{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:6LUDAU4RRPLAK2DLAZ2AVDX26D","short_pith_number":"pith:6LUDAU4R","canonical_record":{"source":{"id":"1202.0061","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-02-01T00:26:11Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"fc75bd6fc16e61bf39d1160799cac7f1e9ad6296cb057a47ef58acaa5b395fbb","abstract_canon_sha256":"c8e74fd0ee69a9c4ae32cf710d3ae4534e156502d5b0b1cbe48fcdf95a5ad9f3"},"schema_version":"1.0"},"canonical_sha256":"f2e83053918bd605686b06740a8efaf0e2c64d0d6706a6492959ca64df87eea3","source":{"kind":"arxiv","id":"1202.0061","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.0061","created_at":"2026-05-18T04:03:20Z"},{"alias_kind":"arxiv_version","alias_value":"1202.0061v1","created_at":"2026-05-18T04:03:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.0061","created_at":"2026-05-18T04:03:20Z"},{"alias_kind":"pith_short_12","alias_value":"6LUDAU4RRPLA","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6LUDAU4RRPLAK2DL","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6LUDAU4R","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:6LUDAU4RRPLAK2DLAZ2AVDX26D","target":"record","payload":{"canonical_record":{"source":{"id":"1202.0061","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-02-01T00:26:11Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"fc75bd6fc16e61bf39d1160799cac7f1e9ad6296cb057a47ef58acaa5b395fbb","abstract_canon_sha256":"c8e74fd0ee69a9c4ae32cf710d3ae4534e156502d5b0b1cbe48fcdf95a5ad9f3"},"schema_version":"1.0"},"canonical_sha256":"f2e83053918bd605686b06740a8efaf0e2c64d0d6706a6492959ca64df87eea3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:03:20.614423Z","signature_b64":"AVWLtX7xQxuBbss0ILo7jrIECF+XCyNCYvvoMmp/bf1p1GcpJhQQCyCxDoI9IY5KKImSXx6iWSr+V2ZrKOM3DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2e83053918bd605686b06740a8efaf0e2c64d0d6706a6492959ca64df87eea3","last_reissued_at":"2026-05-18T04:03:20.614013Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:03:20.614013Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.0061","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":"2026-05-18T04:03:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AFCOah9BVCCLna9tDFwfcFbeS3E0M5sP/s4ukaF3dB75LxwzrSmWSew8dCa25p+D35TtA0XqkI6GkQCTr2b4Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T01:21:49.515205Z"},"content_sha256":"d65b4cf6766266267f90f5d37b8cf7b48c76725bb911748012e6c1bcd61a512c","schema_version":"1.0","event_id":"sha256:d65b4cf6766266267f90f5d37b8cf7b48c76725bb911748012e6c1bcd61a512c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:6LUDAU4RRPLAK2DLAZ2AVDX26D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Picard crossed module of a braided tensor category","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.QA","authors_text":"Alexei Davydov, Dmitri Nikshych","submitted_at":"2012-02-01T00:26:11Z","abstract_excerpt":"For a finite braided tensor category we introduce its Picard crossed module consisting of the group of invertible module categories and the group of braided tensor autoequivalences. We describe the Picard crossed module in terms of braided autoequivalences of the Drinfeld center of the braided tensor category. As an illustration, we compute the Picard crossed module of a braided pointed fusion category."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0061","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":"2026-05-18T04:03:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6gvYiGKC0zCkRBSNWNUQBECAXd4Pfv9AH64ws9D8JXGCpljOCjwW2vs1AiJzrHTplEzeyO4/+XXNS6An1z7ACA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T01:21:49.515572Z"},"content_sha256":"33a2dd5c856c40bf06c97a8b11a99d495e233f1f038548232a5d361fdfa90d14","schema_version":"1.0","event_id":"sha256:33a2dd5c856c40bf06c97a8b11a99d495e233f1f038548232a5d361fdfa90d14"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6LUDAU4RRPLAK2DLAZ2AVDX26D/bundle.json","state_url