{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:OIKRGXXIPT7RNIKDRPRJUEEOJP","short_pith_number":"pith:OIKRGXXI","schema_version":"1.0","canonical_sha256":"7215135ee87cff16a1438be29a108e4bc5d0368da0d4f959d7fa27328a0f7fff","source":{"kind":"arxiv","id":"1410.6587","version":2},"attestation_state":"computed","paper":{"title":"Smooth geometry of the noncommutative pillow, cones and lens spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Andrzej Sitarz, Tomasz Brzezi\\'nski","submitted_at":"2014-10-24T06:17:50Z","abstract_excerpt":"This paper proposes a new notion of smoothness of algebras, termed differential smoothness, that combines the existence of a top form in a differential calculus over an algebra together with a strong version of the Poincar\\'e duality realized as an isomorphism between complexes of differential and integral forms. The quantum two- and three-spheres, disc, plane and the noncommutative torus are all smooth in this sense. Noncommutative coordinate algebras of deformations of several examples of classical orbifolds such as the pillow orbifold, singular cones and lens spaces are also differentially "},"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":"1410.6587","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-10-24T06:17:50Z","cross_cats_sorted":[],"title_canon_sha256":"fab5b3e67d244c7f7cf1941cc0b7773ef679128f72526006e5d6b1fa2054fbf7","abstract_canon_sha256":"ac4ca912aab8cacfefb98affb2ff9fc73df4898f4fba064a6637b4b347cbd8b8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:16:51.083731Z","signature_b64":"LNdvuQ1fbEJDfE7jmSrtI4g7mDJ2a//lA91LLvAWIks44WDFThb8AdK1vQWNjyBcTdg6zn0sC2MuGaGZmBWGAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7215135ee87cff16a1438be29a108e4bc5d0368da0d4f959d7fa27328a0f7fff","last_reissued_at":"2026-05-18T02:16:51.083165Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:16:51.083165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Smooth geometry of the noncommutative pillow, cones and lens spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Andrzej Sitarz, Tomasz Brzezi\\'nski","submitted_at":"2014-10-24T06:17:50Z","abstract_excerpt":"This paper proposes a new notion of smoothness of algebras, termed differential smoothness, that combines the existence of a top form in a differential calculus over an algebra together with a strong version of the Poincar\\'e duality realized as an isomorphism between complexes of differential and integral forms. The quantum two- and three-spheres, disc, plane and the noncommutative torus are all smooth in this sense. Noncommutative coordinate algebras of deformations of several examples of classical orbifolds such as the pillow orbifold, singular cones and lens spaces are also differentially "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6587","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":"1410.6587","created_at":"2026-05-18T02:16:51.083243+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.6587v2","created_at":"2026-05-18T02:16:51.083243+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.6587","created_at":"2026-05-18T02:16:51.083243+00:00"},{"alias_kind":"pith_short_12","alias_value":"OIKRGXXIPT7R","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_16","alias_value":"OIKRGXXIPT7RNIKD","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_8","alias_value":"OIKRGXXI","created_at":"2026-05-18T12:28:41.024544+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/OIKRGXXIPT7RNIKDRPRJUEEOJP","json":"https://pith.science/pith/OIKRGXXIPT7RNIKDRPRJUEEOJP.json","graph_json":"https://pith.science/api/pith-number/OIKRGXXIPT7RNIKDRPRJUEEOJP/graph.json","events_json":"https://pith.science/api/pith-number/OIKRGXXIPT7RNIKDRPRJUEEOJP/events.json","paper":"https://pith.science/paper/OIKRGXXI"},"agent_actions":{"view_html":"https://pith.science/pith/OIKRGXXIPT7RNIKDRPRJUEEOJP","download_json":"https://pith.science/pith/OIKRGXXIPT7RNIKDRPRJUEEOJP.json","view_paper":"https://pith.science/paper/OIKRGXXI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.6587&json=true","fetch_graph":"https://pith.science/api/pith-number/OIKRGXXIPT7RNIKDRPRJUEEOJP/graph.json","fetch_events":"https://pith.science/api/pith-number/OIKRGXXIPT7RNIKDRPRJUEEOJP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OIKRGXXIPT7RNIKDRPRJUEEOJP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OIKRGXXIPT7RNIKDRPRJUEEOJP/action/storage_attestation","attest_author":"https://pith.science/pith/OIKRGXXIPT7RNIKDRPRJUEEOJP/action/author_attestation","sign_citation":"https://pith.science/pith/OIKRGXXIPT7RNIKDRPRJUEEOJP/action/citation_signature","submit_replication":"https://pith.science/pith/OIKRGXXIPT7RNIKDRPRJUEEOJP/action/replication_record"}},"created_at":"2026-05-18T02:16:51.083243+00:00","updated_at":"2026-05-18T02:16:51.083243+00:00"}