{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:HFVOLK4TESNEOP22GUSPBDZGBM","short_pith_number":"pith:HFVOLK4T","canonical_record":{"source":{"id":"1309.5026","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-09-19T15:30:12Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"64865af54316d6bd747a9094b48695061acbbcee816bf2ad9a90f602f3c1ade1","abstract_canon_sha256":"9ea43c9fefe1cf167c6043ba8190fac9a66a389b739ab04f008d84b623184fbf"},"schema_version":"1.0"},"canonical_sha256":"396ae5ab93249a473f5a3524f08f260b0967c80975e3d0e14340b4fb68647838","source":{"kind":"arxiv","id":"1309.5026","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.5026","created_at":"2026-05-18T01:18:57Z"},{"alias_kind":"arxiv_version","alias_value":"1309.5026v2","created_at":"2026-05-18T01:18:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5026","created_at":"2026-05-18T01:18:57Z"},{"alias_kind":"pith_short_12","alias_value":"HFVOLK4TESNE","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HFVOLK4TESNEOP22","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HFVOLK4T","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:HFVOLK4TESNEOP22GUSPBDZGBM","target":"record","payload":{"canonical_record":{"source":{"id":"1309.5026","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-09-19T15:30:12Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"64865af54316d6bd747a9094b48695061acbbcee816bf2ad9a90f602f3c1ade1","abstract_canon_sha256":"9ea43c9fefe1cf167c6043ba8190fac9a66a389b739ab04f008d84b623184fbf"},"schema_version":"1.0"},"canonical_sha256":"396ae5ab93249a473f5a3524f08f260b0967c80975e3d0e14340b4fb68647838","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:57.740342Z","signature_b64":"QAwfoMZ3jWAJQ2/DcbuYWvxVldzvWw1agg5AsneYKETeNIl5q9cZE368BbDg+/nhJBXyWXQkZSsACA09Fe/8Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"396ae5ab93249a473f5a3524f08f260b0967c80975e3d0e14340b4fb68647838","last_reissued_at":"2026-05-18T01:18:57.739788Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:57.739788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.5026","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":"2026-05-18T01:18:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"seb7abNgNBtUyGa12iFZzupld2R0EnuTaXPzDlri4TU18wCXbpXT1Cw6SagvtMIioTncV51p0r2Ft1770O0cDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T08:00:12.179293Z"},"content_sha256":"bd9b13b842d0b1f60186a8084b2e8e68138b60e6a416b55d303af6f012671f71","schema_version":"1.0","event_id":"sha256:bd9b13b842d0b1f60186a8084b2e8e68138b60e6a416b55d303af6f012671f71"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:HFVOLK4TESNEOP22GUSPBDZGBM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Categorical Lagrangian Grassmannians and Brauer-Picard groups of pointed fusion categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.QA","authors_text":"Brianna Riepel, Dmitri Nikshych","submitted_at":"2013-09-19T15:30:12Z","abstract_excerpt":"We analyze the action of the Brauer-Picard group of a pointed fusion category on the set of Lagrangian subcategories of its center. Using this action we compute the Brauer-Picard groups of pointed fusion categories associated to several classical finite groups. As an application, we construct new examples of weakly group-theoretical fusion categories."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5026","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":"2026-05-18T01:18:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jngYoUdY/ilhEyYmHVhIpUOfXMG7MH//G+cjOboACeiHQzBAOK0hwtSGhQV2c6Y89on93XHc/RbHaYy0INyTAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T08:00:12.179652Z"},"content_sha256":"b571674c926766c9f08c21f4dbfa2de94c8875cea5678d873072ccdb78a2a215","schema_version":"1.0","event_id":"sha256:b571674c926766c9f08c21f4dbfa2de94c8875cea5678d873072ccdb78a2a215"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HFVOLK4TESNEOP22GUSPBDZGBM/bundle.json","state_url":