{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3AHU37KQ5EY7XM3GCZWSEWDY4U","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":"3c555560345ae4cb162c234e72b3eb06d3a4a72b1b1783c27cde8e326cb29fe1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-09-06T11:20:24Z","title_canon_sha256":"21292b0110d2e4ce075c61c465d19b5fd2ceb82609fed36076dc0db77a40972b"},"schema_version":"1.0","source":{"id":"1709.01770","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.01770","created_at":"2026-05-18T00:15:10Z"},{"alias_kind":"arxiv_version","alias_value":"1709.01770v2","created_at":"2026-05-18T00:15:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.01770","created_at":"2026-05-18T00:15:10Z"},{"alias_kind":"pith_short_12","alias_value":"3AHU37KQ5EY7","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3AHU37KQ5EY7XM3G","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3AHU37KQ","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:1a34a4e35ca44f02f6d9230168b2b394541a2495edc7dfbeb11f96cfcd096057","target":"graph","created_at":"2026-05-18T00:15:10Z","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 an appropriate notion of inner amenability for locally compact quantum groups, study its basic properties, related notions, and examples arising from the bicrossed product construction. We relate these notions to homological properties of the dual quantum group, which allow us to generalize a well-known result of Lau--Paterson, resolve a recent conjecture of Ng--Viselter, and prove that, for inner amenable quantum groups $\\mathbb{G}$, approximation properties of the dual operator algebras can be averaged to approximation properties $\\mathbb{G}$. Similar homological techniques are ","authors_text":"Jason Crann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-09-06T11:20:24Z","title":"Inner amenability and approximation properties of locally compact quantum groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01770","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":"sha256:748718c0d8bdccd0c66ffe79bc22ed138342834ba6eb92ccfaeb0f9edfe5697d","target":"record","created_at":"2026-05-18T00:15:10Z","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":"3c555560345ae4cb162c234e72b3eb06d3a4a72b1b1783c27cde8e326cb29fe1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-09-06T11:20:24Z","title_canon_sha256":"21292b0110d2e4ce075c61c465d19b5fd2ceb82609fed36076dc0db77a40972b"},"schema_version":"1.0","source":{"id":"1709.01770","kind":"arxiv","version":2}},"canonical_sha256":"d80f4dfd50e931fbb366166d225878e53be2058df9efcba3f2e4282e56a87a0b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d80f4dfd50e931fbb366166d225878e53be2058df9efcba3f2e4282e56a87a0b","first_computed_at":"2026-05-18T00:15:10.211938Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:10.211938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1UkJrHp1JcSEhTLJ0pN4l+oLkfgfZF5URYyqouippiR9J8KqL/m7C2McvaixdybeAVq70mL4gs0pMfQDvCAJDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:10.212822Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.01770","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:748718c0d8bdccd0c66ffe79bc22ed138342834ba6eb92ccfaeb0f9edfe5697d","sha256:1a34a4e35ca44f02f6d9230168b2b394541a2495edc7dfbeb11f96cfcd096057"],"state_sha256":"915b3a56932fda939730a1182bf7269d7b863260230716b8a0f051e45ae7ce0a"}