{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:L4JJSPV3PJL2EALEG6JSPOWHV7","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":"0abe2a52cd87579706e7e96a27d66e3e86aa1dace8fe36304e9d52810f7c1300","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-03-07T14:52:26Z","title_canon_sha256":"a9b28432321bf1dd0c10f5ea2439fe2407006e817e7500ff5d2618501acab993"},"schema_version":"1.0","source":{"id":"1803.02691","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.02691","created_at":"2026-05-18T00:05:50Z"},{"alias_kind":"arxiv_version","alias_value":"1803.02691v2","created_at":"2026-05-18T00:05:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.02691","created_at":"2026-05-18T00:05:50Z"},{"alias_kind":"pith_short_12","alias_value":"L4JJSPV3PJL2","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"L4JJSPV3PJL2EALE","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"L4JJSPV3","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:869c27c28023b614d02246ade58c26660ecb411680ddd4f86ed1355a3c65a853","target":"graph","created_at":"2026-05-18T00:05:50Z","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"},"paper":{"abstract_excerpt":"We introduce the bicategory of bialgebras with coverings (which can be thought of as coalgebra-indexed families of morphisms), and provide a motivating application to the transfer of formulas for primitives and antipode. Additionally, we study properties of this bicategory and various sub-bicategories, and describe some universal constructions. Finally, we generalize Nichols' result on bialgebra quotients of Hopf algebra, which gives conditions on when the resulting bialgebra quotient is a Hopf algebra.","authors_text":"Aaron Lauve, Mitja Mastnak","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-03-07T14:52:26Z","title":"Bialgebra Coverings and Transfer of Structure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02691","kind":"arxiv","version":2},"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:dba4a068355bef55289f2b4e0d9212d55c82eb0bd21fc64e077ba41573fd5a0a","target":"record","created_at":"2026-05-18T00:05:50Z","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":"0abe2a52cd87579706e7e96a27d66e3e86aa1dace8fe36304e9d52810f7c1300","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-03-07T14:52:26Z","title_canon_sha256":"a9b28432321bf1dd0c10f5ea2439fe2407006e817e7500ff5d2618501acab993"},"schema_version":"1.0","source":{"id":"1803.02691","kind":"arxiv","version":2}},"canonical_sha256":"5f12993ebb7a57a20164379327bac7aff343b099afa32d7b6a3055419736b23c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f12993ebb7a57a20164379327bac7aff343b099afa32d7b6a3055419736b23c","first_computed_at":"2026-05-18T00:05:50.922120Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:50.922120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pPjpYZqiBsiOHe+X2WQLn4aIcEBnooXFHSarjTyPbe3PL94YAwuk2bqqMqaxmDGGcCm+dz0nqyravzziPhV2Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:50.922752Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.02691","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dba4a068355bef55289f2b4e0d9212d55c82eb0bd21fc64e077ba41573fd5a0a","sha256:869c27c28023b614d02246ade58c26660ecb411680ddd4f86ed1355a3c65a853"],"state_sha256":"37d8cab4ad678855f90899a4e214cb322b523baa3b880a4df115c693ece2d28f"}