{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:VONBSRNFNOZCXY25PLPO3HZTHJ","short_pith_number":"pith:VONBSRNF","canonical_record":{"source":{"id":"2109.14605","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2021-09-29T17:57:39Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"20902d107594b938cca24ebd27453b641b254a120cd2db17ac56e9eea96a4fa5","abstract_canon_sha256":"184ff34d46c9008b307b762430e5dcf751dd60b7b48957b2bafa7287ef8306b6"},"schema_version":"1.0"},"canonical_sha256":"ab9a1945a56bb22be35d7adeed9f333a5b4f185440cc8ce71b8c04edc64b27f1","source":{"kind":"arxiv","id":"2109.14605","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.14605","created_at":"2026-07-05T07:21:23Z"},{"alias_kind":"arxiv_version","alias_value":"2109.14605v2","created_at":"2026-07-05T07:21:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.14605","created_at":"2026-07-05T07:21:23Z"},{"alias_kind":"pith_short_12","alias_value":"VONBSRNFNOZC","created_at":"2026-07-05T07:21:23Z"},{"alias_kind":"pith_short_16","alias_value":"VONBSRNFNOZCXY25","created_at":"2026-07-05T07:21:23Z"},{"alias_kind":"pith_short_8","alias_value":"VONBSRNF","created_at":"2026-07-05T07:21:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:VONBSRNFNOZCXY25PLPO3HZTHJ","target":"record","payload":{"canonical_record":{"source":{"id":"2109.14605","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2021-09-29T17:57:39Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"20902d107594b938cca24ebd27453b641b254a120cd2db17ac56e9eea96a4fa5","abstract_canon_sha256":"184ff34d46c9008b307b762430e5dcf751dd60b7b48957b2bafa7287ef8306b6"},"schema_version":"1.0"},"canonical_sha256":"ab9a1945a56bb22be35d7adeed9f333a5b4f185440cc8ce71b8c04edc64b27f1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:21:23.823268Z","signature_b64":"gKldQ7czg6A/OOggPJMf3sHC+TTD9TSj8NGEyWFIgw1lq1tjMqGME0UQxEw8o/LnSpc/1WD3e7wN6f4SZwNaAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab9a1945a56bb22be35d7adeed9f333a5b4f185440cc8ce71b8c04edc64b27f1","last_reissued_at":"2026-07-05T07:21:23.822749Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:21:23.822749Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2109.14605","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":"2026-07-05T07:21:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DB2qkb9h3sL3rIzppHHddLbYDWUUnWKADT0yx+zfS7e2Ehj4pD1sgvKAuLGCaAkWIhbENR8wsnHN/QIskZNcBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-12T14:36:36.859396Z"},"content_sha256":"fd85a6da8e530d51c22f441b0c19f758f461b03aa03e68f3ef70006890f40569","schema_version":"1.0","event_id":"sha256:fd85a6da8e530d51c22f441b0c19f758f461b03aa03e68f3ef70006890f40569"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:VONBSRNFNOZCXY25PLPO3HZTHJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Braided symmetries of $SU_{q,\\phi}(2)$ and Podle\\'s Spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.QA","authors_text":"Andrzej Sitarz, Rafa{\\l} Bistro\\'n","submitted_at":"2021-09-29T17:57:39Z","abstract_excerpt":"We present an explicit form of braided symmetries of the quantum spheres, by introducing a braided quantum Hopf algebra $\\cU_{q, \\phi}$ and demonstrating that they are braided Hopf modules over this braided Hopf algebra. To obtain this result, we systematically develop braided versions of structures like pairing between Hopf algebras, left module algebra as well as their compatibility with the $*$-structure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.14605","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2109.14605/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T07:21:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L8tJqENDQgbzbRiQTQPt6gLf+VvJOAUX4pg4NnrZZJZ+g/XYp12khnAcu2rpFNS9Ehvn16kXM6tj5gEYkENqAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-12T14:36:36.860177Z"},"content_sha256":"7e15f0ea3446ecc29747ea64b84b155db71fa3fedd6cf7131246f212b6f38047","schema_version":"1.0","event_id":"sha256:7e15f0ea3446ecc29747ea64b84b155db71fa3fedd6cf7131246f212b6f38047"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VONBSRNFNOZCXY25PLPO3HZTHJ/bundle.json","state_url":