{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:C2LZL75AN3FS6RIH2MKNTLWDP6","short_pith_number":"pith:C2LZL75A","canonical_record":{"source":{"id":"1801.10058","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-01-30T15:34:41Z","cross_cats_sorted":["cs.LG","math.IT"],"title_canon_sha256":"9d7104016e0a3a94c57427e2dc6a00659bb58920297dd84ed5c507f275441aef","abstract_canon_sha256":"511902329aadd7376f08cfa56dbdd9214ede9266cd6543fcedf5402f41170d74"},"schema_version":"1.0"},"canonical_sha256":"169795ffa06ecb2f4507d314d9aec37f83b2acb505d1f06e08fbca23a1621d2a","source":{"kind":"arxiv","id":"1801.10058","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.10058","created_at":"2026-05-18T00:24:46Z"},{"alias_kind":"arxiv_version","alias_value":"1801.10058v1","created_at":"2026-05-18T00:24:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.10058","created_at":"2026-05-18T00:24:46Z"},{"alias_kind":"pith_short_12","alias_value":"C2LZL75AN3FS","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"C2LZL75AN3FS6RIH","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"C2LZL75A","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:C2LZL75AN3FS6RIH2MKNTLWDP6","target":"record","payload":{"canonical_record":{"source":{"id":"1801.10058","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-01-30T15:34:41Z","cross_cats_sorted":["cs.LG","math.IT"],"title_canon_sha256":"9d7104016e0a3a94c57427e2dc6a00659bb58920297dd84ed5c507f275441aef","abstract_canon_sha256":"511902329aadd7376f08cfa56dbdd9214ede9266cd6543fcedf5402f41170d74"},"schema_version":"1.0"},"canonical_sha256":"169795ffa06ecb2f4507d314d9aec37f83b2acb505d1f06e08fbca23a1621d2a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:46.021683Z","signature_b64":"J3I0vICKOVASCtI54uVdcUQP++iFjfYBxufJ9JWMZGihpe3QQ1KbI9n63dL7SCOPKSHk5x8l3pAlRdKfXRb3AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"169795ffa06ecb2f4507d314d9aec37f83b2acb505d1f06e08fbca23a1621d2a","last_reissued_at":"2026-05-18T00:24:46.021007Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:46.021007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.10058","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:24:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0fvgYSQ7jKxvvBMdvg4zwQbUBnsio3TF3BjFK1oqim1buH65O/YfX+lFWEnRJpRgQLj8Zvf0YjGgIDnphGeJDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T12:22:55.127471Z"},"content_sha256":"9ba480ad8cf2ecf7e466b409ea24aa6fc858610eee72b681e9581596039d64aa","schema_version":"1.0","event_id":"sha256:9ba480ad8cf2ecf7e466b409ea24aa6fc858610eee72b681e9581596039d64aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:C2LZL75AN3FS6RIH2MKNTLWDP6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rigorous Restricted Isometry Property of Low-Dimensional Subspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.IT"],"primary_cat":"cs.IT","authors_text":"Gen Li, Qinghua Liu, Yuantao Gu","submitted_at":"2018-01-30T15:34:41Z","abstract_excerpt":"Dimensionality reduction is in demand to reduce the complexity of solving large-scale problems with data lying in latent low-dimensional structures in machine learning and computer version. Motivated by such need, in this work we study the Restricted Isometry Property (RIP) of Gaussian random projections for low-dimensional subspaces in $\\mathbb{R}^N$, and rigorously prove that the projection Frobenius norm distance between any two subspaces spanned by the projected data in $\\mathbb{R}^n$ ($n<N$) remain almost the same as the distance between the original subspaces with probability no less tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.10058","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:24:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kQts/ZhCzrqpSwGBtI3hS9C06l/mkiczPA2tmnQbFIrG21zOAe47yT9loVOIixWiH0wnNsrWX0n3r07er7vHDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T12:22:55.128129Z"},"content_sha256":"a1ef4c681cd39382544bba15bc8abbdcff0295379f8aa324934298bb811eac71","schema_version":"1.0","event_id":"sha256:a1ef4c681cd39382544bba15bc8abbdcff0295379f8aa324934298bb811eac71"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C2LZL75AN3FS6RIH2MKNTLWDP6/bundle.json","state_url":"https://pith.science/pith/C2LZL75AN3FS6RIH2MKNTLWDP6