{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:E73EOAKSLJGC7TK2E3HI55XIIJ","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":"322767513f3a868edbef5f44488f371daf62f6c189273529f933ca024fc67baf","cross_cats_sorted":["math-ph","math.CT","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2022-11-03T16:34:01Z","title_canon_sha256":"3bf9b3c2cd2bbc619a7bac79ad6718581611a964e005954e43d8b38f16202dfe"},"schema_version":"1.0","source":{"id":"2211.01947","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.01947","created_at":"2026-07-05T07:40:50Z"},{"alias_kind":"arxiv_version","alias_value":"2211.01947v1","created_at":"2026-07-05T07:40:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.01947","created_at":"2026-07-05T07:40:50Z"},{"alias_kind":"pith_short_12","alias_value":"E73EOAKSLJGC","created_at":"2026-07-05T07:40:50Z"},{"alias_kind":"pith_short_16","alias_value":"E73EOAKSLJGC7TK2","created_at":"2026-07-05T07:40:50Z"},{"alias_kind":"pith_short_8","alias_value":"E73EOAKS","created_at":"2026-07-05T07:40:50Z"}],"graph_snapshots":[{"event_id":"sha256:67cb5c652cd654c8127846be98501e1b2ade472174f21cc0afcfbe18f4d57dd1","target":"graph","created_at":"2026-07-05T07:40:50Z","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/2211.01947/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Schur orthogonality relations are a cornerstone in the representation theory of groups. We utilize a generalization to weak Hopf algebras to provide a new, readily verifiable condition on the skeletal data for deciding whether a given bimodule category is invertible and therefore defines a Morita equivalence. As a first application, we provide an algorithm for the construction of the full skeletal data of the invertible bimodule category associated to a given module category, which is obtained in a unitary gauge when the underlying categories are unitary. As a second application, we show t","authors_text":"Frank Verstraete, Jacob C. Bridgeman, Laurens Lootens","cross_cats":["math-ph","math.CT","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2022-11-03T16:34:01Z","title":"Invertible bimodule categories and generalized Schur orthogonality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.01947","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":"sha256:2b7ffe479d9c7e569cef2cf68f1347e8fce30ef2a4f84646cd78b28efd71f61d","target":"record","created_at":"2026-07-05T07:40:50Z","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":"322767513f3a868edbef5f44488f371daf62f6c189273529f933ca024fc67baf","cross_cats_sorted":["math-ph","math.CT","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2022-11-03T16:34:01Z","title_canon_sha256":"3bf9b3c2cd2bbc619a7bac79ad6718581611a964e005954e43d8b38f16202dfe"},"schema_version":"1.0","source":{"id":"2211.01947","kind":"arxiv","version":1}},"canonical_sha256":"27f64701525a4c2fcd5a26ce8ef6e842424703873e234957c2193b34b0e2c189","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27f64701525a4c2fcd5a26ce8ef6e842424703873e234957c2193b34b0e2c189","first_computed_at":"2026-07-05T07:40:50.242417Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:40:50.242417Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QgSxlqFP9e911R+ZxlunE33WvZwyFh5cWlPLQyyGuXmAkg6UADWFtR4pPfTclqFiOpAIjNu9li/H7B0X36WBBw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:40:50.242915Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.01947","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b7ffe479d9c7e569cef2cf68f1347e8fce30ef2a4f84646cd78b28efd71f61d","sha256:67cb5c652cd654c8127846be98501e1b2ade472174f21cc0afcfbe18f4d57dd1"],"state_sha256":"502165fb9b8a1ba88b38ffd61e29e70d8b5857de30284ffe14cb1064d9fb8ff4"}