{"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"}