{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:IC3MZ6KLFRKDGDENWLIQZE2FIR","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"447276666d8e8ad4432bb2e548a2696e4a90d8515b190bff678bb1a3973c9e9c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-08-05T09:16:31Z","title_canon_sha256":"528cc7e73a979ff4cdeeb3031953e1a91d715f57df252a4e3b06aa8580d0744f"},"schema_version":"1.0","source":{"id":"1108.1283","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.1283","created_at":"2026-05-18T04:05:57Z"},{"alias_kind":"arxiv_version","alias_value":"1108.1283v3","created_at":"2026-05-18T04:05:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.1283","created_at":"2026-05-18T04:05:57Z"},{"alias_kind":"pith_short_12","alias_value":"IC3MZ6KLFRKD","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"IC3MZ6KLFRKDGDEN","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"IC3MZ6KL","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:110298fc4fd27969f66ee9f964a7009014d3fbb5e67847ccde49ecd101247c33","target":"graph","created_at":"2026-05-18T04:05:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Oded Regev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-08-05T09:16:31Z","title":"Entropy-based Bounds on Dimension Reduction in L_1"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.1283","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:fa3fc95faec2bf8c33ab21b0fb956a5952b060ed1a205c291ca9c4686ec958db","target":"record","created_at":"2026-05-18T04:05:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"447276666d8e8ad4432bb2e548a2696e4a90d8515b190bff678bb1a3973c9e9c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-08-05T09:16:31Z","title_canon_sha256":"528cc7e73a979ff4cdeeb3031953e1a91d715f57df252a4e3b06aa8580d0744f"},"schema_version":"1.0","source":{"id":"1108.1283","kind":"arxiv","version":3}},"canonical_sha256":"40b6ccf94b2c54330c8db2d10c9345444fe3c792a3e26c4e2a766979b818e33f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40b6ccf94b2c54330c8db2d10c9345444fe3c792a3e26c4e2a766979b818e33f","first_computed_at":"2026-05-18T04:05:57.540059Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:57.540059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dQKZ5A4pgHjeCJ4gk3jzYGUUpBg0LN9shaos+GlStcptQ3ISgmDndoSLK2KCWgYeC1dThkFCbkXDZIEwgvpHCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:57.540572Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.1283","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa3fc95faec2bf8c33ab21b0fb956a5952b060ed1a205c291ca9c4686ec958db","sha256:110298fc4fd27969f66ee9f964a7009014d3fbb5e67847ccde49ecd101247c33"],"state_sha256":"e5bce164a2734db92dcdb71537c21290a1e2bdc6cf9a356fab2c388579230c07"}