{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:AQEB76APE4CFCZBNXKJXPC3YWS","short_pith_number":"pith:AQEB76AP","schema_version":"1.0","canonical_sha256":"04081ff80f270451642dba93778b78b4880efcd51441c2e380fed6be07c8c8bb","source":{"kind":"arxiv","id":"1501.05229","version":2},"attestation_state":"computed","paper":{"title":"Quantum isometries of noncommutative polygonal spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.OA","authors_text":"Teodor Banica","submitted_at":"2015-01-21T17:00:46Z","abstract_excerpt":"The real sphere $S^{N-1}_\\mathbb R$ appears as increasing union, over $d\\in\\{1,...,N\\}$, of its \"polygonal\" versions $S^{N-1,d-1}_\\mathbb R=\\{x\\in S^{N-1}_\\mathbb R|x_{i_0}... x_{i_d}=0,\\forall i_0,...,i_d\\ {\\rm distinct}\\}$. Motivated by general classification questions for the undeformed noncommutative spheres, smooth or not, we study here the quantum isometries of $S^{N-1,d-1}_\\mathbb R$, and of its various noncommutative analogues, obtained via liberation and twisting. We discuss as well a complex version of these results, with $S^{N-1}_\\mathbb R$ replaced by the complex sphere $S^{N-1}_\\m"},"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":"1501.05229","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-01-21T17:00:46Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"ad52583be271b9f4ab63e60dd1aa373b66318141aac35ac75dcbf4d05b7541c3","abstract_canon_sha256":"99c64c66b56d9558e1ad6d4e3467579012d60d6436c1a5120132f244e14570c9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:26.705425Z","signature_b64":"hVObB8ZfS3SNvUoJkoEIbBq8W+YkEzTYLt3wZc0ZyZtBoQgBNoblaG5MOkZdnsyNovkP/o0R0bSlL52RmsovCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04081ff80f270451642dba93778b78b4880efcd51441c2e380fed6be07c8c8bb","last_reissued_at":"2026-05-18T01:08:26.704750Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:26.704750Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum isometries of noncommutative polygonal spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.OA","authors_text":"Teodor Banica","submitted_at":"2015-01-21T17:00:46Z","abstract_excerpt":"The real sphere $S^{N-1}_\\mathbb R$ appears as increasing union, over $d\\in\\{1,...,N\\}$, of its \"polygonal\" versions $S^{N-1,d-1}_\\mathbb R=\\{x\\in S^{N-1}_\\mathbb R|x_{i_0}... x_{i_d}=0,\\forall i_0,...,i_d\\ {\\rm distinct}\\}$. Motivated by general classification questions for the undeformed noncommutative spheres, smooth or not, we study here the quantum isometries of $S^{N-1,d-1}_\\mathbb R$, and of its various noncommutative analogues, obtained via liberation and twisting. We discuss as well a complex version of these results, with $S^{N-1}_\\mathbb R$ replaced by the complex sphere $S^{N-1}_\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05229","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":"1501.05229","created_at":"2026-05-18T01:08:26.704853+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.05229v2","created_at":"2026-05-18T01:08:26.704853+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.05229","created_at":"2026-05-18T01:08:26.704853+00:00"},{"alias_kind":"pith_short_12","alias_value":"AQEB76APE4CF","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"AQEB76APE4CFCZBN","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"AQEB76AP","created_at":"2026-05-18T12:29:10.953037+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/AQEB76APE4CFCZBNXKJXPC3YWS","json":"https://pith.science/pith/AQEB76APE4CFCZBNXKJXPC3YWS.json","graph_json":"https://pith.science/api/pith-number/AQEB76APE4CFCZBNXKJXPC3YWS/graph.json","events_json":"https://pith.science/api/pith-number/AQEB76APE4CFCZBNXKJXPC3YWS/events.json","paper":"https://pith.science/paper/AQEB76AP"},"agent_actions":{"view_html":"https://pith.science/pith/AQEB76APE4CFCZBNXKJXPC3YWS","download_json":"https://pith.science/pith/AQEB76APE4CFCZBNXKJXPC3YWS.json","view_paper":"https://pith.science/paper/AQEB76AP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.05229&json=true","fetch_graph":"https://pith.science/api/pith-number/AQEB76APE4CFCZBNXKJXPC3YWS/graph.json","fetch_events":"https://pith.science/api/pith-number/AQEB76APE4CFCZBNXKJXPC3YWS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AQEB76APE4CFCZBNXKJXPC3YWS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AQEB76APE4CFCZBNXKJXPC3YWS/action/storage_attestation","attest_author":"https://pith.science/pith/AQEB76APE4CFCZBNXKJXPC3YWS/action/author_attestation","sign_citation":"https://pith.science/pith/AQEB76APE4CFCZBNXKJXPC3YWS/action/citation_signature","submit_replication":"https://pith.science/pith/AQEB76APE4CFCZBNXKJXPC3YWS/action/replication_record"}},"created_at":"2026-05-18T01:08:26.704853+00:00","updated_at":"2026-05-18T01:08:26.704853+00:00"}