{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7D3GK4MF2RQAS66H56ARQL5PHV","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"95838bb2993a9c86ae751b585508a0c59a9f665b85d02ec6a6457b1542754c3b","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-01-09T21:38:04Z","title_canon_sha256":"d778fc61b3674faa0e08331e8a47302c80e3baaa9450a6b30f5ad2dae0f59727"},"schema_version":"1.0","source":{"id":"1601.02159","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.02159","created_at":"2026-05-18T00:46:32Z"},{"alias_kind":"arxiv_version","alias_value":"1601.02159v2","created_at":"2026-05-18T00:46:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.02159","created_at":"2026-05-18T00:46:32Z"},{"alias_kind":"pith_short_12","alias_value":"7D3GK4MF2RQA","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7D3GK4MF2RQAS66H","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7D3GK4MF","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:7b1bc749c1770ecdb324d035c265718338161f7f5debaa11be86c5d4eb80d785","target":"graph","created_at":"2026-05-18T00:46:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The sphere $S^{N-1}_\\mathbb R$ has a half-liberated analogue $S^{N-1}_{\\mathbb R,*}$, and a free analogue $S^{N-1}_{\\mathbb R,+}$. This is a presentation of the construction and main properties of these noncommutative spheres, $S^{N-1}_\\mathbb R\\subset S^{N-1}_{\\mathbb R,*}\\subset S^{N-1}_{\\mathbb R,+}$, and of their quantum isometry groups.","authors_text":"Teodor Banica","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-01-09T21:38:04Z","title":"Quantum isometries, noncommutative spheres, and related integrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02159","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:36d16f8aa928abfd979ef77802efc42c6d3e4386974ee4433f62a6bb39a00f79","target":"record","created_at":"2026-05-18T00:46:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"95838bb2993a9c86ae751b585508a0c59a9f665b85d02ec6a6457b1542754c3b","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-01-09T21:38:04Z","title_canon_sha256":"d778fc61b3674faa0e08331e8a47302c80e3baaa9450a6b30f5ad2dae0f59727"},"schema_version":"1.0","source":{"id":"1601.02159","kind":"arxiv","version":2}},"canonical_sha256":"f8f6657185d460097bc7ef81182faf3d682e94f30c033285d342419251e76cd1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8f6657185d460097bc7ef81182faf3d682e94f30c033285d342419251e76cd1","first_computed_at":"2026-05-18T00:46:32.071372Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:32.071372Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FJwkZ7ZheGnbvhww3oMHUjuGceTG1uHn7DJ5qAR81MbRkG2Kj1vipZwpO6XJLqOM4/KjacD9Q4H/yMq1msZbDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:32.072068Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.02159","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36d16f8aa928abfd979ef77802efc42c6d3e4386974ee4433f62a6bb39a00f79","sha256:7b1bc749c1770ecdb324d035c265718338161f7f5debaa11be86c5d4eb80d785"],"state_sha256":"22248bcb3169b0bad7cebd847347b1bff246d211d0c983316d211b4ced84ab02"}