{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BOMKU7LTN2AKU4XC6QBW6LSJOL","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":"f29591a1152f14da24ae36b089445b9441454c923889a3c765c59b0f0d92882d","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-07-27T20:36:17Z","title_canon_sha256":"273bd29c887cb292fd720c5517a816746108c9cbba1d73ed9d9f897099a92ed8"},"schema_version":"1.0","source":{"id":"1307.7304","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.7304","created_at":"2026-05-18T03:17:23Z"},{"alias_kind":"arxiv_version","alias_value":"1307.7304v1","created_at":"2026-05-18T03:17:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.7304","created_at":"2026-05-18T03:17:23Z"},{"alias_kind":"pith_short_12","alias_value":"BOMKU7LTN2AK","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BOMKU7LTN2AKU4XC","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BOMKU7LT","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:a1a2613e5fd21c1e8f7103ed40abfeaaa320c9f7b7e7882384e7174de81eafbf","target":"graph","created_at":"2026-05-18T03:17:23Z","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 consider Frobenius algebras in the monoidal category of right comodules over a Hopf algebra $H$. If $H$ is a group Hopf algebra, we study a more general Frobenius type property and uncover the structure of graded Frobenius algebras. Graded symmetric algebras are also investigated.","authors_text":"Constantin Nastasescu, Laura Nastasescu, Sorin Dascalescu","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-07-27T20:36:17Z","title":"Frobenius algebras of corepresentations: gradings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7304","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":"sha256:31e3e8faaa8147998d31c1466a10ef8cda1b9650340b16fbd4474b980b9ff41a","target":"record","created_at":"2026-05-18T03:17:23Z","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":"f29591a1152f14da24ae36b089445b9441454c923889a3c765c59b0f0d92882d","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-07-27T20:36:17Z","title_canon_sha256":"273bd29c887cb292fd720c5517a816746108c9cbba1d73ed9d9f897099a92ed8"},"schema_version":"1.0","source":{"id":"1307.7304","kind":"arxiv","version":1}},"canonical_sha256":"0b98aa7d736e80aa72e2f4036f2e4972e6ed475812fe0343888aad42968980be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b98aa7d736e80aa72e2f4036f2e4972e6ed475812fe0343888aad42968980be","first_computed_at":"2026-05-18T03:17:23.627253Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:23.627253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w8TBr4Yu5Y0UBJtnAaq88nCucUcOMJpKtMLFKsAVyqv/boFTrZYHQg8yaj+DaULIWIv9Y2ZlTH4cxqqACTZqCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:23.628003Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.7304","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31e3e8faaa8147998d31c1466a10ef8cda1b9650340b16fbd4474b980b9ff41a","sha256:a1a2613e5fd21c1e8f7103ed40abfeaaa320c9f7b7e7882384e7174de81eafbf"],"state_sha256":"3ecbbe33ca69c63acd0df47652af5d21d73ba37bb689c6fa8cca36b75712bf39"}