{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:7LTEJJL6JHUPQBOTTFXZJA5JSC","short_pith_number":"pith:7LTEJJL6","canonical_record":{"source":{"id":"1410.8686","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-10-31T09:57:18Z","cross_cats_sorted":[],"title_canon_sha256":"9f1071f4c90f5d9983b1fd2bad558fcbec740ef5cc55c28b19b20dfa47715e58","abstract_canon_sha256":"dc2a79449918d21ee88c00aa33b9991739ad4be1dc3211d4ab88786448e382e7"},"schema_version":"1.0"},"canonical_sha256":"fae644a57e49e8f805d3996f9483a990b50d820747a8cdf92efc3f130ff00c60","source":{"kind":"arxiv","id":"1410.8686","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.8686","created_at":"2026-05-18T02:38:53Z"},{"alias_kind":"arxiv_version","alias_value":"1410.8686v1","created_at":"2026-05-18T02:38:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.8686","created_at":"2026-05-18T02:38:53Z"},{"alias_kind":"pith_short_12","alias_value":"7LTEJJL6JHUP","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7LTEJJL6JHUPQBOT","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7LTEJJL6","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:7LTEJJL6JHUPQBOTTFXZJA5JSC","target":"record","payload":{"canonical_record":{"source":{"id":"1410.8686","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-10-31T09:57:18Z","cross_cats_sorted":[],"title_canon_sha256":"9f1071f4c90f5d9983b1fd2bad558fcbec740ef5cc55c28b19b20dfa47715e58","abstract_canon_sha256":"dc2a79449918d21ee88c00aa33b9991739ad4be1dc3211d4ab88786448e382e7"},"schema_version":"1.0"},"canonical_sha256":"fae644a57e49e8f805d3996f9483a990b50d820747a8cdf92efc3f130ff00c60","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:53.922588Z","signature_b64":"SP18Qa6KpLAQwjmJHbkFzhRuU8OGl+fSS93FOSfaEH2Q3Umr8f1PAQ+mJ68HrTYBtDhtfxg6QInORdS3TadoBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fae644a57e49e8f805d3996f9483a990b50d820747a8cdf92efc3f130ff00c60","last_reissued_at":"2026-05-18T02:38:53.922191Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:53.922191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.8686","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:38:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jyHEM2KPWZ9EDYjpqMPRJk2m+ayWDK8iNPshpKV34GlbBR99QQtP2JOHLr0Gz5KgF1F53zBM/aeHTylSnkQnAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T12:46:35.258583Z"},"content_sha256":"78365f1aa83aa418ceddbd8bf27a838a4ca322d42e2dda57fec526458fe623c9","schema_version":"1.0","event_id":"sha256:78365f1aa83aa418ceddbd8bf27a838a4ca322d42e2dda57fec526458fe623c9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:7LTEJJL6JHUPQBOTTFXZJA5JSC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Braided autoequivalences and the equivariant Brauer group of a quasitriangular Hopf algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Jeroen Dello, Yinhuo Zhang","submitted_at":"2014-10-31T09:57:18Z","abstract_excerpt":"Let $(H, R)$ be a finite dimensional quasitriangular Hopf algebra over a field $k$, and $_H\\mathcal{M}$ the representation category of $H$. In this paper, we study the braided autoequivalences of the Drinfeld center $^H_H\\mathcal{YD}$ trivializable on $_H\\mathcal{M}$. We establish a group isomorphism between the group of those autoequivalences and the group of quantum commutative bi-Galois objects of the transmutation braided Hopf algebra $_RH$. We then apply this isomorphism to obtain a categorical interpretation of the exact sequence of the equivariant Brauer group $\\mathrm{BM}(k, H,R)$ in ["},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8686","kind":"arxiv","version":1},"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":"2026-05-18T02:38:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4D8GGDahVg5TwBLh8JkGo8gCxx/eTYBUJr99f3zeOJEnfPkeuyV44mYY6EcExHon3210AUdvnZ4InHSO00czAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T12:46:35.258921Z"},"content_sha256":"d4086cfed2e7aeab091bf42e47ee732c6adfa099ceb864043c36c66d428d8fbd","schema_version":"1.0","event_id":"sha256:d4086cfed2e7aeab091bf42e47ee732c6adfa099ceb864043c36c66d428d8fbd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7LTEJJL6JHUPQBOTTFXZJA5JSC/bundle.json","state_url":"https://pith.science/pith/7LTEJJL6JHUPQBOTTFXZJA5JSC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7LTEJJL6JHUPQBOTTFXZJA5JSC/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":"2026-06-28T12:46:35Z","links":{"resolver":"https://pith.science/pith/7LTEJJL6JHUPQBOTTFXZJA5JSC","bundle":"https://pith.science/pith/7LTEJJL6JHUPQBOTTFXZJA5JSC/bundle.json","state":"https://pith.science/pith/7LTEJJL6JHUPQBOTTFXZJA5JSC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7LTEJJL6JHUPQBOTTFXZJA5JSC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7LTEJJL6JHUPQBOTTFXZJA5JSC","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":"dc2a79449918d21ee88c00aa33b9991739ad4be1dc3211d4ab88786448e382e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-10-31T09:57:18Z","title_canon_sha256":"9f1071f4c90f5d9983b1fd2bad558fcbec740ef5cc55c28b19b20dfa47715e58"},"schema_version":"1.0","source":{"id":"1410.8686","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.8686","created_at":"2026-05-18T02:38:53Z"},{"alias_kind":"arxiv_version","alias_value":"1410.8686v1","created_at":"2026-05-18T02:38:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.8686","created_at":"2026-05-18T02:38:53Z"},{"alias_kind":"pith_short_12","alias_value":"7LTEJJL6JHUP","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7LTEJJL6JHUPQBOT","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7LTEJJL6","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:d4086cfed2e7aeab091bf42e47ee732c6adfa099ceb864043c36c66d428d8fbd","target":"graph","created_at":"2026-05-18T02:38:53Z","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":"Let $(H, R)$ be a finite dimensional quasitriangular Hopf algebra over a field $k$, and $_H\\mathcal{M}$ the representation category of $H$. In this paper, we study the braided autoequivalences of the Drinfeld center $^H_H\\mathcal{YD}$ trivializable on $_H\\mathcal{M}$. We establish a group isomorphism between the group of those autoequivalences and the group of quantum commutative bi-Galois objects of the transmutation braided Hopf algebra $_RH$. We then apply this isomorphism to obtain a categorical interpretation of the exact sequence of the equivariant Brauer group $\\mathrm{BM}(k, H,R)$ in [","authors_text":"Jeroen Dello, Yinhuo Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-10-31T09:57:18Z","title":"Braided autoequivalences and the equivariant Brauer group of a quasitriangular Hopf algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8686","kind":"arxiv","version":1},"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":"sha256:78365f1aa83aa418ceddbd8bf27a838a4ca322d42e2dda57fec526458fe623c9","target":"record","created_at":"2026-05-18T02:38:53Z","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":"dc2a79449918d21ee88c00aa33b9991739ad4be1dc3211d4ab88786448e382e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-10-31T09:57:18Z","title_canon_sha256":"9f1071f4c90f5d9983b1fd2bad558fcbec740ef5cc55c28b19b20dfa47715e58"},"schema_version":"1.0","source":{"id":"1410.8686","kind":"arxiv","version":1}},"canonical_sha256":"fae644a57e49e8f805d3996f9483a990b50d820747a8cdf92efc3f130ff00c60","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fae644a57e49e8f805d3996f9483a990b50d820747a8cdf92efc3f130ff00c60","first_computed_at":"2026-05-18T02:38:53.922191Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:53.922191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SP18Qa6KpLAQwjmJHbkFzhRuU8OGl+fSS93FOSfaEH2Q3Umr8f1PAQ+mJ68HrTYBtDhtfxg6QInORdS3TadoBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:53.922588Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.8686","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:78365f1aa83aa418ceddbd8bf27a838a4ca322d42e2dda57fec526458fe623c9","sha256:d4086cfed2e7aeab091bf42e47ee732c6adfa099ceb864043c36c66d428d8fbd"],"state_sha256":"00ef02aa0a7861aeb24a04c9fc2edb5c61160576e342004475a61a8d771c4758"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FOTQximcAsF8NasbI0tcMapCyWesvUu1Iuq02B+w+7lXs6SncVKnAQtXLPLmy6sG2NC7cDrSARJQ0ZXBow7hCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T12:46:35.260832Z","bundle_sha256":"7abbeeb45d87289f39359154ce02399b7fc9301ae91e6148735d1e00f5581c36"}}