{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:633PCPDISJQGYYVZEMIH6SK2KC","short_pith_number":"pith:633PCPDI","canonical_record":{"source":{"id":"1211.5279","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-11-22T13:17:42Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"13a8f709f24b7b8a235b7399b9c52020ec7927e2f4b0da220262540d69984c3b","abstract_canon_sha256":"acfe2ba8b00403831d4aea90b00fa731b6a89dc95c55bcf3972614c9387b9a72"},"schema_version":"1.0"},"canonical_sha256":"f6f6f13c6892606c62b923107f495a50b28c38bd9310a5de4c78d432f0e7d50b","source":{"kind":"arxiv","id":"1211.5279","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.5279","created_at":"2026-05-18T03:34:02Z"},{"alias_kind":"arxiv_version","alias_value":"1211.5279v2","created_at":"2026-05-18T03:34:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.5279","created_at":"2026-05-18T03:34:02Z"},{"alias_kind":"pith_short_12","alias_value":"633PCPDISJQG","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"633PCPDISJQGYYVZ","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"633PCPDI","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:633PCPDISJQGYYVZEMIH6SK2KC","target":"record","payload":{"canonical_record":{"source":{"id":"1211.5279","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-11-22T13:17:42Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"13a8f709f24b7b8a235b7399b9c52020ec7927e2f4b0da220262540d69984c3b","abstract_canon_sha256":"acfe2ba8b00403831d4aea90b00fa731b6a89dc95c55bcf3972614c9387b9a72"},"schema_version":"1.0"},"canonical_sha256":"f6f6f13c6892606c62b923107f495a50b28c38bd9310a5de4c78d432f0e7d50b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:02.677480Z","signature_b64":"WidrMH5hb+/9q5Z3TdZlwUjJwwFBSNaQvGnsDITfWvUTQ8mO85AudZQNiGb77xH68UXyFamG3InVPQIO8NgNDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6f6f13c6892606c62b923107f495a50b28c38bd9310a5de4c78d432f0e7d50b","last_reissued_at":"2026-05-18T03:34:02.676807Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:02.676807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.5279","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":"2026-05-18T03:34:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hx7Y1vUcriJgWqLelxSt+Wegjad3v11CISyagTrvNFNFjgw+tIEIov4GtBiC5FSkZjy3EWCkOCQhMnWTEzFMBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T05:26:30.387357Z"},"content_sha256":"11097df53f5c916ed13a0d01c43d101632a7eb40f970d7fc9db3113c10358875","schema_version":"1.0","event_id":"sha256:11097df53f5c916ed13a0d01c43d101632a7eb40f970d7fc9db3113c10358875"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:633PCPDISJQGYYVZEMIH6SK2KC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cocycle Twists and Extensions of Braided Doubles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Arkady Berenstein, Yuri Bazlov","submitted_at":"2012-11-22T13:17:42Z","abstract_excerpt":"It is well known that central extensions of a group G correspond to 2-cocycles on G. Cocycles can be used to construct extensions of G-graded algebras via a version of the Drinfeld twist introduced by Majid. We show how 2-cocycles can be defined for an abstract monoidal category C, following Panaite, Staic and Van Oystaeyen. A braiding on C leads to analogues of Nichols algebras in C, and we explain how the recent work on twists of Nichols algebras by Andruskiewitsch, Fantino, Garcia and Vendramin fits in this context.\n  Furthermore, we propose an approach to twisting the multiplication in bra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5279","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":"2026-05-18T03:34:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DmyX+65GevhhiFrtTAcrzKP2K2+Dmcm0az0bxKwa1vgSD4wrATQTdAGwJDWp6k8LjknVNFH4lrXEG0BeXY3rDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T05:26:30.388022Z"},"content_sha256":"9919a7a37b0ebbb363a15e4a539d650de661d52f03cce1c90da695c64e12665d","schema_version":"1.0","event_id":"sha256:9919a7a37b0ebbb363a15e4a539d650de661d52f03cce1c90da695c64e12665d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/633PCPDISJQGYYVZEMIH6SK2KC/bundle.json","state_url":"https://pith.science