{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:FVVLO2U22F2Q7STW4W6FM5IM4O","short_pith_number":"pith:FVVLO2U2","schema_version":"1.0","canonical_sha256":"2d6ab76a9ad1750fca76e5bc56750ce3823d9a82e29aa483f6e53428f7b4ccb1","source":{"kind":"arxiv","id":"1703.01507","version":5},"attestation_state":"computed","paper":{"title":"Machine Learning Friendly Set Version of Johnson-Lindenstrauss Lemma","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.DS","authors_text":"Mieczys{\\l}aw A. K{\\l}opotek","submitted_at":"2017-03-04T19:08:22Z","abstract_excerpt":"In this paper we make a novel use of the Johnson-Lindenstrauss Lemma. The Lemma has an existential form saying that there exists a JL transformation $f$ of the data points into lower dimensional space such that all of them fall into predefined error range $\\delta$.\n  We formulate in this paper a theorem stating that we can choose the target dimensionality in a random projection type JL linear transformation in such a way that with probability $1-\\epsilon$ all of them fall into predefined error range $\\delta$ for any user-predefined failure probability $\\epsilon$.\n  This result is important for"},"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":"1703.01507","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-03-04T19:08:22Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"2b1f9793fe9854fb1f6358f56bd73faa737a6648ea3c44aa44dce6595f974a6e","abstract_canon_sha256":"b6bb3c10b581b57ec6e71c4063fe62f58c5bd35d149c274a5daf2b4cfcb7efd6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:00.095495Z","signature_b64":"5tmVjip1kDas2v+4xL30uLyuhqr57dxWE24W5KeOdnmzfDWVZJTqzdbgzC+BqRgDTcNFjHfjMlH2KlDt7qq6BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d6ab76a9ad1750fca76e5bc56750ce3823d9a82e29aa483f6e53428f7b4ccb1","last_reissued_at":"2026-05-18T00:31:00.094774Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:00.094774Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Machine Learning Friendly Set Version of Johnson-Lindenstrauss Lemma","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.DS","authors_text":"Mieczys{\\l}aw A. K{\\l}opotek","submitted_at":"2017-03-04T19:08:22Z","abstract_excerpt":"In this paper we make a novel use of the Johnson-Lindenstrauss Lemma. The Lemma has an existential form saying that there exists a JL transformation $f$ of the data points into lower dimensional space such that all of them fall into predefined error range $\\delta$.\n  We formulate in this paper a theorem stating that we can choose the target dimensionality in a random projection type JL linear transformation in such a way that with probability $1-\\epsilon$ all of them fall into predefined error range $\\delta$ for any user-predefined failure probability $\\epsilon$.\n  This result is important for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.01507","kind":"arxiv","version":5},"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":"1703.01507","created_at":"2026-05-18T00:31:00.094877+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.01507v5","created_at":"2026-05-18T00:31:00.094877+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.01507","created_at":"2026-05-18T00:31:00.094877+00:00"},{"alias_kind":"pith_short_12","alias_value":"FVVLO2U22F2Q","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_16","alias_value":"FVVLO2U22F2Q7STW","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_8","alias_value":"FVVLO2U2","created_at":"2026-05-18T12:31:15.632608+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/FVVLO2U22F2Q7STW4W6FM5IM4O","json":"https://pith.science/pith/FVVLO2U22F2Q7STW4W6FM5IM4O.json","graph_json":"https://pith.science/api/pith-number/FVVLO2U22F2Q7STW4W6FM5IM4O/graph.json","events_json":"https://pith.science/api/pith-number/FVVLO2U22F2Q7STW4W6FM5IM4O/events.json","paper":"https://pith.science/paper/FVVLO2U2"},"agent_actions":{"view_html":"https://pith.science/pith/FVVLO2U22F2Q7STW4W6FM5IM4O","download_json":"https://pith.science/pith/FVVLO2U22F2Q7STW4W6FM5IM4O.json","view_paper":"https://pith.science/paper/FVVLO2U2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.01507&json=true","fetch_graph":"https://pith.science/api/pith-number/FVVLO2U22F2Q7STW4W6FM5IM4O/graph.json","fetch_events":"https://pith.science/api/pith-number/FVVLO2U22F2Q7STW4W6FM5IM4O/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FVVLO2U22F2Q7STW4W6FM5IM4O/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FVVLO2U22F2Q7STW4W6FM5IM4O/action/storage_attestation","attest_author":"https://pith.science/pith/FVVLO2U22F2Q7STW4W6FM5IM4O/action/author_attestation","sign_citation":"https://pith.science/pith/FVVLO2U22F2Q7STW4W6FM5IM4O/action/citation_signature","submit_replication":"https://pith.science/pith/FVVLO2U22F2Q7STW4W6FM5IM4O/action/replication_record"}},"created_at":"2026-05-18T00:31:00.094877+00:00","updated_at":"2026-05-18T00:31:00.094877+00:00"}