{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:ODG2ZI6QBP27KKKIKDDQK3CS5X","short_pith_number":"pith:ODG2ZI6Q","schema_version":"1.0","canonical_sha256":"70cdaca3d00bf5f5294850c7056c52edc5fd6d038e15e936947c7d182cf1ee1f","source":{"kind":"arxiv","id":"1909.04801","version":3},"attestation_state":"computed","paper":{"title":"Faster Johnson-Lindenstrauss Transforms via Kronecker Products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.IT","math.NA","math.PR"],"primary_cat":"cs.IT","authors_text":"Rachel Ward, Ruhui Jin, Tamara G. Kolda","submitted_at":"2019-09-11T00:33:51Z","abstract_excerpt":"The Kronecker product is an important matrix operation with a wide range of applications in supporting fast linear transforms, including signal processing, graph theory, quantum computing and deep learning. In this work, we introduce a generalization of the fast Johnson-Lindenstrauss projection for embedding vectors with Kronecker product structure, the Kronecker fast Johnson-Lindenstrauss transform (KFJLT). The KFJLT reduces the embedding cost to an exponential factor of the standard fast Johnson-Lindenstrauss transform (FJLT)'s cost when applied to vectors with Kronecker structure, by avoidi"},"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":"1909.04801","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-09-11T00:33:51Z","cross_cats_sorted":["cs.NA","math.IT","math.NA","math.PR"],"title_canon_sha256":"29c06edf06e08941b853ac66b61325c8e35d29e1051278b5eee8293c588b5b3b","abstract_canon_sha256":"30407e096f7d68847fc57908d28612e398d0b5c572392575f4fb4f55dd1144a7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:53:46.449044Z","signature_b64":"JU2aa5Cf7GTt+h8DqnLe9cJTX2XEYkUNVzifyIClqxzxo4Ef3Op+RGPb0Ojf36Tzn9J0rDIdk9qdpRMwM6pKDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70cdaca3d00bf5f5294850c7056c52edc5fd6d038e15e936947c7d182cf1ee1f","last_reissued_at":"2026-07-05T01:53:46.448559Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:53:46.448559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Faster Johnson-Lindenstrauss Transforms via Kronecker Products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.IT","math.NA","math.PR"],"primary_cat":"cs.IT","authors_text":"Rachel Ward, Ruhui Jin, Tamara G. Kolda","submitted_at":"2019-09-11T00:33:51Z","abstract_excerpt":"The Kronecker product is an important matrix operation with a wide range of applications in supporting fast linear transforms, including signal processing, graph theory, quantum computing and deep learning. In this work, we introduce a generalization of the fast Johnson-Lindenstrauss projection for embedding vectors with Kronecker product structure, the Kronecker fast Johnson-Lindenstrauss transform (KFJLT). The KFJLT reduces the embedding cost to an exponential factor of the standard fast Johnson-Lindenstrauss transform (FJLT)'s cost when applied to vectors with Kronecker structure, by avoidi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.04801","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1909.04801/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1909.04801","created_at":"2026-07-05T01:53:46.448620+00:00"},{"alias_kind":"arxiv_version","alias_value":"1909.04801v3","created_at":"2026-07-05T01:53:46.448620+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.04801","created_at":"2026-07-05T01:53:46.448620+00:00"},{"alias_kind":"pith_short_12","alias_value":"ODG2ZI6QBP27","created_at":"2026-07-05T01:53:46.448620+00:00"},{"alias_kind":"pith_short_16","alias_value":"ODG2ZI6QBP27KKKI","created_at":"2026-07-05T01:53:46.448620+00:00"},{"alias_kind":"pith_short_8","alias_value":"ODG2ZI6Q","created_at":"2026-07-05T01:53:46.448620+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2608.10523","citing_title":"Improving TensorSketch Using Complex Random Variables","ref_index":28,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ODG2ZI6QBP27KKKIKDDQK3CS5X","json":"https://pith.science/pith/ODG2ZI6QBP27KKKIKDDQK3CS5X.json","graph_json":"https://pith.science/api/pith-number/ODG2ZI6QBP27KKKIKDDQK3CS5X/graph.json","events_json":"https://pith.science/api/pith-number/ODG2ZI6QBP27KKKIKDDQK3CS5X/events.json","paper":"https://pith.science/paper/ODG2ZI6Q"},"agent_actions":{"view_html":"https://pith.science/pith/ODG2ZI6QBP27KKKIKDDQK3CS5X","download_json":"https://pith.science/pith/ODG2ZI6QBP27KKKIKDDQK3CS5X.json","view_paper":"https://pith.science/paper/ODG2ZI6Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1909.04801&json=true","fetch_graph":"https://pith.science/api/pith-number/ODG2ZI6QBP27KKKIKDDQK3CS5X/graph.json","fetch_events":"https://pith.science/api/pith-number/ODG2ZI6QBP27KKKIKDDQK3CS5X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ODG2ZI6QBP27KKKIKDDQK3CS5X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ODG2ZI6QBP27KKKIKDDQK3CS5X/action/storage_attestation","attest_author":"https://pith.science/pith/ODG2ZI6QBP27KKKIKDDQK3CS5X/action/author_attestation","sign_citation":"https://pith.science/pith/ODG2ZI6QBP27KKKIKDDQK3CS5X/action/citation_signature","submit_replication":"https://pith.science/pith/ODG2ZI6QBP27KKKIKDDQK3CS5X/action/replication_record"}},"created_at":"2026-07-05T01:53:46.448620+00:00","updated_at":"2026-07-05T01:53:46.448620+00:00"}