{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:Y43Q6ZAYP6BXDL2K75PUR443C4","short_pith_number":"pith:Y43Q6ZAY","canonical_record":{"source":{"id":"1605.02800","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-05-09T22:15:42Z","cross_cats_sorted":["math.DS","math.FA"],"title_canon_sha256":"1ff37f3ba6ce06d1f69bed2217f830143b1474f279bde083d0c7bb7bafd9e43c","abstract_canon_sha256":"546cba437e4a38f7ec43ea25131f44a1033897e8002a4d79c228de30f70c76a4"},"schema_version":"1.0"},"canonical_sha256":"c7370f64187f8371af4aff5f48f39b1720df3136e0cd043af77202e9cf352322","source":{"kind":"arxiv","id":"1605.02800","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.02800","created_at":"2026-05-18T00:45:49Z"},{"alias_kind":"arxiv_version","alias_value":"1605.02800v2","created_at":"2026-05-18T00:45:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.02800","created_at":"2026-05-18T00:45:49Z"},{"alias_kind":"pith_short_12","alias_value":"Y43Q6ZAYP6BX","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"Y43Q6ZAYP6BXDL2K","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"Y43Q6ZAY","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:Y43Q6ZAYP6BXDL2K75PUR443C4","target":"record","payload":{"canonical_record":{"source":{"id":"1605.02800","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-05-09T22:15:42Z","cross_cats_sorted":["math.DS","math.FA"],"title_canon_sha256":"1ff37f3ba6ce06d1f69bed2217f830143b1474f279bde083d0c7bb7bafd9e43c","abstract_canon_sha256":"546cba437e4a38f7ec43ea25131f44a1033897e8002a4d79c228de30f70c76a4"},"schema_version":"1.0"},"canonical_sha256":"c7370f64187f8371af4aff5f48f39b1720df3136e0cd043af77202e9cf352322","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:49.494857Z","signature_b64":"e2dGUwcuGxWPepw6clOEcE/Ei7lloVZfYUcTd0PQSx4S7mVn1Ay2AqutpIFM24YKbl8HGOnuODpu8KAtzh+tBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c7370f64187f8371af4aff5f48f39b1720df3136e0cd043af77202e9cf352322","last_reissued_at":"2026-05-18T00:45:49.494252Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:49.494252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.02800","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":"2026-05-18T00:45:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7c7wGipT0MFypItMZOTBIMyivIwSCHSdVSTdWf2wXcV0cDylt2OVuonHOMApTvQNxxbfKcAXyBnQMDv+Gq8xCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T09:52:28.786053Z"},"content_sha256":"14f4cae118c8d0bf8709e777bbc7bf097103e49ae4fde2a2c0695c403dc4e59f","schema_version":"1.0","event_id":"sha256:14f4cae118c8d0bf8709e777bbc7bf097103e49ae4fde2a2c0695c403dc4e59f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:Y43Q6ZAYP6BXDL2K75PUR443C4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Around Property (T) for quantum groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.FA"],"primary_cat":"math.OA","authors_text":"Adam Skalski, Ami Viselter, Matthew Daws","submitted_at":"2016-05-09T22:15:42Z","abstract_excerpt":"We study Property (T) for locally compact quantum groups, providing several new characterisations, especially related to operator algebraic ergodic theory. Quantum Property (T) is described in terms of the existence of various Kazhdan type pairs, and some earlier structural results of Kyed, Chen and Ng are strengthened and generalised. For second countable discrete unimodular quantum groups with low duals Property (T) is shown to be equivalent to Property (T)$^{1,1}$ of Bekka and Valette. This is used to extend to this class of quantum groups classical theorems on 'typical' representations (du"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02800","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":"2026-05-18T00:45:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K0qM67sOQIl9/TgHuKoCblI/QTZmPXJJjobJvzm60/Pu7Ntd2T77LlMcLecXV/Lzx/SGOm8FGVbZ1r+8JtpmCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T09:52:28.786415Z"},"content_sha256":"80bfd2aa623d7c041d36ca4a7752d43810513424d746aeadc99b0928307bedc8","schema_version":"1.0","event_id":"sha256:80bfd2aa623d7c041d36ca4a7752d43810513424d746aeadc99b0928307bedc8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y43Q6ZAYP6BXDL2K75PUR443C4/bundle.json","state_url":"https://pith.science/pith/Y43Q6ZAYP6BXDL2K75PUR443C4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y43Q6ZAYP6BXDL2K75PUR443C4/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":"2026-06-22T09:52:28Z","links":{"resolver":"https://pith.science/pith/Y43Q6ZAYP6BXDL2K75PUR443C4","bundle":"https://pith.science/pith/Y43Q6ZAYP6BXDL2K75PUR443C4/bundle.json","state":"https://pith.science/pith/Y43Q6ZAYP6BXDL2K75PUR443C4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y43Q6ZAYP6BXDL2K75PUR443C4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:Y43Q6ZAYP6BXDL2K75PUR443C4","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":"546cba437e4a38f7ec43ea25131f44a1033897e8002a4d79c228de30f70c76a4","cross_cats_sorted":["math.DS","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-05-09T22:15:42Z","title_canon_sha256":"1ff37f3ba6ce06d1f69bed2217f830143b1474f279bde083d0c7bb7bafd9e43c"},"schema_version":"1.0","source":{"id":"1605.02800","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.02800","created_at":"2026-05-18T00:45:49Z"},{"alias_kind":"arxiv_version","alias_value":"1605.02800v2","created_at":"2026-05-18T00:45:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.02800","created_at":"2026-05-18T00:45:49Z"},{"alias_kind":"pith_short_12","alias_value":"Y43Q6ZAYP6BX","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"Y43Q6ZAYP6BXDL2K","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"Y43Q6ZAY","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:80bfd2aa623d7c041d36ca4a7752d43810513424d746aeadc99b0928307bedc8","target":"graph","created_at":"2026-05-18T00:45:49Z","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 study Property (T) for locally compact quantum groups, providing several new characterisations, especially related to operator algebraic ergodic theory. Quantum Property (T) is described in terms of the existence of various Kazhdan type pairs, and some earlier structural results of Kyed, Chen and Ng are strengthened and generalised. For second countable discrete unimodular quantum groups with low duals Property (T) is shown to be equivalent to Property (T)$^{1,1}$ of Bekka and Valette. This is used to extend to this class of quantum groups classical theorems on 'typical' representations (du","authors_text":"Adam Skalski, Ami Viselter, Matthew Daws","cross_cats":["math.DS","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-05-09T22:15:42Z","title":"Around Property (T) for quantum groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02800","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":"sha256:14f4cae118c8d0bf8709e777bbc7bf097103e49ae4fde2a2c0695c403dc4e59f","target":"record","created_at":"2026-05-18T00:45:49Z","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":"546cba437e4a38f7ec43ea25131f44a1033897e8002a4d79c228de30f70c76a4","cross_cats_sorted":["math.DS","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-05-09T22:15:42Z","title_canon_sha256":"1ff37f3ba6ce06d1f69bed2217f830143b1474f279bde083d0c7bb7bafd9e43c"},"schema_version":"1.0","source":{"id":"1605.02800","kind":"arxiv","version":2}},"canonical_sha256":"c7370f64187f8371af4aff5f48f39b1720df3136e0cd043af77202e9cf352322","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c7370f64187f8371af4aff5f48f39b1720df3136e0cd043af77202e9cf352322","first_computed_at":"2026-05-18T00:45:49.494252Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:49.494252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e2dGUwcuGxWPepw6clOEcE/Ei7lloVZfYUcTd0PQSx4S7mVn1Ay2AqutpIFM24YKbl8HGOnuODpu8KAtzh+tBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:49.494857Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.02800","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:14f4cae118c8d0bf8709e777bbc7bf097103e49ae4fde2a2c0695c403dc4e59f","sha256:80bfd2aa623d7c041d36ca4a7752d43810513424d746aeadc99b0928307bedc8"],"state_sha256":"ca5a12e3e61331ce19a3f641ff2fdeb7a532c7187941d9124451b5fe7f31c831"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CELh/3GSVqfvgzauJrYqn99W92CwZOm992HqKmruI5zBokYawUY6k44NqetoBoYEK5FyNgBYCl3sSXCF5CCfDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T09:52:28.788337Z","bundle_sha256":"3f8e323f69382cfd975e1ea1bc5b42953559ac92ed4cc96ca351499ffc3cc4dd"}}