{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:WQNNO4CWW46TJ46ISC6FUHVOQ4","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":"d586f5928077693757f0a43d94e0eb499686ca32c35f7ede8150b4a414f4edd1","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2026-06-01T10:36:38Z","title_canon_sha256":"c0d309398bddced40963d75a5c6450c24ca102691ce99bdb38c97c90024ecb08"},"schema_version":"1.0","source":{"id":"2606.02046","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.02046","created_at":"2026-06-02T02:05:04Z"},{"alias_kind":"arxiv_version","alias_value":"2606.02046v1","created_at":"2026-06-02T02:05:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.02046","created_at":"2026-06-02T02:05:04Z"},{"alias_kind":"pith_short_12","alias_value":"WQNNO4CWW46T","created_at":"2026-06-02T02:05:04Z"},{"alias_kind":"pith_short_16","alias_value":"WQNNO4CWW46TJ46I","created_at":"2026-06-02T02:05:04Z"},{"alias_kind":"pith_short_8","alias_value":"WQNNO4CW","created_at":"2026-06-02T02:05:04Z"}],"graph_snapshots":[{"event_id":"sha256:5890ac18856af6a669ea06c2a3071aa6990eae6f3be2334b59c033d703060096","target":"graph","created_at":"2026-06-02T02:05:04Z","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/2606.02046/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We explicitly construct dual bimodules in a semistrict monoidal 2-category, using Frobenius algebra structure. The main result shows that a coherent dual of the underlying object can be promoted to a coherent dual of the bimodule, with zigzag 2-isomorphisms additionally require special Frobenius structures. We also prove that every special Frobenius algebra in $\\mathbf{2Vect}$ is rigid, via a categorified Casimir object argument, and discuss the relationship between the Frobenius, rigid, special Frobenius, and separable algebra hierarchies.","authors_text":"Hao Xu","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2026-06-01T10:36:38Z","title":"Frobenius Algebras and Dual Bimodules in Monoidal 2-Categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02046","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":"sha256:420b65e6837975d0e88a75ccd5ff80d39bfb0b986b0bdcdf7b3846b22ef71815","target":"record","created_at":"2026-06-02T02:05:04Z","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":"d586f5928077693757f0a43d94e0eb499686ca32c35f7ede8150b4a414f4edd1","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2026-06-01T10:36:38Z","title_canon_sha256":"c0d309398bddced40963d75a5c6450c24ca102691ce99bdb38c97c90024ecb08"},"schema_version":"1.0","source":{"id":"2606.02046","kind":"arxiv","version":1}},"canonical_sha256":"b41ad77056b73d34f3c890bc5a1eae87366b2a01d64a94428fa602c67220129c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b41ad77056b73d34f3c890bc5a1eae87366b2a01d64a94428fa602c67220129c","first_computed_at":"2026-06-02T02:05:04.421734Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T02:05:04.421734Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yrlvaK3Vz6JeMHkmkoaU311VP2FwkoBZDg5d4Dn81vPQdGrbf+9gFcf6Uqn5xCPjUNUWTG6fomvPdk6cnClpBg==","signature_status":"signed_v1","signed_at":"2026-06-02T02:05:04.422139Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.02046","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:420b65e6837975d0e88a75ccd5ff80d39bfb0b986b0bdcdf7b3846b22ef71815","sha256:5890ac18856af6a669ea06c2a3071aa6990eae6f3be2334b59c033d703060096"],"state_sha256":"5f1a6b09bb0b63b71632427ae0fefb2f112566a4cc4c0e60518e4da02aaeeb44"}