{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:ZAMLJVO64XNCTRLJUONJSHCCEQ","short_pith_number":"pith:ZAMLJVO6","schema_version":"1.0","canonical_sha256":"c818b4d5dee5da29c569a39a991c422403f64c17e6c457175868f1235ec4f2f6","source":{"kind":"arxiv","id":"1307.2475","version":3},"attestation_state":"computed","paper":{"title":"Towards Strong Banach property (T) for SL(3,R)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.MG"],"primary_cat":"math.GR","authors_text":"Mikael de la Salle","submitted_at":"2013-07-09T14:34:30Z","abstract_excerpt":"We prove that SL(3,R) has Strong Banach property (T) in Lafforgue's sense with respect to the Banach spaces that are $\\theta>0$ interpolation spaces (for the complex interpolation method) between an arbitrary Banach space and a Banach space with sufficiently good type and cotype. As a consequence, every action of SL(3,R) or its lattices by affine isometries on such a Banach space X has a fixed point, and the expanders contructed from SL(3,Z) do not admit a coarse embedding into X. We also prove a quantitative decay of matrix coefficients (Howe-Moore property) for representations with small exp"},"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":"1307.2475","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-07-09T14:34:30Z","cross_cats_sorted":["math.FA","math.MG"],"title_canon_sha256":"7b169d5c4fc3224cead32094df3ab6888e49201488d2115357e58660b0e4ec6a","abstract_canon_sha256":"29329db9c12b14f8a9edb967a93bfe62a2797b9f8a05073d1b4645dc65422497"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:44.443093Z","signature_b64":"j+SJDWWrIdPdAn43EKy6cyrK38tunGF62micdV/JvIwgS4zmtS1KdFbcKj5UXYO6jSgSbr8fY3ilpGFeIqSHDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c818b4d5dee5da29c569a39a991c422403f64c17e6c457175868f1235ec4f2f6","last_reissued_at":"2026-05-18T00:33:44.442644Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:44.442644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Towards Strong Banach property (T) for SL(3,R)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.MG"],"primary_cat":"math.GR","authors_text":"Mikael de la Salle","submitted_at":"2013-07-09T14:34:30Z","abstract_excerpt":"We prove that SL(3,R) has Strong Banach property (T) in Lafforgue's sense with respect to the Banach spaces that are $\\theta>0$ interpolation spaces (for the complex interpolation method) between an arbitrary Banach space and a Banach space with sufficiently good type and cotype. As a consequence, every action of SL(3,R) or its lattices by affine isometries on such a Banach space X has a fixed point, and the expanders contructed from SL(3,Z) do not admit a coarse embedding into X. We also prove a quantitative decay of matrix coefficients (Howe-Moore property) for representations with small exp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2475","kind":"arxiv","version":3},"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":"1307.2475","created_at":"2026-05-18T00:33:44.442710+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.2475v3","created_at":"2026-05-18T00:33:44.442710+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.2475","created_at":"2026-05-18T00:33:44.442710+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZAMLJVO64XNC","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZAMLJVO64XNCTRLJ","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZAMLJVO6","created_at":"2026-05-18T12:28:09.283467+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/ZAMLJVO64XNCTRLJUONJSHCCEQ","json":"https://pith.science/pith/ZAMLJVO64XNCTRLJUONJSHCCEQ.json","graph_json":"https://pith.science/api/pith-number/ZAMLJVO64XNCTRLJUONJSHCCEQ/graph.json","events_json":"https://pith.science/api/pith-number/ZAMLJVO64XNCTRLJUONJSHCCEQ/events.json","paper":"https://pith.science/paper/ZAMLJVO6"},"agent_actions":{"view_html":"https://pith.science/pith/ZAMLJVO64XNCTRLJUONJSHCCEQ","download_json":"https://pith.science/pith/ZAMLJVO64XNCTRLJUONJSHCCEQ.json","view_paper":"https://pith.science/paper/ZAMLJVO6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.2475&json=true","fetch_graph":"https://pith.science/api/pith-number/ZAMLJVO64XNCTRLJUONJSHCCEQ/graph.json","fetch_events":"https://pith.science/api/pith-number/ZAMLJVO64XNCTRLJUONJSHCCEQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZAMLJVO64XNCTRLJUONJSHCCEQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZAMLJVO64XNCTRLJUONJSHCCEQ/action/storage_attestation","attest_author":"https://pith.science/pith/ZAMLJVO64XNCTRLJUONJSHCCEQ/action/author_attestation","sign_citation":"https://pith.science/pith/ZAMLJVO64XNCTRLJUONJSHCCEQ/action/citation_signature","submit_replication":"https://pith.science/pith/ZAMLJVO64XNCTRLJUONJSHCCEQ/action/replication_record"}},"created_at":"2026-05-18T00:33:44.442710+00:00","updated_at":"2026-05-18T00:33:44.442710+00:00"}