5Teu5U7AjhtxMCuM1XdCcWYus2DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7aeb5f9895f2a7b3ed4d8d718d346e97ceafba81d421084cb65cf4327d02af6f","last_reissued_at":"2026-05-18T03:04:05.689928Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:05.689928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Representing distributive lattices with Galois connections in terms of rough sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.RA","authors_text":"Jouni J\\\"arvinen, Michiro Kondo, Wojciech Dzik","submitted_at":"2013-12-21T15:16:34Z","abstract_excerpt":"This paper studies expansions of bounded distributive lattices equipped with a Galois connection. We introduce GC-frames and canonical frames for these algebras. The complex algebras of GC-frames are defined in terms of rough set approximation operators. We prove that each bounded distributive lattice with a Galois connection can be embedded into the complex algebra of its canonical frame. We show that for every spatial Heyting algebra $L$ equipped with a Galois connection, there exists a GC-frame such that $L$ is isomorphic to the complex algebra of this frame, and an analogous result holds f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6263","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":"1312.6263","created_at":"2026-05-18T03:04:05.690010+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.6263v1","created_at":"2026-05-18T03:04:05.690010+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.6263","created_at":"2026-05-18T03:04:05.690010+00:00"},{"alias_kind":"pith_short_12","alias_value":"PLVV7GEV6KT3","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"PLVV7GEV6KT3H3KN","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"PLVV7GEV","created_at":"2026-05-18T12:27:54.935989+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/PLVV7GEV6KT3H3KNRVYY2NDOS7","json":"https://pith.science/pith/PLVV7GEV6KT3H3KNRVYY2NDOS7.json","graph_json":"https://pith.science/api/pith-number/PLVV7GEV6KT3H3KNRVYY2NDOS7/graph.json","events_json":"https://pith.science/api/pith-number/PLVV7GEV6KT3H3KNRVYY2NDOS7/events.json","paper":"https://pith.science/paper/PLVV7GEV"},"agent_actions":{"view_html":"https://pith.science/pith/PLVV7GEV6KT3H3KNRVYY2NDOS7","download_json":"https://pith.science/pith/PLVV7GEV6KT3H3KNRVYY2NDOS7.json","view_paper":"https://pith.science/paper/PLVV7GEV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.6263&json=true","fetch_graph":"https://pith.science/api/pith-number/PLVV7GEV6KT3H3KNRVYY2NDOS7/graph.json","fetch_events":"https://pith.science/api/pith-number/PLVV7GEV6KT3H3KNRVYY2NDOS7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PLVV7GEV6KT3H3KNRVYY2NDOS7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PLVV7GEV6KT3H3KNRVYY2NDOS7/action/storage_attestation","attest_author":"https://pith.science/pith/PLVV7GEV6KT3H3KNRVYY2NDOS7/action/author_attestation","sign_citation":"https://pith.science/pith/PLVV7GEV6KT3H3KNRVYY2NDOS7/action/citation_signature","submit_replication":"https://pith.science/pith/PLVV7GEV6KT3H3KNRVYY2NDOS7/action/replication_record"}},"created_at":"2026-05-18T03:04:05.690010+00:00","updated_at":"2026-05-18T03:04:05.690010+00:00"}