{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:R27LYZPLGEV6WRWX3AZB5YGIU7","short_pith_number":"pith:R27LYZPL","schema_version":"1.0","canonical_sha256":"8ebebc65eb312beb46d7d8321ee0c8a7e6c846785675e94a1c5c622692698375","source":{"kind":"arxiv","id":"1206.5848","version":2},"attestation_state":"computed","paper":{"title":"A non-commutative Priestley duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.RA","authors_text":"Andrej Bauer, Ganna Kudryavtseva, Karin Cvetko-Vah, Mai Gehrke, Sam van Gool","submitted_at":"2012-06-25T21:28:23Z","abstract_excerpt":"We prove that the category of left-handed strongly distributive skew lattices with zero and proper homomorphisms is dually equivalent to a category of sheaves over local Priestley spaces. Our result thus provides a non-commutative version of classical Priestley duality for distributive lattices and generalizes the recent development of Stone duality for skew Boolean algebras.\n  From the point of view of skew lattices, Leech showed early on that any strongly distributive skew lattice can be embedded in the skew lattice of partial functions on some set with the operations being given by restrict"},"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":"1206.5848","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-06-25T21:28:23Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"c995e5a49344487dac234846af2fbf95ee2da518e2bb49958cd788002776b3f1","abstract_canon_sha256":"a2721fbb02394f2cc627d96eeaa9a00b6e635735d86d8cdeb644b6fc0dba58e5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:10.737607Z","signature_b64":"9ZNgxk92H7v9qKXg6fLuRa4hb+Yw7HRDqr7opNvXN/CdVtDMjg9r0xPlICdvT/8lSzDhqBRwQlQ6EiYZ41vNBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ebebc65eb312beb46d7d8321ee0c8a7e6c846785675e94a1c5c622692698375","last_reissued_at":"2026-05-18T02:25:10.737087Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:10.737087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A non-commutative Priestley duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.RA","authors_text":"Andrej Bauer, Ganna Kudryavtseva, Karin Cvetko-Vah, Mai Gehrke, Sam van Gool","submitted_at":"2012-06-25T21:28:23Z","abstract_excerpt":"We prove that the category of left-handed strongly distributive skew lattices with zero and proper homomorphisms is dually equivalent to a category of sheaves over local Priestley spaces. Our result thus provides a non-commutative version of classical Priestley duality for distributive lattices and generalizes the recent development of Stone duality for skew Boolean algebras.\n  From the point of view of skew lattices, Leech showed early on that any strongly distributive skew lattice can be embedded in the skew lattice of partial functions on some set with the operations being given by restrict"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5848","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":"1206.5848","created_at":"2026-05-18T02:25:10.737171+00:00"},{"alias_kind":"arxiv_version","alias_value":"1206.5848v2","created_at":"2026-05-18T02:25:10.737171+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5848","created_at":"2026-05-18T02:25:10.737171+00:00"},{"alias_kind":"pith_short_12","alias_value":"R27LYZPLGEV6","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_16","alias_value":"R27LYZPLGEV6WRWX","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_8","alias_value":"R27LYZPL","created_at":"2026-05-18T12:27:20.899486+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/R27LYZPLGEV6WRWX3AZB5YGIU7","json":"https://pith.science/pith/R27LYZPLGEV6WRWX3AZB5YGIU7.json","graph_json":"https://pith.science/api/pith-number/R27LYZPLGEV6WRWX3AZB5YGIU7/graph.json","events_json":"https://pith.science/api/pith-number/R27LYZPLGEV6WRWX3AZB5YGIU7/events.json","paper":"https://pith.science/paper/R27LYZPL"},"agent_actions":{"view_html":"https://pith.science/pith/R27LYZPLGEV6WRWX3AZB5YGIU7","download_json":"https://pith.science/pith/R27LYZPLGEV6WRWX3AZB5YGIU7.json","view_paper":"https://pith.science/paper/R27LYZPL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1206.5848&json=true","fetch_graph":"https://pith.science/api/pith-number/R27LYZPLGEV6WRWX3AZB5YGIU7/graph.json","fetch_events":"https://pith.science/api/pith-number/R27LYZPLGEV6WRWX3AZB5YGIU7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R27LYZPLGEV6WRWX3AZB5YGIU7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R27LYZPLGEV6WRWX3AZB5YGIU7/action/storage_attestation","attest_author":"https://pith.science/pith/R27LYZPLGEV6WRWX3AZB5YGIU7/action/author_attestation","sign_citation":"https://pith.science/pith/R27LYZPLGEV6WRWX3AZB5YGIU7/action/citation_signature","submit_replication":"https://pith.science/pith/R27LYZPLGEV6WRWX3AZB5YGIU7/action/replication_record"}},"created_at":"2026-05-18T02:25:10.737171+00:00","updated_at":"2026-05-18T02:25:10.737171+00:00"}