{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:DO2SQ6SRLABYUHQPBTKKUU5R4T","short_pith_number":"pith:DO2SQ6SR","schema_version":"1.0","canonical_sha256":"1bb5287a5158038a1e0f0cd4aa53b1e4ce6d801b447ea699de65fc141e6dcca6","source":{"kind":"arxiv","id":"1904.05798","version":1},"attestation_state":"computed","paper":{"title":"2-categories of symmetric bimodules and their 2-representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Vanessa Miemietz, Volodymyr Mazorchuk, Xiaoting Zhang","submitted_at":"2019-04-11T15:57:43Z","abstract_excerpt":"In this article we analyze the structure of $2$-categories of symmetric projective bimodules over a finite dimensional algebra with respect to the action of a finite abelian group. We determine under which condition the resulting $2$-category is fiat (in the sense of \\cite{MM1}) and classify simple transitive $2$-representations of this $2$-category (under some mild technical assumption). We also study several classes of examples in detail."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1904.05798","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-04-11T15:57:43Z","cross_cats_sorted":[],"title_canon_sha256":"404ff2684b6e3ddefea782864747eb64596ea6cc4a8c543b44f768d39351daf9","abstract_canon_sha256":"3e4bcacf523255240034cc5323a82df4bc7312fbbf5ab1490b290609590287e8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:48.401219Z","signature_b64":"Nw2GTosNjzrdlMurLigfjaURVC6Y+ZuQnlBJrHAXQKPiYFAYpB5CHZw5upCvReVj9Kq/KaAiUnI5d7STYIwJAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1bb5287a5158038a1e0f0cd4aa53b1e4ce6d801b447ea699de65fc141e6dcca6","last_reissued_at":"2026-05-17T23:48:48.400751Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:48.400751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"2-categories of symmetric bimodules and their 2-representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Vanessa Miemietz, Volodymyr Mazorchuk, Xiaoting Zhang","submitted_at":"2019-04-11T15:57:43Z","abstract_excerpt":"In this article we analyze the structure of $2$-categories of symmetric projective bimodules over a finite dimensional algebra with respect to the action of a finite abelian group. We determine under which condition the resulting $2$-category is fiat (in the sense of \\cite{MM1}) and classify simple transitive $2$-representations of this $2$-category (under some mild technical assumption). We also study several classes of examples in detail."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.05798","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1904.05798","created_at":"2026-05-17T23:48:48.400826+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.05798v1","created_at":"2026-05-17T23:48:48.400826+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.05798","created_at":"2026-05-17T23:48:48.400826+00:00"},{"alias_kind":"pith_short_12","alias_value":"DO2SQ6SRLABY","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_16","alias_value":"DO2SQ6SRLABYUHQP","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_8","alias_value":"DO2SQ6SR","created_at":"2026-05-18T12:33:15.570797+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DO2SQ6SRLABYUHQPBTKKUU5R4T","json":"https://pith.science/pith/DO2SQ6SRLABYUHQPBTKKUU5R4T.json","graph_json":"https://pith.science/api/pith-number/DO2SQ6SRLABYUHQPBTKKUU5R4T/graph.json","events_json":"https://pith.science/api/pith-number/DO2SQ6SRLABYUHQPBTKKUU5R4T/events.json","paper":"https://pith.science/paper/DO2SQ6SR"},"agent_actions":{"view_html":"https://pith.science/pith/DO2SQ6SRLABYUHQPBTKKUU5R4T","download_json":"https://pith.science/pith/DO2SQ6SRLABYUHQPBTKKUU5R4T.json","view_paper":"https://pith.science/paper/DO2SQ6SR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.05798&json=true","fetch_graph":"https://pith.science/api/pith-number/DO2SQ6SRLABYUHQPBTKKUU5R4T/graph.json","fetch_events":"https://pith.science/api/pith-number/DO2SQ6SRLABYUHQPBTKKUU5R4T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DO2SQ6SRLABYUHQPBTKKUU5R4T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DO2SQ6SRLABYUHQPBTKKUU5R4T/action/storage_attestation","attest_author":"https://pith.science/pith/DO2SQ6SRLABYUHQPBTKKUU5R4T/action/author_attestation","sign_citation":"https://pith.science/pith/DO2SQ6SRLABYUHQPBTKKUU5R4T/action/citation_signature","submit_replication":"https://pith.science/pith/DO2SQ6SRLABYUHQPBTKKUU5R4T/action/replication_record"}},"created_at":"2026-05-17T23:48:48.400826+00:00","updated_at":"2026-05-17T23:48:48.400826+00:00"}