{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ODG2ZI6QBP27KKKIKDDQK3CS5X","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":"30407e096f7d68847fc57908d28612e398d0b5c572392575f4fb4f55dd1144a7","cross_cats_sorted":["cs.NA","math.IT","math.NA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-09-11T00:33:51Z","title_canon_sha256":"29c06edf06e08941b853ac66b61325c8e35d29e1051278b5eee8293c588b5b3b"},"schema_version":"1.0","source":{"id":"1909.04801","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.04801","created_at":"2026-07-05T01:53:46Z"},{"alias_kind":"arxiv_version","alias_value":"1909.04801v3","created_at":"2026-07-05T01:53:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.04801","created_at":"2026-07-05T01:53:46Z"},{"alias_kind":"pith_short_12","alias_value":"ODG2ZI6QBP27","created_at":"2026-07-05T01:53:46Z"},{"alias_kind":"pith_short_16","alias_value":"ODG2ZI6QBP27KKKI","created_at":"2026-07-05T01:53:46Z"},{"alias_kind":"pith_short_8","alias_value":"ODG2ZI6Q","created_at":"2026-07-05T01:53:46Z"}],"graph_snapshots":[{"event_id":"sha256:31f6e33a4afa58793d02405a261617f3a67529a55975a18c242075795f359e69","target":"graph","created_at":"2026-07-05T01:53:46Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1909.04801/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Rachel Ward, Ruhui Jin, Tamara G. Kolda","cross_cats":["cs.NA","math.IT","math.NA","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-09-11T00:33:51Z","title":"Faster Johnson-Lindenstrauss Transforms via Kronecker Products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.04801","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":"sha256:522adf9133978664ab99e1d10812a830ff77e422c8d197b37cb68c55d178ab29","target":"record","created_at":"2026-07-05T01:53:46Z","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":"30407e096f7d68847fc57908d28612e398d0b5c572392575f4fb4f55dd1144a7","cross_cats_sorted":["cs.NA","math.IT","math.NA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-09-11T00:33:51Z","title_canon_sha256":"29c06edf06e08941b853ac66b61325c8e35d29e1051278b5eee8293c588b5b3b"},"schema_version":"1.0","source":{"id":"1909.04801","kind":"arxiv","version":3}},"canonical_sha256":"70cdaca3d00bf5f5294850c7056c52edc5fd6d038e15e936947c7d182cf1ee1f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70cdaca3d00bf5f5294850c7056c52edc5fd6d038e15e936947c7d182cf1ee1f","first_computed_at":"2026-07-05T01:53:46.448559Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:53:46.448559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JU2aa5Cf7GTt+h8DqnLe9cJTX2XEYkUNVzifyIClqxzxo4Ef3Op+RGPb0Ojf36Tzn9J0rDIdk9qdpRMwM6pKDw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:53:46.449044Z","signed_message":"canonical_sha256_bytes"},"source_id":"1909.04801","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:522adf9133978664ab99e1d10812a830ff77e422c8d197b37cb68c55d178ab29","sha256:31f6e33a4afa58793d02405a261617f3a67529a55975a18c242075795f359e69"],"state_sha256":"e8d06c1089d48974de9b3466152e7f0813587708793eaad778d8d1cb7bf42ce7"}