{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:GRY4QTY43SHKG2MVY5FTSJQ6WN","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":"cc6f6f7f2a16d046b143e3f5aae9951d6647a77aa170e0fee07686c719e28ba8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CT","submitted_at":"2024-11-20T14:48:34Z","title_canon_sha256":"501ea5c74221a827791c4bb459a5c5b4a65fbcde31ab1863c62df9e3d8621dae"},"schema_version":"1.0","source":{"id":"2411.13367","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.13367","created_at":"2026-07-05T09:38:09Z"},{"alias_kind":"arxiv_version","alias_value":"2411.13367v1","created_at":"2026-07-05T09:38:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.13367","created_at":"2026-07-05T09:38:09Z"},{"alias_kind":"pith_short_12","alias_value":"GRY4QTY43SHK","created_at":"2026-07-05T09:38:09Z"},{"alias_kind":"pith_short_16","alias_value":"GRY4QTY43SHKG2MV","created_at":"2026-07-05T09:38:09Z"},{"alias_kind":"pith_short_8","alias_value":"GRY4QTY4","created_at":"2026-07-05T09:38:09Z"}],"graph_snapshots":[{"event_id":"sha256:3dda412e8d72d990188632b8452dc5d9440af1f60184c5f2fc2827f68691634c","target":"graph","created_at":"2026-07-05T09:38:09Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2411.13367/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We classify all connected and Lagrangian \\'etale algebras in the Drinfeld center $\\mathscr{Z}_1(\\mathbf{2Vect}^\\pi_G)$, where $G$ is a finite group and $\\pi$ is a 4-cocycle on $G$. By D\\'ecoppet's result every bosonic fusion 2-category $\\mathfrak{C}$ has its Drinfeld center equivalent to $\\mathscr{Z}_1(\\mathbf{2Vect}^\\pi_G)$ for some $G$ and $\\pi$. Combining this fact with classification of Lagrangian algebras in $\\mathscr{Z}_1(\\mathbf{2Vect}^\\pi_G)$, we obtain a classification of bosonic fusion 2-categories.","authors_text":"Hao Xu","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CT","submitted_at":"2024-11-20T14:48:34Z","title":"On \\'Etale Algebras and Bosonic Fusion 2-Categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.13367","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:f2db6339781d92ec65b222de8a4453914326f6c3d14ce0524afece055e1e9ef8","target":"record","created_at":"2026-07-05T09:38:09Z","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":"cc6f6f7f2a16d046b143e3f5aae9951d6647a77aa170e0fee07686c719e28ba8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CT","submitted_at":"2024-11-20T14:48:34Z","title_canon_sha256":"501ea5c74221a827791c4bb459a5c5b4a65fbcde31ab1863c62df9e3d8621dae"},"schema_version":"1.0","source":{"id":"2411.13367","kind":"arxiv","version":1}},"canonical_sha256":"3471c84f1cdc8ea36995c74b39261eb37053425dac72e9070d882a87fa22e050","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3471c84f1cdc8ea36995c74b39261eb37053425dac72e9070d882a87fa22e050","first_computed_at":"2026-07-05T09:38:09.339008Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:38:09.339008Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QP1fWFriMqcHzWnsheMjiwbjdh20nAqBY6iGfZMGQ+maC9QcUBzElBar5w0iwyAoGb9t3CkhiJlFGWG5wMyaCA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:38:09.339513Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.13367","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2db6339781d92ec65b222de8a4453914326f6c3d14ce0524afece055e1e9ef8","sha256:3dda412e8d72d990188632b8452dc5d9440af1f60184c5f2fc2827f68691634c"],"state_sha256":"26d83b43a57563c885e5d96223c4c73c3a8421ef1b78d863f47458b2dfcc6aab"}