{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:37Z5ZMJWFKXINW577NNE4I3HJL","short_pith_number":"pith:37Z5ZMJW","canonical_record":{"source":{"id":"1506.07832","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-06-25T17:44:44Z","cross_cats_sorted":["hep-th","math.RT"],"title_canon_sha256":"cfa223dc8e1461453e10a2cd5df02db2a0e6987b875e1c7f263e757701a5da6a","abstract_canon_sha256":"898538781da630a8ff17b6ad9a7420a6c07494c328fa5959598665cb929c78a9"},"schema_version":"1.0"},"canonical_sha256":"dff3dcb1362aae86dbbffb5a4e23674aeee99c76983b90952dc872910663f2a8","source":{"kind":"arxiv","id":"1506.07832","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.07832","created_at":"2026-05-18T01:12:36Z"},{"alias_kind":"arxiv_version","alias_value":"1506.07832v3","created_at":"2026-05-18T01:12:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.07832","created_at":"2026-05-18T01:12:36Z"},{"alias_kind":"pith_short_12","alias_value":"37Z5ZMJWFKXI","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"37Z5ZMJWFKXINW57","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"37Z5ZMJW","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:37Z5ZMJWFKXINW577NNE4I3HJL","target":"record","payload":{"canonical_record":{"source":{"id":"1506.07832","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-06-25T17:44:44Z","cross_cats_sorted":["hep-th","math.RT"],"title_canon_sha256":"cfa223dc8e1461453e10a2cd5df02db2a0e6987b875e1c7f263e757701a5da6a","abstract_canon_sha256":"898538781da630a8ff17b6ad9a7420a6c07494c328fa5959598665cb929c78a9"},"schema_version":"1.0"},"canonical_sha256":"dff3dcb1362aae86dbbffb5a4e23674aeee99c76983b90952dc872910663f2a8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:36.266227Z","signature_b64":"v6O34Ls6DHNvR6croPxYHgcOPltkPLfFAAjM44J7Wnrc9gtSXoOygiFAaGYKfVGf1TFPWAFD0A+FAyCplZdXDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dff3dcb1362aae86dbbffb5a4e23674aeee99c76983b90952dc872910663f2a8","last_reissued_at":"2026-05-18T01:12:36.265605Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:36.265605Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.07832","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":"2026-05-18T01:12:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hjeGBD9czugSRywJJHQQ+9Zzf1B4vfGxtfQYb0tONucWAIrH2AUgbfysWNRFTF3eJmSa7OSab4b2wi9KkmhbCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T12:05:58.305283Z"},"content_sha256":"8d053ea973a0be5cd4801e1b5288f8b19d24c3132d75c0a90ce9810942dd30ae","schema_version":"1.0","event_id":"sha256:8d053ea973a0be5cd4801e1b5288f8b19d24c3132d75c0a90ce9810942dd30ae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:37Z5ZMJWFKXINW577NNE4I3HJL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A decomposition of the Brauer-Picard group of the representation category of a finite group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.RT"],"primary_cat":"math.QA","authors_text":"Jan Priel, Simon Lentner","submitted_at":"2015-06-25T17:44:44Z","abstract_excerpt":"We present an approach of calculating the group of braided autoequivalences of the category of representations of the Drinfeld double of a finite dimensional Hopf algebra $H$ and thus the Brauer-Picard group of $H$-$\\mathrm{mod}$. We consider two natural subgroups and a subset as candidates for generators. In this article $H$ is the group algebra of a finite group $G$. As our main result we prove that any element of the Brauer-Picard group, fulfilling an additional cohomological condition, decomposes into an ordered product of our candidates. For elementary abelian groups $G$ our decomposition"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07832","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":"2026-05-18T01:12:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FejrHE2eJ2injx0w2ychXIif5W/TpIGBo2qqLrGea0tRMzgvGpgRThq+IQXSUVI8dF53/9kL05up24TpMneqBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T12:05:58.305992Z"},"content_sha256":"dfe24b11cabf1e90a2f145bee60faa3d57d65f5ef79d0ce340ae952e6462ea7f","schema_version":"1.0","event_id":"sha256:dfe24b11cabf1e90a2f145bee60faa3d57d65f5ef79d0ce340ae952e6462ea7f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/37Z5ZMJWFKXINW577NNE4I3HJL/bundle.json","state_url":"https://pith.science