{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:KTAYK6VMG4A5PJ43KBMADAHGVE","short_pith_number":"pith:KTAYK6VM","schema_version":"1.0","canonical_sha256":"54c1857aac3701d7a79b50580180e6a9346c876b146ce1be9f39de2cb09ba143","source":{"kind":"arxiv","id":"1709.01972","version":3},"attestation_state":"computed","paper":{"title":"A Quasi-isometric Embedding Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","cs.LG"],"primary_cat":"stat.ML","authors_text":"David W. Dreisigmeyer","submitted_at":"2017-09-06T19:35:02Z","abstract_excerpt":"The Whitney embedding theorem gives an upper bound on the smallest embedding dimension of a manifold. If a data set lies on a manifold, a random projection into this reduced dimension will retain the manifold structure. Here we present an algorithm to find a projection that distorts the data as little as possible."},"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":"1709.01972","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-09-06T19:35:02Z","cross_cats_sorted":["cs.CG","cs.LG"],"title_canon_sha256":"11d240e16c87b5f6383556f76410f71a66aad0741fbaca0d16103028d3a7a870","abstract_canon_sha256":"26e521879be680a8d38407f32fc807d1bdb5528ae73297bccd817b2becc6e893"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:23.555311Z","signature_b64":"bpe9niBGgPg3Mk6gGSFPtAjGze5bBnCpTtvIK+dwLkOlYNIR6gMvpHj/QrOoExYmaVAC7iXZSnViz/NCnAziDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54c1857aac3701d7a79b50580180e6a9346c876b146ce1be9f39de2cb09ba143","last_reissued_at":"2026-05-18T00:31:23.554748Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:23.554748Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Quasi-isometric Embedding Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","cs.LG"],"primary_cat":"stat.ML","authors_text":"David W. Dreisigmeyer","submitted_at":"2017-09-06T19:35:02Z","abstract_excerpt":"The Whitney embedding theorem gives an upper bound on the smallest embedding dimension of a manifold. If a data set lies on a manifold, a random projection into this reduced dimension will retain the manifold structure. Here we present an algorithm to find a projection that distorts the data as little as possible."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01972","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":"1709.01972","created_at":"2026-05-18T00:31:23.554858+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.01972v3","created_at":"2026-05-18T00:31:23.554858+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.01972","created_at":"2026-05-18T00:31:23.554858+00:00"},{"alias_kind":"pith_short_12","alias_value":"KTAYK6VMG4A5","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_16","alias_value":"KTAYK6VMG4A5PJ43","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_8","alias_value":"KTAYK6VM","created_at":"2026-05-18T12:31:28.150371+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/KTAYK6VMG4A5PJ43KBMADAHGVE","json":"https://pith.science/pith/KTAYK6VMG4A5PJ43KBMADAHGVE.json","graph_json":"https://pith.science/api/pith-number/KTAYK6VMG4A5PJ43KBMADAHGVE/graph.json","events_json":"https://pith.science/api/pith-number/KTAYK6VMG4A5PJ43KBMADAHGVE/events.json","paper":"https://pith.science/paper/KTAYK6VM"},"agent_actions":{"view_html":"https://pith.science/pith/KTAYK6VMG4A5PJ43KBMADAHGVE","download_json":"https://pith.science/pith/KTAYK6VMG4A5PJ43KBMADAHGVE.json","view_paper":"https://pith.science/paper/KTAYK6VM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.01972&json=true","fetch_graph":"https://pith.science/api/pith-number/KTAYK6VMG4A5PJ43KBMADAHGVE/graph.json","fetch_events":"https://pith.science/api/pith-number/KTAYK6VMG4A5PJ43KBMADAHGVE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KTAYK6VMG4A5PJ43KBMADAHGVE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KTAYK6VMG4A5PJ43KBMADAHGVE/action/storage_attestation","attest_author":"https://pith.science/pith/KTAYK6VMG4A5PJ43KBMADAHGVE/action/author_attestation","sign_citation":"https://pith.science/pith/KTAYK6VMG4A5PJ43KBMADAHGVE/action/citation_signature","submit_replication":"https://pith.science/pith/KTAYK6VMG4A5PJ43KBMADAHGVE/action/replication_record"}},"created_at":"2026-05-18T00:31:23.554858+00:00","updated_at":"2026-05-18T00:31:23.554858+00:00"}