{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:BXYFNUAQ2ZSEVMLE44V34ZXKV6","short_pith_number":"pith:BXYFNUAQ","schema_version":"1.0","canonical_sha256":"0df056d010d6644ab164e72bbe66eaaf861820abdf96a88bef740d78e0d048e7","source":{"kind":"arxiv","id":"1803.05350","version":1},"attestation_state":"computed","paper":{"title":"Optimal Bounds for Johnson-Lindenstrauss Transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"cs.DM","authors_text":"Fiona Knoll, Michael Burr, Shuhong Gao","submitted_at":"2018-03-14T15:22:27Z","abstract_excerpt":"In 1984, Johnson and Lindenstrauss proved that any finite set of data in a high-dimensional space can be projected to a lower-dimensional space while preserving the pairwise Euclidean distance between points up to a bounded relative error. If the desired dimension of the image is too small, however, Kane, Meka, and Nelson (2011) and Jayram and Woodruff (2013) independently proved that such a projection does not exist. In this paper, we provide a precise asymptotic threshold for the dimension of the image, above which, there exists a projection preserving the Euclidean distance, but, below whic"},"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":"1803.05350","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-03-14T15:22:27Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"e8dd9660fbab2c53d9664277c99104dec9e1b64af5768c6e90b7bb458405c97b","abstract_canon_sha256":"64c3d2fc212cc90bccd0210912c45b8f3d8072ffbfc025e15341394536724d98"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:01.533201Z","signature_b64":"VJ2Fxhz1D0bXmNnA6jKE8rY1WWh0UGWEH1wlfkVYRRiBupgmjAYLqvJ8Di3G4x5pkD8TeCtzb11d4OnrPfGQBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0df056d010d6644ab164e72bbe66eaaf861820abdf96a88bef740d78e0d048e7","last_reissued_at":"2026-05-18T00:21:01.532756Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:01.532756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal Bounds for Johnson-Lindenstrauss Transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"cs.DM","authors_text":"Fiona Knoll, Michael Burr, Shuhong Gao","submitted_at":"2018-03-14T15:22:27Z","abstract_excerpt":"In 1984, Johnson and Lindenstrauss proved that any finite set of data in a high-dimensional space can be projected to a lower-dimensional space while preserving the pairwise Euclidean distance between points up to a bounded relative error. If the desired dimension of the image is too small, however, Kane, Meka, and Nelson (2011) and Jayram and Woodruff (2013) independently proved that such a projection does not exist. In this paper, we provide a precise asymptotic threshold for the dimension of the image, above which, there exists a projection preserving the Euclidean distance, but, below whic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05350","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":"1803.05350","created_at":"2026-05-18T00:21:01.532826+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.05350v1","created_at":"2026-05-18T00:21:01.532826+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.05350","created_at":"2026-05-18T00:21:01.532826+00:00"},{"alias_kind":"pith_short_12","alias_value":"BXYFNUAQ2ZSE","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_16","alias_value":"BXYFNUAQ2ZSEVMLE","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_8","alias_value":"BXYFNUAQ","created_at":"2026-05-18T12:32:16.446611+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/BXYFNUAQ2ZSEVMLE44V34ZXKV6","json":"https://pith.science/pith/BXYFNUAQ2ZSEVMLE44V34ZXKV6.json","graph_json":"https://pith.science/api/pith-number/BXYFNUAQ2ZSEVMLE44V34ZXKV6/graph.json","events_json":"https://pith.science/api/pith-number/BXYFNUAQ2ZSEVMLE44V34ZXKV6/events.json","paper":"https://pith.science/paper/BXYFNUAQ"},"agent_actions":{"view_html":"https://pith.science/pith/BXYFNUAQ2ZSEVMLE44V34ZXKV6","download_json":"https://pith.science/pith/BXYFNUAQ2ZSEVMLE44V34ZXKV6.json","view_paper":"https://pith.science/paper/BXYFNUAQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.05350&json=true","fetch_graph":"https://pith.science/api/pith-number/BXYFNUAQ2ZSEVMLE44V34ZXKV6/graph.json","fetch_events":"https://pith.science/api/pith-number/BXYFNUAQ2ZSEVMLE44V34ZXKV6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BXYFNUAQ2ZSEVMLE44V34ZXKV6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BXYFNUAQ2ZSEVMLE44V34ZXKV6/action/storage_attestation","attest_author":"https://pith.science/pith/BXYFNUAQ2ZSEVMLE44V34ZXKV6/action/author_attestation","sign_citation":"https://pith.science/pith/BXYFNUAQ2ZSEVMLE44V34ZXKV6/action/citation_signature","submit_replication":"https://pith.science/pith/BXYFNUAQ2ZSEVMLE44V34ZXKV6/action/replication_record"}},"created_at":"2026-05-18T00:21:01.532826+00:00","updated_at":"2026-05-18T00:21:01.532826+00:00"}