{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:AQEB76APE4CFCZBNXKJXPC3YWS","short_pith_number":"pith:AQEB76AP","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"},"canonical_sha256":"04081ff80f270451642dba93778b78b4880efcd51441c2e380fed6be07c8c8bb","source":{"kind":"arxiv","id":"1501.05229","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.05229","created_at":"2026-05-18T01:08:26Z"},{"alias_kind":"arxiv_version","alias_value":"1501.05229v2","created_at":"2026-05-18T01:08:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.05229","created_at":"2026-05-18T01:08:26Z"},{"alias_kind":"pith_short_12","alias_value":"AQEB76APE4CF","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AQEB76APE4CFCZBN","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AQEB76AP","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:AQEB76APE4CFCZBNXKJXPC3YWS","target":"record","payload":{"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"},"canonical_sha256":"04081ff80f270451642dba93778b78b4880efcd51441c2e380fed6be07c8c8bb","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"},"source_kind":"arxiv","source_id":"1501.05229","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:08:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Egt28udtRr3Pmv5D8JirXTHCTiJDTCM1QZ3RnD9uxx3ybepgTPA4RurIEcodAac0gNVoHORezvUf5jz+vdRmAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T01:27:19.137890Z"},"content_sha256":"d7bfb1ddd3f7980d91ab66a5e7cbf2d130dd559515756c79400118211f5ee825","schema_version":"1.0","event_id":"sha256:d7bfb1ddd3f7980d91ab66a5e7cbf2d130dd559515756c79400118211f5ee825"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:AQEB76APE4CFCZBNXKJXPC3YWS","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:08:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iocqlIcxg/ITeDGGxgacu+Fr77xdLygfaNSQE41YPONuoUV5mEPT5T/ptDkkdSTs1OKE9Y1U2IyCwgmMCxV7BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T01:27:19.138247Z"},"content_sha256":"557e8e8b3d56ecd24cd4c3eefb4f0bf9ed8b7ad9e3faf578b45cdb246b636ea4","schema_version":"1.0","event_id":"sha256:557e8e8b3d56ecd24cd4c3eefb4f0bf9ed8b7ad9e3faf578b45cdb246b636ea4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AQEB76APE4CFCZBNXKJXPC3YWS/bundle.json","state_url":"https://pith.science/pith/AQEB76APE4CFCZBNXKJXPC3YWS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AQEB76APE4CFCZBNXKJXPC3YWS/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T01:27:19Z","links":{"resolver":"https://pith.science/pith/AQEB76APE4CFCZBNXKJXPC3YWS","bundle":"https://pith.science/pith/AQEB76APE4CFCZBNXKJXPC3YWS/bundle.json","state":"https://pith.science/pith/AQEB76APE4CFCZBNXKJXPC3YWS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AQEB76APE4CFCZBNXKJXPC3YWS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:AQEB76APE4CFCZBNXKJXPC3YWS","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":"99c64c66b56d9558e1ad6d4e3467579012d60d6436c1a5120132f244e14570c9","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-01-21T17:00:46Z","title_canon_sha256":"ad52583be271b9f4ab63e60dd1aa373b66318141aac35ac75dcbf4d05b7541c3"},"schema_version":"1.0","source":{"id":"1501.05229","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.05229","created_at":"2026-05-18T01:08:26Z"},{"alias_kind":"arxiv_version","alias_value":"1501.05229v2","created_at":"2026-05-18T01:08:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.05229","created_at":"2026-05-18T01:08:26Z"},{"alias_kind":"pith_short_12","alias_value":"AQEB76APE4CF","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AQEB76APE4CFCZBN","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AQEB76AP","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:557e8e8b3d56ecd24cd4c3eefb4f0bf9ed8b7ad9e3faf578b45cdb246b636ea4","target":"graph","created_at":"2026-05-18T01:08:26Z","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 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","authors_text":"Teodor Banica","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-01-21T17:00:46Z","title":"Quantum isometries of noncommutative polygonal spheres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05229","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:d7bfb1ddd3f7980d91ab66a5e7cbf2d130dd559515756c79400118211f5ee825","target":"record","created_at":"2026-05-18T01:08:26Z","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":"99c64c66b56d9558e1ad6d4e3467579012d60d6436c1a5120132f244e14570c9","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-01-21T17:00:46Z","title_canon_sha256":"ad52583be271b9f4ab63e60dd1aa373b66318141aac35ac75dcbf4d05b7541c3"},"schema_version":"1.0","source":{"id":"1501.05229","kind":"arxiv","version":2}},"canonical_sha256":"04081ff80f270451642dba93778b78b4880efcd51441c2e380fed6be07c8c8bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"04081ff80f270451642dba93778b78b4880efcd51441c2e380fed6be07c8c8bb","first_computed_at":"2026-05-18T01:08:26.704750Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:26.704750Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hVObB8ZfS3SNvUoJkoEIbBq8W+YkEzTYLt3wZc0ZyZtBoQgBNoblaG5MOkZdnsyNovkP/o0R0bSlL52RmsovCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:26.705425Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.05229","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7bfb1ddd3f7980d91ab66a5e7cbf2d130dd559515756c79400118211f5ee825","sha256:557e8e8b3d56ecd24cd4c3eefb4f0bf9ed8b7ad9e3faf578b45cdb246b636ea4"],"state_sha256":"0adcc9b61d7fcf69e159460819993b00481e033689a3dbd9385b704e9e744bf5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h/PSKX9hAby7ybwjbZiEnAYOCdL6rq4lXGILENdUnm9hGWhsNGlMG9uPmEDG63syWMwrPmDCTg541yfqUTK0AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T01:27:19.140740Z","bundle_sha256":"a17e7b2fd7d6c4634af00067ff49b0ef6ca55b43ac143e32e2c2837caf8afd42"}}