/pith/37Z5ZMJWFKXINW577NNE4I3HJL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/37Z5ZMJWFKXINW577NNE4I3HJL/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":"2026-06-09T12:05:58Z","links":{"resolver":"https://pith.science/pith/37Z5ZMJWFKXINW577NNE4I3HJL","bundle":"https://pith.science/pith/37Z5ZMJWFKXINW577NNE4I3HJL/bundle.json","state":"https://pith.science/pith/37Z5ZMJWFKXINW577NNE4I3HJL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/37Z5ZMJWFKXINW577NNE4I3HJL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:37Z5ZMJWFKXINW577NNE4I3HJL","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":"898538781da630a8ff17b6ad9a7420a6c07494c328fa5959598665cb929c78a9","cross_cats_sorted":["hep-th","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-06-25T17:44:44Z","title_canon_sha256":"cfa223dc8e1461453e10a2cd5df02db2a0e6987b875e1c7f263e757701a5da6a"},"schema_version":"1.0","source":{"id":"1506.07832","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.07832","created_at":"2026-05-18T01:12:36Z"},{"alias_kind":"arxiv_version","alias_value":"1506.07832v3","created_at":"2026-05-18T01:12:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.07832","created_at":"2026-05-18T01:12:36Z"},{"alias_kind":"pith_short_12","alias_value":"37Z5ZMJWFKXI","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"37Z5ZMJWFKXINW57","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"37Z5ZMJW","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:dfe24b11cabf1e90a2f145bee60faa3d57d65f5ef79d0ce340ae952e6462ea7f","target":"graph","created_at":"2026-05-18T01:12:36Z","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 present an approach of calculating the group of braided autoequivalences of the category of representations of the Drinfeld double of a finite dimensional Hopf algebra $H$ and thus the Brauer-Picard group of $H$-$\\mathrm{mod}$. We consider two natural subgroups and a subset as candidates for generators. In this article $H$ is the group algebra of a finite group $G$. As our main result we prove that any element of the Brauer-Picard group, fulfilling an additional cohomological condition, decomposes into an ordered product of our candidates. For elementary abelian groups $G$ our decomposition","authors_text":"Jan Priel, Simon Lentner","cross_cats":["hep-th","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-06-25T17:44:44Z","title":"A decomposition of the Brauer-Picard group of the representation category of a finite group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07832","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":"sha256:8d053ea973a0be5cd4801e1b5288f8b19d24c3132d75c0a90ce9810942dd30ae","target":"record","created_at":"2026-05-18T01:12:36Z","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":"898538781da630a8ff17b6ad9a7420a6c07494c328fa5959598665cb929c78a9","cross_cats_sorted":["hep-th","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-06-25T17:44:44Z","title_canon_sha256":"cfa223dc8e1461453e10a2cd5df02db2a0e6987b875e1c7f263e757701a5da6a"},"schema_version":"1.0","source":{"id":"1506.07832","kind":"arxiv","version":3}},"canonical_sha256":"dff3dcb1362aae86dbbffb5a4e23674aeee99c76983b90952dc872910663f2a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dff3dcb1362aae86dbbffb5a4e23674aeee99c76983b90952dc872910663f2a8","first_computed_at":"2026-05-18T01:12:36.265605Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:36.265605Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v6O34Ls6DHNvR6croPxYHgcOPltkPLfFAAjM44J7Wnrc9gtSXoOygiFAaGYKfVGf1TFPWAFD0A+FAyCplZdXDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:36.266227Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.07832","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d053ea973a0be5cd4801e1b5288f8b19d24c3132d75c0a90ce9810942dd30ae","sha256:dfe24b11cabf1e90a2f145bee60faa3d57d65f5ef79d0ce340ae952e6462ea7f"],"state_sha256":"eca153c7af4cb737df27df045a33d41753e3ca66f7325dd995d65a0b524d0b1e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C3YAEHWWnLsPaqgXNwJA8CtZL/TZRTXy0V9luEAQpnjE773eahzdgwNjUOONXT4pQEexMpn3G3ovjPpMjD36CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T12:05:58.310021Z","bundle_sha256":"613607b47b5cfd30927aefe282e3fb6b35aec383c6830efca84a766e17b710c3"}}