{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1992:GST6DDBZLBBTGO67VP722LLKFC","short_pith_number":"pith:GST6DDBZ","schema_version":"1.0","canonical_sha256":"34a7e18c395843333bdfabffad2d6a28b28dbfab1111dc64f25cf801db4404e5","source":{"kind":"arxiv","id":"math/9204213","version":1},"attestation_state":"computed","paper":{"title":"The Distorion Problem","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Edward Odell, Thomas Schlumprecht","submitted_at":"1992-04-21T19:29:09Z","abstract_excerpt":"We prove that Hilbert space is distortable and, in fact, arbitrarily distortable. This means that for all lambda >1 there exists an equivalent norm |.| on l_2 such that for all infinite dimensional subspaces Y of l_2 there exist x,y in Y with ||x||_2 = ||y||_2 =1 yet |x| >lambda |y|.\n  We also prove that if X is any infinite dimensional Banach space with an unconditional basis then the unit sphere of X and the unit sphere of l_1 are uniformly homeomorphic if and only if X does not contain l_infty^n's uniformly."},"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":"math/9204213","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"1992-04-21T19:29:09Z","cross_cats_sorted":[],"title_canon_sha256":"a1c5a443cc7fdda43186901f89a2b83db6e405863dbd4aba222efc67fec71443","abstract_canon_sha256":"79e4501161fc22afadfac7b358a920a5b611b22c37e714e77a9ab2a68d9ab901"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:52.920617Z","signature_b64":"jmCBwK006ByYC3XzWjOsdfPyJTuCkJAXYpwi60JXB5yso/6YDC/owd23XUxRNIBkTQwa/Um0cnDeEw68ON97BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34a7e18c395843333bdfabffad2d6a28b28dbfab1111dc64f25cf801db4404e5","last_reissued_at":"2026-05-18T01:05:52.920020Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:52.920020Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Distorion Problem","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Edward Odell, Thomas Schlumprecht","submitted_at":"1992-04-21T19:29:09Z","abstract_excerpt":"We prove that Hilbert space is distortable and, in fact, arbitrarily distortable. This means that for all lambda >1 there exists an equivalent norm |.| on l_2 such that for all infinite dimensional subspaces Y of l_2 there exist x,y in Y with ||x||_2 = ||y||_2 =1 yet |x| >lambda |y|.\n  We also prove that if X is any infinite dimensional Banach space with an unconditional basis then the unit sphere of X and the unit sphere of l_1 are uniformly homeomorphic if and only if X does not contain l_infty^n's uniformly."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9204213","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":"math/9204213","created_at":"2026-05-18T01:05:52.920104+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9204213v1","created_at":"2026-05-18T01:05:52.920104+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9204213","created_at":"2026-05-18T01:05:52.920104+00:00"},{"alias_kind":"pith_short_12","alias_value":"GST6DDBZLBBT","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_16","alias_value":"GST6DDBZLBBTGO67","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_8","alias_value":"GST6DDBZ","created_at":"2026-05-18T12:25:47.102015+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/GST6DDBZLBBTGO67VP722LLKFC","json":"https://pith.science/pith/GST6DDBZLBBTGO67VP722LLKFC.json","graph_json":"https://pith.science/api/pith-number/GST6DDBZLBBTGO67VP722LLKFC/graph.json","events_json":"https://pith.science/api/pith-number/GST6DDBZLBBTGO67VP722LLKFC/events.json","paper":"https://pith.science/paper/GST6DDBZ"},"agent_actions":{"view_html":"https://pith.science/pith/GST6DDBZLBBTGO67VP722LLKFC","download_json":"https://pith.science/pith/GST6DDBZLBBTGO67VP722LLKFC.json","view_paper":"https://pith.science/paper/GST6DDBZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9204213&json=true","fetch_graph":"https://pith.science/api/pith-number/GST6DDBZLBBTGO67VP722LLKFC/graph.json","fetch_events":"https://pith.science/api/pith-number/GST6DDBZLBBTGO67VP722LLKFC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GST6DDBZLBBTGO67VP722LLKFC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GST6DDBZLBBTGO67VP722LLKFC/action/storage_attestation","attest_author":"https://pith.science/pith/GST6DDBZLBBTGO67VP722LLKFC/action/author_attestation","sign_citation":"https://pith.science/pith/GST6DDBZLBBTGO67VP722LLKFC/action/citation_signature","submit_replication":"https://pith.science/pith/GST6DDBZLBBTGO67VP722LLKFC/action/replication_record"}},"created_at":"2026-05-18T01:05:52.920104+00:00","updated_at":"2026-05-18T01:05:52.920104+00:00"}