":"https://pith.science/pith/6LUDAU4RRPLAK2DLAZ2AVDX26D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6LUDAU4RRPLAK2DLAZ2AVDX26D/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":"2026-06-02T01:21:49Z","links":{"resolver":"https://pith.science/pith/6LUDAU4RRPLAK2DLAZ2AVDX26D","bundle":"https://pith.science/pith/6LUDAU4RRPLAK2DLAZ2AVDX26D/bundle.json","state":"https://pith.science/pith/6LUDAU4RRPLAK2DLAZ2AVDX26D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6LUDAU4RRPLAK2DLAZ2AVDX26D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6LUDAU4RRPLAK2DLAZ2AVDX26D","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":"c8e74fd0ee69a9c4ae32cf710d3ae4534e156502d5b0b1cbe48fcdf95a5ad9f3","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-02-01T00:26:11Z","title_canon_sha256":"fc75bd6fc16e61bf39d1160799cac7f1e9ad6296cb057a47ef58acaa5b395fbb"},"schema_version":"1.0","source":{"id":"1202.0061","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.0061","created_at":"2026-05-18T04:03:20Z"},{"alias_kind":"arxiv_version","alias_value":"1202.0061v1","created_at":"2026-05-18T04:03:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.0061","created_at":"2026-05-18T04:03:20Z"},{"alias_kind":"pith_short_12","alias_value":"6LUDAU4RRPLA","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6LUDAU4RRPLAK2DL","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6LUDAU4R","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:33a2dd5c856c40bf06c97a8b11a99d495e233f1f038548232a5d361fdfa90d14","target":"graph","created_at":"2026-05-18T04:03:20Z","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 finite braided tensor category we introduce its Picard crossed module consisting of the group of invertible module categories and the group of braided tensor autoequivalences. We describe the Picard crossed module in terms of braided autoequivalences of the Drinfeld center of the braided tensor category. As an illustration, we compute the Picard crossed module of a braided pointed fusion category.","authors_text":"Alexei Davydov, Dmitri Nikshych","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-02-01T00:26:11Z","title":"The Picard crossed module of a braided tensor category"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0061","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:d65b4cf6766266267f90f5d37b8cf7b48c76725bb911748012e6c1bcd61a512c","target":"record","created_at":"2026-05-18T04:03:20Z","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":"c8e74fd0ee69a9c4ae32cf710d3ae4534e156502d5b0b1cbe48fcdf95a5ad9f3","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-02-01T00:26:11Z","title_canon_sha256":"fc75bd6fc16e61bf39d1160799cac7f1e9ad6296cb057a47ef58acaa5b395fbb"},"schema_version":"1.0","source":{"id":"1202.0061","kind":"arxiv","version":1}},"canonical_sha256":"f2e83053918bd605686b06740a8efaf0e2c64d0d6706a6492959ca64df87eea3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2e83053918bd605686b06740a8efaf0e2c64d0d6706a6492959ca64df87eea3","first_computed_at":"2026-05-18T04:03:20.614013Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:03:20.614013Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AVWLtX7xQxuBbss0ILo7jrIECF+XCyNCYvvoMmp/bf1p1GcpJhQQCyCxDoI9IY5KKImSXx6iWSr+V2ZrKOM3DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:03:20.614423Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.0061","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d65b4cf6766266267f90f5d37b8cf7b48c76725bb911748012e6c1bcd61a512c","sha256:33a2dd5c856c40bf06c97a8b11a99d495e233f1f038548232a5d361fdfa90d14"],"state_sha256":"55982552ca31e733694af166f98d7d7ff3c01a04d4340005969b48336bc6bba9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0vodgy6OKHTyBXbc34m/su+EOgYhLb/wzT+rQDj5HaO+GhEBYZiPUtkD2txZDkXakuTQB/PJ/SKN1QsN8xVQAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T01:21:49.517507Z","bundle_sha256":"8576407b25998668230c838ed9fd5c23adb937c684dd0aacb3c95e73d062ebf2"}}