{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:3AHU37KQ5EY7XM3GCZWSEWDY4U","short_pith_number":"pith:3AHU37KQ","canonical_record":{"source":{"id":"1709.01770","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-09-06T11:20:24Z","cross_cats_sorted":[],"title_canon_sha256":"21292b0110d2e4ce075c61c465d19b5fd2ceb82609fed36076dc0db77a40972b","abstract_canon_sha256":"3c555560345ae4cb162c234e72b3eb06d3a4a72b1b1783c27cde8e326cb29fe1"},"schema_version":"1.0"},"canonical_sha256":"d80f4dfd50e931fbb366166d225878e53be2058df9efcba3f2e4282e56a87a0b","source":{"kind":"arxiv","id":"1709.01770","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:3AHU37KQ5EY7XM3GCZWSEWDY4U","target":"record","payload":{"canonical_record":{"source":{"id":"1709.01770","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-09-06T11:20:24Z","cross_cats_sorted":[],"title_canon_sha256":"21292b0110d2e4ce075c61c465d19b5fd2ceb82609fed36076dc0db77a40972b","abstract_canon_sha256":"3c555560345ae4cb162c234e72b3eb06d3a4a72b1b1783c27cde8e326cb29fe1"},"schema_version":"1.0"},"canonical_sha256":"d80f4dfd50e931fbb366166d225878e53be2058df9efcba3f2e4282e56a87a0b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:10.212822Z","signature_b64":"1UkJrHp1JcSEhTLJ0pN4l+oLkfgfZF5URYyqouippiR9J8KqL/m7C2McvaixdybeAVq70mL4gs0pMfQDvCAJDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d80f4dfd50e931fbb366166d225878e53be2058df9efcba3f2e4282e56a87a0b","last_reissued_at":"2026-05-18T00:15:10.211938Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:10.211938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.01770","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:15:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7ZhakdtnOO1ShouXWxRe7p94f7PA7QjY/EqxcMO42keURNDWW42acZOQgqEb9jpW49FOfoBDimufxEHWLf/6DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T11:17:12.237662Z"},"content_sha256":"748718c0d8bdccd0c66ffe79bc22ed138342834ba6eb92ccfaeb0f9edfe5697d","schema_version":"1.0","event_id":"sha256:748718c0d8bdccd0c66ffe79bc22ed138342834ba6eb92ccfaeb0f9edfe5697d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:3AHU37KQ5EY7XM3GCZWSEWDY4U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Inner amenability and approximation properties of locally compact quantum groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Jason Crann","submitted_at":"2017-09-06T11:20:24Z","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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01770","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:15:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QRNHxrRI404yAck+fsxdkioBNbq1TqX4fXm9roBKlYuLT3Su+EEAuOqCcfHUJtzOw13JrkrQhq06+PRyO/7yDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T11:17:12.238030Z"},"content_sha256":"1a34a4e35ca44f02f6d9230168b2b394541a2495edc7dfbeb11f96cfcd096057","schema_version":"1.0","event_id":"sha256:1a34a4e35ca44f02f6d9230168b2b394541a2495edc7dfbeb11f96cfcd096057"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3AHU37KQ5EY7XM3GCZWSEWDY4U/bundle.json","state_url":"https://pith.science/pith/3AHU37KQ5EY7XM3GCZWSEWDY4U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3AHU37KQ5EY7XM3GCZWSEWDY4U/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-23T11:17:12Z","links":{"resolver":"https://pith.science/pith/3AHU37KQ5EY7XM3GCZWSEWDY4U","bundle":"https://pith.science/pith/3AHU37KQ5EY7XM3GCZWSEWDY4U/bundle.json","state":"https://pith.science/pith/3AHU37KQ5EY7XM3GCZWSEWDY4U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3AHU37KQ5EY7XM3GCZWSEWDY4U/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UCU07gAfw8voZJpbJXJGGL05OhUiAZsCsBSyteWlpOSKnT2Hi53cKki4KW6EEAAMdNNzCJSqGmXfsoKRsZSqDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T11:17:12.240070Z","bundle_sha256":"6c5ef5005869baffa25e016eddbd28d07b0f98cf143c0fd516c3a048108b0a26"}}