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C2LZL75AN3FS6RIH2MKNTLWDP6/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-25T12:22:55Z","links":{"resolver":"https://pith.science/pith/C2LZL75AN3FS6RIH2MKNTLWDP6","bundle":"https://pith.science/pith/C2LZL75AN3FS6RIH2MKNTLWDP6/bundle.json","state":"https://pith.science/pith/C2LZL75AN3FS6RIH2MKNTLWDP6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C2LZL75AN3FS6RIH2MKNTLWDP6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:C2LZL75AN3FS6RIH2MKNTLWDP6","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":"511902329aadd7376f08cfa56dbdd9214ede9266cd6543fcedf5402f41170d74","cross_cats_sorted":["cs.LG","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-01-30T15:34:41Z","title_canon_sha256":"9d7104016e0a3a94c57427e2dc6a00659bb58920297dd84ed5c507f275441aef"},"schema_version":"1.0","source":{"id":"1801.10058","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.10058","created_at":"2026-05-18T00:24:46Z"},{"alias_kind":"arxiv_version","alias_value":"1801.10058v1","created_at":"2026-05-18T00:24:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.10058","created_at":"2026-05-18T00:24:46Z"},{"alias_kind":"pith_short_12","alias_value":"C2LZL75AN3FS","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"C2LZL75AN3FS6RIH","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"C2LZL75A","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:a1ef4c681cd39382544bba15bc8abbdcff0295379f8aa324934298bb811eac71","target":"graph","created_at":"2026-05-18T00:24:46Z","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"},"paper":{"abstract_excerpt":"Dimensionality reduction is in demand to reduce the complexity of solving large-scale problems with data lying in latent low-dimensional structures in machine learning and computer version. Motivated by such need, in this work we study the Restricted Isometry Property (RIP) of Gaussian random projections for low-dimensional subspaces in $\\mathbb{R}^N$, and rigorously prove that the projection Frobenius norm distance between any two subspaces spanned by the projected data in $\\mathbb{R}^n$ ($n<N$) remain almost the same as the distance between the original subspaces with probability no less tha","authors_text":"Gen Li, Qinghua Liu, Yuantao Gu","cross_cats":["cs.LG","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-01-30T15:34:41Z","title":"Rigorous Restricted Isometry Property of Low-Dimensional Subspaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.10058","kind":"arxiv","version":1},"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":"sha256:9ba480ad8cf2ecf7e466b409ea24aa6fc858610eee72b681e9581596039d64aa","target":"record","created_at":"2026-05-18T00:24:46Z","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":"511902329aadd7376f08cfa56dbdd9214ede9266cd6543fcedf5402f41170d74","cross_cats_sorted":["cs.LG","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-01-30T15:34:41Z","title_canon_sha256":"9d7104016e0a3a94c57427e2dc6a00659bb58920297dd84ed5c507f275441aef"},"schema_version":"1.0","source":{"id":"1801.10058","kind":"arxiv","version":1}},"canonical_sha256":"169795ffa06ecb2f4507d314d9aec37f83b2acb505d1f06e08fbca23a1621d2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"169795ffa06ecb2f4507d314d9aec37f83b2acb505d1f06e08fbca23a1621d2a","first_computed_at":"2026-05-18T00:24:46.021007Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:46.021007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J3I0vICKOVASCtI54uVdcUQP++iFjfYBxufJ9JWMZGihpe3QQ1KbI9n63dL7SCOPKSHk5x8l3pAlRdKfXRb3AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:46.021683Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.10058","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ba480ad8cf2ecf7e466b409ea24aa6fc858610eee72b681e9581596039d64aa","sha256:a1ef4c681cd39382544bba15bc8abbdcff0295379f8aa324934298bb811eac71"],"state_sha256":"83d64aad2c0200d0ddac4da907e1345e6ab868a2ce985a89653be78e51a7616c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"627p2A0Vlx+BIdZmtochFIjuZr8+OXR04GKrWWjssZ+pGFvoyHG1fpYtYHv7ICuCktUBv4M988C2dJY4p3hiDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T12:22:55.131852Z","bundle_sha256":"608e37ed7d0fd739873281e4d8646011fc73719e1253e461caf03f736d2cf1da"}}