{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:TS2WULQUGUAHQMCV7RTVEZPTK3","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":"9e2f768a48019d6517f52c6138dfb1ce124a1f952d3bc802bffc97f557a1f1fa","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-03-20T20:07:18Z","title_canon_sha256":"661577447f2da364661a1a4c70ea9d65b944a53abe923a8e2cadd9a3646acaa0"},"schema_version":"1.0","source":{"id":"1403.5282","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.5282","created_at":"2026-05-18T02:55:56Z"},{"alias_kind":"arxiv_version","alias_value":"1403.5282v1","created_at":"2026-05-18T02:55:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5282","created_at":"2026-05-18T02:55:56Z"},{"alias_kind":"pith_short_12","alias_value":"TS2WULQUGUAH","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"TS2WULQUGUAHQMCV","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"TS2WULQU","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:e4410ad044eb403a8a62a04ce0c5e333c55a6e63833c8df748cecd310aa2b223","target":"graph","created_at":"2026-05-18T02:55:56Z","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":"A fundamental feature of quantum groups is that many come in pairs of mutually dual objects, like finite-dimensional Hopf algebras and their duals, or quantisations of function algebras and of universal enveloping algebras of Poisson-Lie groups. The same phenomenon was studied for quantum groupoids in various settings. In the purely algebraic setup, the construction of a dual object was given by Schauenburg and by Kadison and Szlach\\'anyi, but required the quantum groupoid to be finite with respect to the base. A sophisticated duality for measured quantum groupoids was developed by Enock, Lesi","authors_text":"Thomas Timmermann","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-03-20T20:07:18Z","title":"Regular multiplier Hopf algebroids II. Integration on and duality of algebraic quantum groupoids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5282","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":"sha256:81deaa43819c98e8f691d4dc50674c9b675a1149bfce2a4354858d447f4278f9","target":"record","created_at":"2026-05-18T02:55:56Z","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":"9e2f768a48019d6517f52c6138dfb1ce124a1f952d3bc802bffc97f557a1f1fa","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-03-20T20:07:18Z","title_canon_sha256":"661577447f2da364661a1a4c70ea9d65b944a53abe923a8e2cadd9a3646acaa0"},"schema_version":"1.0","source":{"id":"1403.5282","kind":"arxiv","version":1}},"canonical_sha256":"9cb56a2e143500783055fc675265f356e15f7fac0573804a886287a3a0edc358","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9cb56a2e143500783055fc675265f356e15f7fac0573804a886287a3a0edc358","first_computed_at":"2026-05-18T02:55:56.761534Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:56.761534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mwoOUgtJP3UT8D2XsM5NSMTvO6EgbXWhlUxmoxFD84E1MrHNlJE/Tka/PxQwV0IeV/+eaLx/fiJjK1VzZqR8CA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:56.762102Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.5282","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81deaa43819c98e8f691d4dc50674c9b675a1149bfce2a4354858d447f4278f9","sha256:e4410ad044eb403a8a62a04ce0c5e333c55a6e63833c8df748cecd310aa2b223"],"state_sha256":"2d63841d6f00b5348b23dfd125e9414b2a56b8b34d20697b3dd04ab97b949fc0"}