{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:725KDI4TOKCXDOREQAXQSP2NYJ","short_pith_number":"pith:725KDI4T","canonical_record":{"source":{"id":"1210.1597","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-10-04T21:20:35Z","cross_cats_sorted":[],"title_canon_sha256":"0845386335b782b9dcf166bf1314b7ba7aad389804fcbd9a1e30938ab4a0db0d","abstract_canon_sha256":"a32a816f83be9c27e5db03730816f0f3fe557cccbdce0c127b41dd02b650890b"},"schema_version":"1.0"},"canonical_sha256":"febaa1a393728571ba24802f093f4dc276f79140a426475eb7ded210c2a80a48","source":{"kind":"arxiv","id":"1210.1597","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.1597","created_at":"2026-05-18T02:56:58Z"},{"alias_kind":"arxiv_version","alias_value":"1210.1597v4","created_at":"2026-05-18T02:56:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.1597","created_at":"2026-05-18T02:56:58Z"},{"alias_kind":"pith_short_12","alias_value":"725KDI4TOKCX","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"725KDI4TOKCXDORE","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"725KDI4T","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:725KDI4TOKCXDOREQAXQSP2NYJ","target":"record","payload":{"canonical_record":{"source":{"id":"1210.1597","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-10-04T21:20:35Z","cross_cats_sorted":[],"title_canon_sha256":"0845386335b782b9dcf166bf1314b7ba7aad389804fcbd9a1e30938ab4a0db0d","abstract_canon_sha256":"a32a816f83be9c27e5db03730816f0f3fe557cccbdce0c127b41dd02b650890b"},"schema_version":"1.0"},"canonical_sha256":"febaa1a393728571ba24802f093f4dc276f79140a426475eb7ded210c2a80a48","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:58.556678Z","signature_b64":"adFowIoQXk9fOyOw9nLfwbQRJNKFU4L/lc8VEINu4RZHgWNR17IWk2Vzel6YxO4rwuE8hOFeJ9WMdRPvwH+9AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"febaa1a393728571ba24802f093f4dc276f79140a426475eb7ded210c2a80a48","last_reissued_at":"2026-05-18T02:56:58.556301Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:58.556301Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.1597","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:56:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JwNddXgr0F4HNQmI7sZ+WgUtmvVJl5i4YXhG3bniOjsrDEsenl6rtm2U4p3UJuG9ItZ5PSaQr+2Upaez4KiDAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:28:36.965965Z"},"content_sha256":"3d2f211f76ba029f60416ef0bdb723e96afdd172141137867beda82974ee9ca6","schema_version":"1.0","event_id":"sha256:3d2f211f76ba029f60416ef0bdb723e96afdd172141137867beda82974ee9ca6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:725KDI4TOKCXDOREQAXQSP2NYJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A global quantum duality principle for subgroups and homogeneous spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Fabio Gavarini, Nicola Ciccoli","submitted_at":"2012-10-04T21:20:35Z","abstract_excerpt":"For a complex or real algebraic group G, with g:=Lie(G), quantizations of global type are suitable Hopf algebras F_q[G] or U_q(g) over C[q,q^{-1}]. Any such quantization yields a structure of Poisson group on G, and one of Lie bialgebra on g : correspondingly, one has dual Poisson groups G^* and a dual Lie bialgebra g^*. In this context, we introduce suitable notions of quantum subgroup and of quantum homogeneous space, in three versions: weak, proper and strict (also called \"flat\" in the literature). The last two notions only apply to those subgroups which are coisotropic, and those homogeneo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1597","kind":"arxiv","version":4},"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":"2026-05-18T02:56:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KP+b5JmPjc/k2EOGuTCzg3UYZjNpSZzIK3zQBXezEUzkHzoN+nldO94kUoGy4DG4/U86KfRbi5M6Tjb31q3mDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:28:36.966355Z"},"content_sha256":"0b222d20ef49ef883f6b50a651f8adc52d25844b109e2b981c801637b389cfd0","schema_version":"1.0","event_id":"sha256:0b222d20ef49ef883f6b50a651f8adc52d25844b109e2b981c801637b389cfd0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/725KDI4TOKCXDOREQAXQSP2NYJ/bundle.json","state_url":"https://pith.science/pith/725KDI4TOKCXDOREQAXQSP2NYJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/725KDI4TOKCXDOREQAXQSP2NYJ/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":"2026-06-01T07:28:36Z","links":{"resolver":"https://pith.science/pith/725KDI4TOKCXDOREQAXQSP2NYJ","bundle":"https://pith.science/pith/725KDI4TOKCXDOREQAXQSP2NYJ/bundle.json","state":"https://pith.science/pith/725KDI4TOKCXDOREQAXQSP2NYJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/725KDI4TOKCXDOREQAXQSP2NYJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:725KDI4TOKCXDOREQAXQSP2NYJ","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":"a32a816f83be9c27e5db03730816f0f3fe557cccbdce0c127b41dd02b650890b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-10-04T21:20:35Z","title_canon_sha256":"0845386335b782b9dcf166bf1314b7ba7aad389804fcbd9a1e30938ab4a0db0d"},"schema_version":"1.0","source":{"id":"1210.1597","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.1597","created_at":"2026-05-18T02:56:58Z"},{"alias_kind":"arxiv_version","alias_value":"1210.1597v4","created_at":"2026-05-18T02:56:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.1597","created_at":"2026-05-18T02:56:58Z"},{"alias_kind":"pith_short_12","alias_value":"725KDI4TOKCX","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"725KDI4TOKCXDORE","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"725KDI4T","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:0b222d20ef49ef883f6b50a651f8adc52d25844b109e2b981c801637b389cfd0","target":"graph","created_at":"2026-05-18T02:56:58Z","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":"For a complex or real algebraic group G, with g:=Lie(G), quantizations of global type are suitable Hopf algebras F_q[G] or U_q(g) over C[q,q^{-1}]. Any such quantization yields a structure of Poisson group on G, and one of Lie bialgebra on g : correspondingly, one has dual Poisson groups G^* and a dual Lie bialgebra g^*. In this context, we introduce suitable notions of quantum subgroup and of quantum homogeneous space, in three versions: weak, proper and strict (also called \"flat\" in the literature). The last two notions only apply to those subgroups which are coisotropic, and those homogeneo","authors_text":"Fabio Gavarini, Nicola Ciccoli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-10-04T21:20:35Z","title":"A global quantum duality principle for subgroups and homogeneous spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1597","kind":"arxiv","version":4},"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":"sha256:3d2f211f76ba029f60416ef0bdb723e96afdd172141137867beda82974ee9ca6","target":"record","created_at":"2026-05-18T02:56:58Z","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":"a32a816f83be9c27e5db03730816f0f3fe557cccbdce0c127b41dd02b650890b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-10-04T21:20:35Z","title_canon_sha256":"0845386335b782b9dcf166bf1314b7ba7aad389804fcbd9a1e30938ab4a0db0d"},"schema_version":"1.0","source":{"id":"1210.1597","kind":"arxiv","version":4}},"canonical_sha256":"febaa1a393728571ba24802f093f4dc276f79140a426475eb7ded210c2a80a48","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"febaa1a393728571ba24802f093f4dc276f79140a426475eb7ded210c2a80a48","first_computed_at":"2026-05-18T02:56:58.556301Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:58.556301Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"adFowIoQXk9fOyOw9nLfwbQRJNKFU4L/lc8VEINu4RZHgWNR17IWk2Vzel6YxO4rwuE8hOFeJ9WMdRPvwH+9AA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:58.556678Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.1597","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d2f211f76ba029f60416ef0bdb723e96afdd172141137867beda82974ee9ca6","sha256:0b222d20ef49ef883f6b50a651f8adc52d25844b109e2b981c801637b389cfd0"],"state_sha256":"9bb11153d5e070532d760b40949ccbb38b5267c1aed582f952134b92c3187008"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LRWig0sMlhdApv+Q/MG4Amw2KCumIjMmHCkRmwKDN3+9AcapWesgYWiuTJPDqZ9ZgMAddL3pWcSlc2E3kzexDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T07:28:36.968590Z","bundle_sha256":"3b42505228f2937ef237eb7e06b56107d3b18d9564c77385cf5900ca26afe40d"}}