"https://pith.science/pith/VONBSRNFNOZCXY25PLPO3HZTHJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VONBSRNFNOZCXY25PLPO3HZTHJ/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":"2026-07-12T14:36:36Z","links":{"resolver":"https://pith.science/pith/VONBSRNFNOZCXY25PLPO3HZTHJ","bundle":"https://pith.science/pith/VONBSRNFNOZCXY25PLPO3HZTHJ/bundle.json","state":"https://pith.science/pith/VONBSRNFNOZCXY25PLPO3HZTHJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VONBSRNFNOZCXY25PLPO3HZTHJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:VONBSRNFNOZCXY25PLPO3HZTHJ","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":"184ff34d46c9008b307b762430e5dcf751dd60b7b48957b2bafa7287ef8306b6","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2021-09-29T17:57:39Z","title_canon_sha256":"20902d107594b938cca24ebd27453b641b254a120cd2db17ac56e9eea96a4fa5"},"schema_version":"1.0","source":{"id":"2109.14605","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.14605","created_at":"2026-07-05T07:21:23Z"},{"alias_kind":"arxiv_version","alias_value":"2109.14605v2","created_at":"2026-07-05T07:21:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.14605","created_at":"2026-07-05T07:21:23Z"},{"alias_kind":"pith_short_12","alias_value":"VONBSRNFNOZC","created_at":"2026-07-05T07:21:23Z"},{"alias_kind":"pith_short_16","alias_value":"VONBSRNFNOZCXY25","created_at":"2026-07-05T07:21:23Z"},{"alias_kind":"pith_short_8","alias_value":"VONBSRNF","created_at":"2026-07-05T07:21:23Z"}],"graph_snapshots":[{"event_id":"sha256:7e15f0ea3446ecc29747ea64b84b155db71fa3fedd6cf7131246f212b6f38047","target":"graph","created_at":"2026-07-05T07:21:23Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2109.14605/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present an explicit form of braided symmetries of the quantum spheres, by introducing a braided quantum Hopf algebra $\\cU_{q, \\phi}$ and demonstrating that they are braided Hopf modules over this braided Hopf algebra. To obtain this result, we systematically develop braided versions of structures like pairing between Hopf algebras, left module algebra as well as their compatibility with the $*$-structure.","authors_text":"Andrzej Sitarz, Rafa{\\l} Bistro\\'n","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2021-09-29T17:57:39Z","title":"Braided symmetries of $SU_{q,\\phi}(2)$ and Podle\\'s Spheres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.14605","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:fd85a6da8e530d51c22f441b0c19f758f461b03aa03e68f3ef70006890f40569","target":"record","created_at":"2026-07-05T07:21:23Z","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":"184ff34d46c9008b307b762430e5dcf751dd60b7b48957b2bafa7287ef8306b6","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2021-09-29T17:57:39Z","title_canon_sha256":"20902d107594b938cca24ebd27453b641b254a120cd2db17ac56e9eea96a4fa5"},"schema_version":"1.0","source":{"id":"2109.14605","kind":"arxiv","version":2}},"canonical_sha256":"ab9a1945a56bb22be35d7adeed9f333a5b4f185440cc8ce71b8c04edc64b27f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab9a1945a56bb22be35d7adeed9f333a5b4f185440cc8ce71b8c04edc64b27f1","first_computed_at":"2026-07-05T07:21:23.822749Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:21:23.822749Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gKldQ7czg6A/OOggPJMf3sHC+TTD9TSj8NGEyWFIgw1lq1tjMqGME0UQxEw8o/LnSpc/1WD3e7wN6f4SZwNaAA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:21:23.823268Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.14605","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd85a6da8e530d51c22f441b0c19f758f461b03aa03e68f3ef70006890f40569","sha256:7e15f0ea3446ecc29747ea64b84b155db71fa3fedd6cf7131246f212b6f38047"],"state_sha256":"c1186902ec21c9cfc8dca6485d141721d5f448a5c1807adce9cb2728d16f9d13"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9tJWStRFXpOQnU08DONdC6dLJX2F3OUjp8Zwirywh1oPjUdL8voUFElNaQX45Yq/WJ3EUUlFtl7VJdTg+LYaBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-12T14:36:36.864049Z","bundle_sha256":"a311ea28d8fb4169704c30fc395fd4ff15d7100e077a2a290bbcb622742f5363"}}