{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:PHMESENE6BIMOVL46FWUR3M33W","short_pith_number":"pith:PHMESENE","schema_version":"1.0","canonical_sha256":"79d84911a4f050c7557cf16d48ed9bdd9a25c5580222a7967cad4edaff7f8e1f","source":{"kind":"arxiv","id":"1303.5183","version":1},"attestation_state":"computed","paper":{"title":"On groups with Property (T_lp)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Bachir Bekka, Baptiste Olivier","submitted_at":"2013-03-21T07:38:47Z","abstract_excerpt":"Let p be a real number with 1<p and different from 2. We study Property (T_lp) for a second countable locally compact group G. Property (T_lp) is a weak version of Kazhdan's Property (T), defined in terms of the orthogonal representations of G on the sequence space lp. We show that Property (T_lp) for a totally disconnected group G is characterized by an isolation property of the trivial representation from the quasi-regular representations associated to open subgroups of G. Groups with Property (T_lp) share some important properties with Kazhdan groups (compact generation, compact abelianizat"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1303.5183","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-03-21T07:38:47Z","cross_cats_sorted":[],"title_canon_sha256":"59227bd84e243f7ae262d7837f36ccf7543467158c2575a36b1530b4cb6ccf74","abstract_canon_sha256":"12a3d210c110ebde326b174e2320a33e4823bceff854d3cb45df2847ff04ceef"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:05.597673Z","signature_b64":"iUcQ/nn2tPq1nai1u0vQnv9GgaWTPpJcMwshSqquC+5u0XvYyJcBhvsq1CpTTF/hQZj4uUBMgqcd2TDgMx9HBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"79d84911a4f050c7557cf16d48ed9bdd9a25c5580222a7967cad4edaff7f8e1f","last_reissued_at":"2026-05-18T02:28:05.597187Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:05.597187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On groups with Property (T_lp)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Bachir Bekka, Baptiste Olivier","submitted_at":"2013-03-21T07:38:47Z","abstract_excerpt":"Let p be a real number with 1<p and different from 2. We study Property (T_lp) for a second countable locally compact group G. Property (T_lp) is a weak version of Kazhdan's Property (T), defined in terms of the orthogonal representations of G on the sequence space lp. We show that Property (T_lp) for a totally disconnected group G is characterized by an isolation property of the trivial representation from the quasi-regular representations associated to open subgroups of G. Groups with Property (T_lp) share some important properties with Kazhdan groups (compact generation, compact abelianizat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5183","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1303.5183","created_at":"2026-05-18T02:28:05.597252+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.5183v1","created_at":"2026-05-18T02:28:05.597252+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.5183","created_at":"2026-05-18T02:28:05.597252+00:00"},{"alias_kind":"pith_short_12","alias_value":"PHMESENE6BIM","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"PHMESENE6BIMOVL4","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"PHMESENE","created_at":"2026-05-18T12:27:54.935989+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PHMESENE6BIMOVL46FWUR3M33W","json":"https://pith.science/pith/PHMESENE6BIMOVL46FWUR3M33W.json","graph_json":"https://pith.science/api/pith-number/PHMESENE6BIMOVL46FWUR3M33W/graph.json","events_json":"https://pith.science/api/pith-number/PHMESENE6BIMOVL46FWUR3M33W/events.json","paper":"https://pith.science/paper/PHMESENE"},"agent_actions":{"view_html":"https://pith.science/pith/PHMESENE6BIMOVL46FWUR3M33W","download_json":"https://pith.science/pith/PHMESENE6BIMOVL46FWUR3M33W.json","view_paper":"https://pith.science/paper/PHMESENE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.5183&json=true","fetch_graph":"https://pith.science/api/pith-number/PHMESENE6BIMOVL46FWUR3M33W/graph.json","fetch_events":"https://pith.science/api/pith-number/PHMESENE6BIMOVL46FWUR3M33W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PHMESENE6BIMOVL46FWUR3M33W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PHMESENE6BIMOVL46FWUR3M33W/action/storage_attestation","attest_author":"https://pith.science/pith/PHMESENE6BIMOVL46FWUR3M33W/action/author_attestation","sign_citation":"https://pith.science/pith/PHMESENE6BIMOVL46FWUR3M33W/action/citation_signature","submit_replication":"https://pith.science/pith/PHMESENE6BIMOVL46FWUR3M33W/action/replication_record"}},"created_at":"2026-05-18T02:28:05.597252+00:00","updated_at":"2026-05-18T02:28:05.597252+00:00"}