{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:CPNXDBFTSFDP3EW46GAR2JI2VV","short_pith_number":"pith:CPNXDBFT","schema_version":"1.0","canonical_sha256":"13db7184b39146fd92dcf1811d251aad745680d78baff8f273fbcd6b98756a51","source":{"kind":"arxiv","id":"1705.06797","version":2},"attestation_state":"computed","paper":{"title":"The coarse geometry of Tsirelson's space and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.KT","math.MG"],"primary_cat":"math.FA","authors_text":"Florent Baudier, Gilles Lancien, Thomas Schlumprecht","submitted_at":"2017-05-18T20:48:50Z","abstract_excerpt":"The main result of this article is a rigidity result pertaining to the spreading model structure for Banach spaces coarsely embeddable into Tsirelson's original space $T^*$. Every Banach space that is coarsely embeddable into $T^*$ must be reflexive and all its spreading models must be isomorphic to $c_0$. Several important consequences follow from our rigidity result. We obtain a coarse version of an influential theorem of Tsirelson: $T^*$ does not coarsely contain $c_0$ nor $\\ell_p$ for $p\\in[1,\\infty)$. We show that there is no infinite dimensional Banach space that coarsely embeds into eve"},"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":"1705.06797","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-05-18T20:48:50Z","cross_cats_sorted":["math.GR","math.KT","math.MG"],"title_canon_sha256":"8c6feee00aab880435030dfd65fc25d50c8d48e948eb46a19c70f3695b6973ea","abstract_canon_sha256":"a00e80e7772f54c4559f76c784a0de3baf52c23628c43e78df4d1b4781af4cf7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:56.563352Z","signature_b64":"tja3+5d97413RbQnLJgcORfXQLMd6AOdIYMRtr3nGes9ytkKaRG4FZ690SQELt4Nta3ZvAwpFGZCl2VRtpZFBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13db7184b39146fd92dcf1811d251aad745680d78baff8f273fbcd6b98756a51","last_reissued_at":"2026-05-18T00:23:56.562514Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:56.562514Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The coarse geometry of Tsirelson's space and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.KT","math.MG"],"primary_cat":"math.FA","authors_text":"Florent Baudier, Gilles Lancien, Thomas Schlumprecht","submitted_at":"2017-05-18T20:48:50Z","abstract_excerpt":"The main result of this article is a rigidity result pertaining to the spreading model structure for Banach spaces coarsely embeddable into Tsirelson's original space $T^*$. Every Banach space that is coarsely embeddable into $T^*$ must be reflexive and all its spreading models must be isomorphic to $c_0$. Several important consequences follow from our rigidity result. We obtain a coarse version of an influential theorem of Tsirelson: $T^*$ does not coarsely contain $c_0$ nor $\\ell_p$ for $p\\in[1,\\infty)$. We show that there is no infinite dimensional Banach space that coarsely embeds into eve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06797","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1705.06797","created_at":"2026-05-18T00:23:56.562764+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.06797v2","created_at":"2026-05-18T00:23:56.562764+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.06797","created_at":"2026-05-18T00:23:56.562764+00:00"},{"alias_kind":"pith_short_12","alias_value":"CPNXDBFTSFDP","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_16","alias_value":"CPNXDBFTSFDP3EW4","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_8","alias_value":"CPNXDBFT","created_at":"2026-05-18T12:31:10.602751+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/CPNXDBFTSFDP3EW46GAR2JI2VV","json":"https://pith.science/pith/CPNXDBFTSFDP3EW46GAR2JI2VV.json","graph_json":"https://pith.science/api/pith-number/CPNXDBFTSFDP3EW46GAR2JI2VV/graph.json","events_json":"https://pith.science/api/pith-number/CPNXDBFTSFDP3EW46GAR2JI2VV/events.json","paper":"https://pith.science/paper/CPNXDBFT"},"agent_actions":{"view_html":"https://pith.science/pith/CPNXDBFTSFDP3EW46GAR2JI2VV","download_json":"https://pith.science/pith/CPNXDBFTSFDP3EW46GAR2JI2VV.json","view_paper":"https://pith.science/paper/CPNXDBFT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.06797&json=true","fetch_graph":"https://pith.science/api/pith-number/CPNXDBFTSFDP3EW46GAR2JI2VV/graph.json","fetch_events":"https://pith.science/api/pith-number/CPNXDBFTSFDP3EW46GAR2JI2VV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CPNXDBFTSFDP3EW46GAR2JI2VV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CPNXDBFTSFDP3EW46GAR2JI2VV/action/storage_attestation","attest_author":"https://pith.science/pith/CPNXDBFTSFDP3EW46GAR2JI2VV/action/author_attestation","sign_citation":"https://pith.science/pith/CPNXDBFTSFDP3EW46GAR2JI2VV/action/citation_signature","submit_replication":"https://pith.science/pith/CPNXDBFTSFDP3EW46GAR2JI2VV/action/replication_record"}},"created_at":"2026-05-18T00:23:56.562764+00:00","updated_at":"2026-05-18T00:23:56.562764+00:00"}