{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VNWKWKOIAXAATV4Y7N7ALKBXLM","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":"8232eec4ee4ac735e55fa47d6b630d28ca68e2dcf1be5a1a5569c072bf4ed8d6","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-02-28T15:39:03Z","title_canon_sha256":"793b89f3715537ca897d441fc5af561eb8a7330bb3033c3daabedf3814953137"},"schema_version":"1.0","source":{"id":"1602.08731","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.08731","created_at":"2026-05-18T01:19:52Z"},{"alias_kind":"arxiv_version","alias_value":"1602.08731v1","created_at":"2026-05-18T01:19:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.08731","created_at":"2026-05-18T01:19:52Z"},{"alias_kind":"pith_short_12","alias_value":"VNWKWKOIAXAA","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VNWKWKOIAXAATV4Y","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VNWKWKOI","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:ff8ecee4bb31c5edd628914e33840be8ca3a6d56598bd501de13071631e285ef","target":"graph","created_at":"2026-05-18T01:19:52Z","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":"The aim of this paper is to define and study Yetter-Drinfeld modules over weak Hom-Hopf algebras. We show that the category ${}_H{\\cal WYD}^H$ of Yetter-Drinfeld modules with bijective structure maps over weak Hom-Hopf algebras is a rigid category and a braided monoidal category, and obtain a new solution of quantum Hom-Yang-Baxter equation. It turns out that, If $H$ is quasitriangular (respectively, coquasitriangular)weak Hom-Hopf algebras, the category of modules (respectively, comodules) with bijective structure maps over $H$ is a braided monoidal subcategory of the category ${}_H{\\cal WYD}","authors_text":"Shengxiang Wang, Shuangjian Guo, Yizheng Li","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-02-28T15:39:03Z","title":"Yetter-Drinfeld modules for weak Hom-Hopf algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.08731","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:dfb552f3f37f69670d4d8763499828f63318904e8c6e597b9eda16946c9ebbc1","target":"record","created_at":"2026-05-18T01:19:52Z","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":"8232eec4ee4ac735e55fa47d6b630d28ca68e2dcf1be5a1a5569c072bf4ed8d6","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-02-28T15:39:03Z","title_canon_sha256":"793b89f3715537ca897d441fc5af561eb8a7330bb3033c3daabedf3814953137"},"schema_version":"1.0","source":{"id":"1602.08731","kind":"arxiv","version":1}},"canonical_sha256":"ab6cab29c805c009d798fb7e05a8375b1ecd719947c195cbbbfc675919508bd3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab6cab29c805c009d798fb7e05a8375b1ecd719947c195cbbbfc675919508bd3","first_computed_at":"2026-05-18T01:19:52.064473Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:52.064473Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cumWVfwv+wcmnJA/KX1fXL4BtbXu1szEXvGEe8lKM6GZ45VmRWcUmnv2JTVKiavImW9zzTBwzlOFEL1oyZyEBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:52.065154Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.08731","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dfb552f3f37f69670d4d8763499828f63318904e8c6e597b9eda16946c9ebbc1","sha256:ff8ecee4bb31c5edd628914e33840be8ca3a6d56598bd501de13071631e285ef"],"state_sha256":"05c299d7d4a0d3fdc8e2b881b137abb2928eed873dcc132559c78393687d9836"}