{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:IC3MZ6KLFRKDGDENWLIQZE2FIR","short_pith_number":"pith:IC3MZ6KL","schema_version":"1.0","canonical_sha256":"40b6ccf94b2c54330c8db2d10c9345444fe3c792a3e26c4e2a766979b818e33f","source":{"kind":"arxiv","id":"1108.1283","version":3},"attestation_state":"computed","paper":{"title":"Entropy-based Bounds on Dimension Reduction in L_1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Oded Regev","submitted_at":"2011-08-05T09:16:31Z","abstract_excerpt":"We show that for every large enough integer $N$, there exists an $N$-point subset of $L_1$ such that for every $D>1$, embedding it into $\\ell_1^d$ with distortion $D$ requires dimension $d$ at least $N^{\\Omega(1/D^2)}$, and that for every $\\eps>0$ and large enough integer $N$, there exists an $N$-point subset of $L_1$ such that embedding it into $\\ell_1^d$ with distortion $1+\\eps$ requires dimension $d$ at least $N^{1-O(1/\\log(1/\\eps))}$. These results were previously proven by Brinkman and Charikar [JACM, 2005] and by Andoni, Charikar, Neiman, and Nguyen [FOCS 2011]. We provide an alternative"},"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":"1108.1283","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-08-05T09:16:31Z","cross_cats_sorted":[],"title_canon_sha256":"528cc7e73a979ff4cdeeb3031953e1a91d715f57df252a4e3b06aa8580d0744f","abstract_canon_sha256":"447276666d8e8ad4432bb2e548a2696e4a90d8515b190bff678bb1a3973c9e9c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:57.540572Z","signature_b64":"dQKZ5A4pgHjeCJ4gk3jzYGUUpBg0LN9shaos+GlStcptQ3ISgmDndoSLK2KCWgYeC1dThkFCbkXDZIEwgvpHCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40b6ccf94b2c54330c8db2d10c9345444fe3c792a3e26c4e2a766979b818e33f","last_reissued_at":"2026-05-18T04:05:57.540059Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:57.540059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Entropy-based Bounds on Dimension Reduction in L_1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Oded Regev","submitted_at":"2011-08-05T09:16:31Z","abstract_excerpt":"We show that for every large enough integer $N$, there exists an $N$-point subset of $L_1$ such that for every $D>1$, embedding it into $\\ell_1^d$ with distortion $D$ requires dimension $d$ at least $N^{\\Omega(1/D^2)}$, and that for every $\\eps>0$ and large enough integer $N$, there exists an $N$-point subset of $L_1$ such that embedding it into $\\ell_1^d$ with distortion $1+\\eps$ requires dimension $d$ at least $N^{1-O(1/\\log(1/\\eps))}$. These results were previously proven by Brinkman and Charikar [JACM, 2005] and by Andoni, Charikar, Neiman, and Nguyen [FOCS 2011]. We provide an alternative"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.1283","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":"1108.1283","created_at":"2026-05-18T04:05:57.540137+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.1283v3","created_at":"2026-05-18T04:05:57.540137+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.1283","created_at":"2026-05-18T04:05:57.540137+00:00"},{"alias_kind":"pith_short_12","alias_value":"IC3MZ6KLFRKD","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_16","alias_value":"IC3MZ6KLFRKDGDEN","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_8","alias_value":"IC3MZ6KL","created_at":"2026-05-18T12:26:30.835961+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/IC3MZ6KLFRKDGDENWLIQZE2FIR","json":"https://pith.science/pith/IC3MZ6KLFRKDGDENWLIQZE2FIR.json","graph_json":"https://pith.science/api/pith-number/IC3MZ6KLFRKDGDENWLIQZE2FIR/graph.json","events_json":"https://pith.science/api/pith-number/IC3MZ6KLFRKDGDENWLIQZE2FIR/events.json","paper":"https://pith.science/paper/IC3MZ6KL"},"agent_actions":{"view_html":"https://pith.science/pith/IC3MZ6KLFRKDGDENWLIQZE2FIR","download_json":"https://pith.science/pith/IC3MZ6KLFRKDGDENWLIQZE2FIR.json","view_paper":"https://pith.science/paper/IC3MZ6KL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.1283&json=true","fetch_graph":"https://pith.science/api/pith-number/IC3MZ6KLFRKDGDENWLIQZE2FIR/graph.json","fetch_events":"https://pith.science/api/pith-number/IC3MZ6KLFRKDGDENWLIQZE2FIR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IC3MZ6KLFRKDGDENWLIQZE2FIR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IC3MZ6KLFRKDGDENWLIQZE2FIR/action/storage_attestation","attest_author":"https://pith.science/pith/IC3MZ6KLFRKDGDENWLIQZE2FIR/action/author_attestation","sign_citation":"https://pith.science/pith/IC3MZ6KLFRKDGDENWLIQZE2FIR/action/citation_signature","submit_replication":"https://pith.science/pith/IC3MZ6KLFRKDGDENWLIQZE2FIR/action/replication_record"}},"created_at":"2026-05-18T04:05:57.540137+00:00","updated_at":"2026-05-18T04:05:57.540137+00:00"}