{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:3AAMLCDFNBEQ3T3CWAMKNQ2ZOS","short_pith_number":"pith:3AAMLCDF","schema_version":"1.0","canonical_sha256":"d800c5886568490dcf62b018a6c35974ac55ec6e4e9a988033f7e57fa906a26c","source":{"kind":"arxiv","id":"1402.1481","version":3},"attestation_state":"computed","paper":{"title":"Relative expanders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.MG"],"primary_cat":"math.GR","authors_text":"Goulnara Arzhantseva, Romain Tessera","submitted_at":"2014-02-06T20:46:54Z","abstract_excerpt":"We exhibit a finitely generated group $G$ and a sequence of finite index normal subgroups $N_n\\trianglelefteq G$ such that for every finite generating subset $S\\subseteq G$, the sequence of finite Cayley graphs $(G/N_n, S)$ does not coarsely embed into any $L^p$-space for $1\\leqslant p<\\infty$ (moreover, into any uniformly curved Banach space), and yet admits no weakly embedded expander. The reason why our examples do not coarsely embed is a new phenomenon called relative expansion, which we define in terms of Poincar\\'e inequalities."},"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":"1402.1481","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-02-06T20:46:54Z","cross_cats_sorted":["math.FA","math.MG"],"title_canon_sha256":"36897fbdfb3f3a2e65921a5d45c807a8e0e5599441470a6e4056dea587569d11","abstract_canon_sha256":"2ff10678774e39cd902c85de3dea9f666c4fb1874bc94e15fe832f3b55277001"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:53.529583Z","signature_b64":"OdQdnkehBBhNKHnTyNb0WNhHLH2dxcJRR9xKf5aQeP8miBf1Xq1Mr5igJBbQQfLmYdYkINr9nf8quBFvPCc1CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d800c5886568490dcf62b018a6c35974ac55ec6e4e9a988033f7e57fa906a26c","last_reissued_at":"2026-05-18T01:15:53.528986Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:53.528986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Relative expanders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.MG"],"primary_cat":"math.GR","authors_text":"Goulnara Arzhantseva, Romain Tessera","submitted_at":"2014-02-06T20:46:54Z","abstract_excerpt":"We exhibit a finitely generated group $G$ and a sequence of finite index normal subgroups $N_n\\trianglelefteq G$ such that for every finite generating subset $S\\subseteq G$, the sequence of finite Cayley graphs $(G/N_n, S)$ does not coarsely embed into any $L^p$-space for $1\\leqslant p<\\infty$ (moreover, into any uniformly curved Banach space), and yet admits no weakly embedded expander. The reason why our examples do not coarsely embed is a new phenomenon called relative expansion, which we define in terms of Poincar\\'e inequalities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.1481","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":"1402.1481","created_at":"2026-05-18T01:15:53.529087+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.1481v3","created_at":"2026-05-18T01:15:53.529087+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.1481","created_at":"2026-05-18T01:15:53.529087+00:00"},{"alias_kind":"pith_short_12","alias_value":"3AAMLCDFNBEQ","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_16","alias_value":"3AAMLCDFNBEQ3T3C","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_8","alias_value":"3AAMLCDF","created_at":"2026-05-18T12:28:11.866339+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/3AAMLCDFNBEQ3T3CWAMKNQ2ZOS","json":"https://pith.science/pith/3AAMLCDFNBEQ3T3CWAMKNQ2ZOS.json","graph_json":"https://pith.science/api/pith-number/3AAMLCDFNBEQ3T3CWAMKNQ2ZOS/graph.json","events_json":"https://pith.science/api/pith-number/3AAMLCDFNBEQ3T3CWAMKNQ2ZOS/events.json","paper":"https://pith.science/paper/3AAMLCDF"},"agent_actions":{"view_html":"https://pith.science/pith/3AAMLCDFNBEQ3T3CWAMKNQ2ZOS","download_json":"https://pith.science/pith/3AAMLCDFNBEQ3T3CWAMKNQ2ZOS.json","view_paper":"https://pith.science/paper/3AAMLCDF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.1481&json=true","fetch_graph":"https://pith.science/api/pith-number/3AAMLCDFNBEQ3T3CWAMKNQ2ZOS/graph.json","fetch_events":"https://pith.science/api/pith-number/3AAMLCDFNBEQ3T3CWAMKNQ2ZOS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3AAMLCDFNBEQ3T3CWAMKNQ2ZOS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3AAMLCDFNBEQ3T3CWAMKNQ2ZOS/action/storage_attestation","attest_author":"https://pith.science/pith/3AAMLCDFNBEQ3T3CWAMKNQ2ZOS/action/author_attestation","sign_citation":"https://pith.science/pith/3AAMLCDFNBEQ3T3CWAMKNQ2ZOS/action/citation_signature","submit_replication":"https://pith.science/pith/3AAMLCDFNBEQ3T3CWAMKNQ2ZOS/action/replication_record"}},"created_at":"2026-05-18T01:15:53.529087+00:00","updated_at":"2026-05-18T01:15:53.529087+00:00"}