{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:WOG3YPTRZ4HMILWLNUXS2EFK2J","short_pith_number":"pith:WOG3YPTR","canonical_record":{"source":{"id":"1603.04318","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-03-14T16:02:29Z","cross_cats_sorted":[],"title_canon_sha256":"5d870aa486b984500186420018771bf32fa7198254538aae488522b899b33a8c","abstract_canon_sha256":"9ba112d171b6a52915d96958b033ad72c339e4b7a99a0e0e28caf5f29d83210d"},"schema_version":"1.0"},"canonical_sha256":"b38dbc3e71cf0ec42ecb6d2f2d10aad275d7f1af7eb11b5c974c69cab26a3016","source":{"kind":"arxiv","id":"1603.04318","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.04318","created_at":"2026-05-18T01:01:28Z"},{"alias_kind":"arxiv_version","alias_value":"1603.04318v3","created_at":"2026-05-18T01:01:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.04318","created_at":"2026-05-18T01:01:28Z"},{"alias_kind":"pith_short_12","alias_value":"WOG3YPTRZ4HM","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"WOG3YPTRZ4HMILWL","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"WOG3YPTR","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:WOG3YPTRZ4HMILWLNUXS2EFK2J","target":"record","payload":{"canonical_record":{"source":{"id":"1603.04318","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-03-14T16:02:29Z","cross_cats_sorted":[],"title_canon_sha256":"5d870aa486b984500186420018771bf32fa7198254538aae488522b899b33a8c","abstract_canon_sha256":"9ba112d171b6a52915d96958b033ad72c339e4b7a99a0e0e28caf5f29d83210d"},"schema_version":"1.0"},"canonical_sha256":"b38dbc3e71cf0ec42ecb6d2f2d10aad275d7f1af7eb11b5c974c69cab26a3016","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:28.675097Z","signature_b64":"AWhIUxB/fq2EAIJ0DpC+cKtvjTxRWSdhQetzuE1AeSkCvfZO7FCGfquAY5vqMt98mWJ6+Ma5m9AMzGZGAf/pAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b38dbc3e71cf0ec42ecb6d2f2d10aad275d7f1af7eb11b5c974c69cab26a3016","last_reissued_at":"2026-05-18T01:01:28.674288Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:28.674288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.04318","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:01:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ftmNwDvJjc0G192wl4ECwdO5mrj+Lzcor6sYcQAO+964aVOgMTw/1nrtNFPGGcPaVlvPov+vgb4ILB7V/49JAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:58:08.144498Z"},"content_sha256":"1424b4ab9979731ba48c6f577aac3c79446a5df4630ad8570de9b93f6ac92302","schema_version":"1.0","event_id":"sha256:1424b4ab9979731ba48c6f577aac3c79446a5df4630ad8570de9b93f6ac92302"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:WOG3YPTRZ4HMILWLNUXS2EFK2J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Brauer-Picard groups of fusion categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Dmitri Nikshych, Ian Marshall","submitted_at":"2016-03-14T16:02:29Z","abstract_excerpt":"We develop methods of computation of the Brauer-Picard groups of fusion categories and apply them to compute such groups for several classes of fusion categories of prime power dimension: representation categories of elementary abelian groups with twisted associativity constraint, extra special p-groups, and the Kac-Paljutkin Hopf algebra. We conclude that many finite groups of Lie type occur as composition factors of the Brauer-Picard groups of pointed fusion categories."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04318","kind":"arxiv","version":3},"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":"2026-05-18T01:01:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ysd+lEQPuof34t/uX7GxbXeuwaR6B8OIbnkKQI1EYlu1M/GUcqMBxNwGr6Ojhs/9BqaGFJBPnkQw+lruW59gAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:58:08.144847Z"},"content_sha256":"3eaff92cd4518714d2e6dc9cb18badc064278fafaf04f8e75d5d64392d399aae","schema_version":"1.0","event_id":"sha256:3eaff92cd4518714d2e6dc9cb18badc064278fafaf04f8e75d5d64392d399aae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WOG3YPTRZ4HMILWLNUXS2EFK2J/bundle.json","state_url":"https://pith.science/pith/WOG3YPTRZ4HMILWLNUXS2EFK2J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WOG3YPTRZ4HMILWLNUXS2EFK2J/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":"2026-06-01T18:58:08Z","links":{"resolver":"https://pith.science/pith/WOG3YPTRZ4HMILWLNUXS2EFK2J","bundle":"https://pith.science/pith/WOG3YPTRZ4HMILWLNUXS2EFK2J/bundle.json","state":"https://pith.science/pith/WOG3YPTRZ4HMILWLNUXS2EFK2J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WOG3YPTRZ4HMILWLNUXS2EFK2J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WOG3YPTRZ4HMILWLNUXS2EFK2J","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":"9ba112d171b6a52915d96958b033ad72c339e4b7a99a0e0e28caf5f29d83210d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-03-14T16:02:29Z","title_canon_sha256":"5d870aa486b984500186420018771bf32fa7198254538aae488522b899b33a8c"},"schema_version":"1.0","source":{"id":"1603.04318","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.04318","created_at":"2026-05-18T01:01:28Z"},{"alias_kind":"arxiv_version","alias_value":"1603.04318v3","created_at":"2026-05-18T01:01:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.04318","created_at":"2026-05-18T01:01:28Z"},{"alias_kind":"pith_short_12","alias_value":"WOG3YPTRZ4HM","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"WOG3YPTRZ4HMILWL","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"WOG3YPTR","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:3eaff92cd4518714d2e6dc9cb18badc064278fafaf04f8e75d5d64392d399aae","target":"graph","created_at":"2026-05-18T01:01:28Z","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 develop methods of computation of the Brauer-Picard groups of fusion categories and apply them to compute such groups for several classes of fusion categories of prime power dimension: representation categories of elementary abelian groups with twisted associativity constraint, extra special p-groups, and the Kac-Paljutkin Hopf algebra. We conclude that many finite groups of Lie type occur as composition factors of the Brauer-Picard groups of pointed fusion categories.","authors_text":"Dmitri Nikshych, Ian Marshall","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-03-14T16:02:29Z","title":"On the Brauer-Picard groups of fusion categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04318","kind":"arxiv","version":3},"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":"sha256:1424b4ab9979731ba48c6f577aac3c79446a5df4630ad8570de9b93f6ac92302","target":"record","created_at":"2026-05-18T01:01:28Z","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":"9ba112d171b6a52915d96958b033ad72c339e4b7a99a0e0e28caf5f29d83210d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-03-14T16:02:29Z","title_canon_sha256":"5d870aa486b984500186420018771bf32fa7198254538aae488522b899b33a8c"},"schema_version":"1.0","source":{"id":"1603.04318","kind":"arxiv","version":3}},"canonical_sha256":"b38dbc3e71cf0ec42ecb6d2f2d10aad275d7f1af7eb11b5c974c69cab26a3016","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b38dbc3e71cf0ec42ecb6d2f2d10aad275d7f1af7eb11b5c974c69cab26a3016","first_computed_at":"2026-05-18T01:01:28.674288Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:28.674288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AWhIUxB/fq2EAIJ0DpC+cKtvjTxRWSdhQetzuE1AeSkCvfZO7FCGfquAY5vqMt98mWJ6+Ma5m9AMzGZGAf/pAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:28.675097Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.04318","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1424b4ab9979731ba48c6f577aac3c79446a5df4630ad8570de9b93f6ac92302","sha256:3eaff92cd4518714d2e6dc9cb18badc064278fafaf04f8e75d5d64392d399aae"],"state_sha256":"63bc5f4aac80de9605ddecfc49da8ae747f37c14f479499fbcc6f3abda29cf77"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/nectuCUQraROPppPBGSaxIPv0n5PWmwXCtIGWiaRBNT4Xh9n/472a7jbSxiAjyUY2aitUMCdmiHaVkZ7FSzBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T18:58:08.146800Z","bundle_sha256":"afcf7f8c28c505779a7bc07341cabfe9fce7e1930523e6b8edd659ebf2bc816a"}}