/pith/633PCPDISJQGYYVZEMIH6SK2KC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/633PCPDISJQGYYVZEMIH6SK2KC/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":"2026-06-06T05:26:30Z","links":{"resolver":"https://pith.science/pith/633PCPDISJQGYYVZEMIH6SK2KC","bundle":"https://pith.science/pith/633PCPDISJQGYYVZEMIH6SK2KC/bundle.json","state":"https://pith.science/pith/633PCPDISJQGYYVZEMIH6SK2KC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/633PCPDISJQGYYVZEMIH6SK2KC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:633PCPDISJQGYYVZEMIH6SK2KC","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":"acfe2ba8b00403831d4aea90b00fa731b6a89dc95c55bcf3972614c9387b9a72","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-11-22T13:17:42Z","title_canon_sha256":"13a8f709f24b7b8a235b7399b9c52020ec7927e2f4b0da220262540d69984c3b"},"schema_version":"1.0","source":{"id":"1211.5279","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.5279","created_at":"2026-05-18T03:34:02Z"},{"alias_kind":"arxiv_version","alias_value":"1211.5279v2","created_at":"2026-05-18T03:34:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.5279","created_at":"2026-05-18T03:34:02Z"},{"alias_kind":"pith_short_12","alias_value":"633PCPDISJQG","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"633PCPDISJQGYYVZ","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"633PCPDI","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:9919a7a37b0ebbb363a15e4a539d650de661d52f03cce1c90da695c64e12665d","target":"graph","created_at":"2026-05-18T03:34:02Z","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":"It is well known that central extensions of a group G correspond to 2-cocycles on G. Cocycles can be used to construct extensions of G-graded algebras via a version of the Drinfeld twist introduced by Majid. We show how 2-cocycles can be defined for an abstract monoidal category C, following Panaite, Staic and Van Oystaeyen. A braiding on C leads to analogues of Nichols algebras in C, and we explain how the recent work on twists of Nichols algebras by Andruskiewitsch, Fantino, Garcia and Vendramin fits in this context.\n  Furthermore, we propose an approach to twisting the multiplication in bra","authors_text":"Arkady Berenstein, Yuri Bazlov","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-11-22T13:17:42Z","title":"Cocycle Twists and Extensions of Braided Doubles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5279","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":"sha256:11097df53f5c916ed13a0d01c43d101632a7eb40f970d7fc9db3113c10358875","target":"record","created_at":"2026-05-18T03:34:02Z","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":"acfe2ba8b00403831d4aea90b00fa731b6a89dc95c55bcf3972614c9387b9a72","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-11-22T13:17:42Z","title_canon_sha256":"13a8f709f24b7b8a235b7399b9c52020ec7927e2f4b0da220262540d69984c3b"},"schema_version":"1.0","source":{"id":"1211.5279","kind":"arxiv","version":2}},"canonical_sha256":"f6f6f13c6892606c62b923107f495a50b28c38bd9310a5de4c78d432f0e7d50b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6f6f13c6892606c62b923107f495a50b28c38bd9310a5de4c78d432f0e7d50b","first_computed_at":"2026-05-18T03:34:02.676807Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:02.676807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WidrMH5hb+/9q5Z3TdZlwUjJwwFBSNaQvGnsDITfWvUTQ8mO85AudZQNiGb77xH68UXyFamG3InVPQIO8NgNDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:02.677480Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.5279","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:11097df53f5c916ed13a0d01c43d101632a7eb40f970d7fc9db3113c10358875","sha256:9919a7a37b0ebbb363a15e4a539d650de661d52f03cce1c90da695c64e12665d"],"state_sha256":"1118a70e94294e4b94ba88ef55fcc1cbaa3e2393c8ec5f5ee8f30ce96a6c4691"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OA253AFr/M7sZRIxYbs+p1GDDmlIfPeA1O6b6aAmN97lXYH3qkeh3qeEG9SgJDOzCZ6+O9kPWe4TxVElyW0bCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T05:26:30.391739Z","bundle_sha256":"a857829d06f0f36c76efe6a6c49d436b5f2a29542c4b2d764e19c399af4b0fa1"}}