{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JYBO2LX3LBWJV2XB6KMX2BY2A5","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":"14fa16ddf071ce74d4841d9e1a5dd6c73216a5632180f2dc5e3e5ef1f82ed688","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-11-13T06:42:01Z","title_canon_sha256":"15d7aee4e8508b520a5af854f3ef37fd3142c10ea25176dfea60f5545aa676bd"},"schema_version":"1.0","source":{"id":"1311.3027","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.3027","created_at":"2026-05-18T03:07:13Z"},{"alias_kind":"arxiv_version","alias_value":"1311.3027v1","created_at":"2026-05-18T03:07:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.3027","created_at":"2026-05-18T03:07:13Z"},{"alias_kind":"pith_short_12","alias_value":"JYBO2LX3LBWJ","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JYBO2LX3LBWJV2XB","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JYBO2LX3","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:8dada57086aa82de7718999ac6cdf3f85810a8a15eff484e6a776e5b754bbebc","target":"graph","created_at":"2026-05-18T03:07:13Z","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 continue the study of the representation theory of a regular weak multiplier bialgebra with full comultiplication, started in arXiv:1306.1466, arXiv:1311.2730. Yetter-Drinfeld modules are defined as modules and comodules, with compatibility conditions that are equivalent to a canonical object being (weakly) central in the category of modules, and equivalent also to another canonical object being (weakly) central in the category of comodules. Yetter-Drinfeld modules are shown to constitute a monoidal category via the (co)module tensor product over the base (co)algebra. Finite dimensional Yet","authors_text":"Gabriella B\\\"ohm","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-11-13T06:42:01Z","title":"Yetter-Drinfeld modules over weak multiplier bialgebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3027","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:f718d9a7dc91bde33034bb3887f11255a4f962c65aa9737f966fdeb87f65249b","target":"record","created_at":"2026-05-18T03:07:13Z","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":"14fa16ddf071ce74d4841d9e1a5dd6c73216a5632180f2dc5e3e5ef1f82ed688","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-11-13T06:42:01Z","title_canon_sha256":"15d7aee4e8508b520a5af854f3ef37fd3142c10ea25176dfea60f5545aa676bd"},"schema_version":"1.0","source":{"id":"1311.3027","kind":"arxiv","version":1}},"canonical_sha256":"4e02ed2efb586c9aeae1f2997d071a0743d6ad775a4e465a71c1736ae0a3318a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e02ed2efb586c9aeae1f2997d071a0743d6ad775a4e465a71c1736ae0a3318a","first_computed_at":"2026-05-18T03:07:13.354561Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:13.354561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oR2VjsIMnr+pxrxklwrQp6MzoGlaod61tmL2Q8vEgl8f0kTZdL3xbb5jEbPw6RUv0fUujP4WmZ1Z8fbmfp85AA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:13.355061Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.3027","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f718d9a7dc91bde33034bb3887f11255a4f962c65aa9737f966fdeb87f65249b","sha256:8dada57086aa82de7718999ac6cdf3f85810a8a15eff484e6a776e5b754bbebc"],"state_sha256":"fce88af42ef2de1e88c13d17d2e298a624afc9b9a226d2ca0c9eed8e428dc96a"}