"https://pith.science/pith/HFVOLK4TESNEOP22GUSPBDZGBM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HFVOLK4TESNEOP22GUSPBDZGBM/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":"2026-06-02T08:00:12Z","links":{"resolver":"https://pith.science/pith/HFVOLK4TESNEOP22GUSPBDZGBM","bundle":"https://pith.science/pith/HFVOLK4TESNEOP22GUSPBDZGBM/bundle.json","state":"https://pith.science/pith/HFVOLK4TESNEOP22GUSPBDZGBM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HFVOLK4TESNEOP22GUSPBDZGBM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HFVOLK4TESNEOP22GUSPBDZGBM","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":"9ea43c9fefe1cf167c6043ba8190fac9a66a389b739ab04f008d84b623184fbf","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-09-19T15:30:12Z","title_canon_sha256":"64865af54316d6bd747a9094b48695061acbbcee816bf2ad9a90f602f3c1ade1"},"schema_version":"1.0","source":{"id":"1309.5026","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.5026","created_at":"2026-05-18T01:18:57Z"},{"alias_kind":"arxiv_version","alias_value":"1309.5026v2","created_at":"2026-05-18T01:18:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5026","created_at":"2026-05-18T01:18:57Z"},{"alias_kind":"pith_short_12","alias_value":"HFVOLK4TESNE","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HFVOLK4TESNEOP22","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HFVOLK4T","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:b571674c926766c9f08c21f4dbfa2de94c8875cea5678d873072ccdb78a2a215","target":"graph","created_at":"2026-05-18T01:18:57Z","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":"We analyze the action of the Brauer-Picard group of a pointed fusion category on the set of Lagrangian subcategories of its center. Using this action we compute the Brauer-Picard groups of pointed fusion categories associated to several classical finite groups. As an application, we construct new examples of weakly group-theoretical fusion categories.","authors_text":"Brianna Riepel, Dmitri Nikshych","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-09-19T15:30:12Z","title":"Categorical Lagrangian Grassmannians and Brauer-Picard groups of pointed fusion categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5026","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:bd9b13b842d0b1f60186a8084b2e8e68138b60e6a416b55d303af6f012671f71","target":"record","created_at":"2026-05-18T01:18:57Z","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":"9ea43c9fefe1cf167c6043ba8190fac9a66a389b739ab04f008d84b623184fbf","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-09-19T15:30:12Z","title_canon_sha256":"64865af54316d6bd747a9094b48695061acbbcee816bf2ad9a90f602f3c1ade1"},"schema_version":"1.0","source":{"id":"1309.5026","kind":"arxiv","version":2}},"canonical_sha256":"396ae5ab93249a473f5a3524f08f260b0967c80975e3d0e14340b4fb68647838","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"396ae5ab93249a473f5a3524f08f260b0967c80975e3d0e14340b4fb68647838","first_computed_at":"2026-05-18T01:18:57.739788Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:57.739788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QAwfoMZ3jWAJQ2/DcbuYWvxVldzvWw1agg5AsneYKETeNIl5q9cZE368BbDg+/nhJBXyWXQkZSsACA09Fe/8Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:57.740342Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.5026","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd9b13b842d0b1f60186a8084b2e8e68138b60e6a416b55d303af6f012671f71","sha256:b571674c926766c9f08c21f4dbfa2de94c8875cea5678d873072ccdb78a2a215"],"state_sha256":"c6495c2d768081f741d3f5956e37c45aac1e05c8e49280f88b72a55dd1f1ce18"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UEWNOE2hTBS9H5cjKi+bRMHPVMXk1V6QPaM/c7WVcuTOSTvqG9BBSWa09vJoQO/KhvMFWBwkuP7+mg9W6sICAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T08:00:12.181550Z","bundle_sha256":"e39a70d5d18fadbec8a39980e9fb7a40a0ba76ccdf2c9ea442bf750c4d4c1e57"}}