{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:GM6KIGWKP7S4MZ5FQUFYA5KS4F","short_pith_number":"pith:GM6KIGWK","canonical_record":{"source":{"id":"1209.2185","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-09-11T00:32:56Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"5ef171be6a9c7fc6872b7a00eab3f6353ecfdc693d83ae9909b6273f53efeb1f","abstract_canon_sha256":"cc29b4f6169b2a64eadd68f55398b46bee31b50d9dcb96023ea1106d5bbcdef6"},"schema_version":"1.0"},"canonical_sha256":"333ca41aca7fe5c667a5850b807552e1490131ef784cfadda6aaae772765cc0e","source":{"kind":"arxiv","id":"1209.2185","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.2185","created_at":"2026-05-18T03:26:41Z"},{"alias_kind":"arxiv_version","alias_value":"1209.2185v4","created_at":"2026-05-18T03:26:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.2185","created_at":"2026-05-18T03:26:41Z"},{"alias_kind":"pith_short_12","alias_value":"GM6KIGWKP7S4","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GM6KIGWKP7S4MZ5F","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GM6KIGWK","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:GM6KIGWKP7S4MZ5FQUFYA5KS4F","target":"record","payload":{"canonical_record":{"source":{"id":"1209.2185","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-09-11T00:32:56Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"5ef171be6a9c7fc6872b7a00eab3f6353ecfdc693d83ae9909b6273f53efeb1f","abstract_canon_sha256":"cc29b4f6169b2a64eadd68f55398b46bee31b50d9dcb96023ea1106d5bbcdef6"},"schema_version":"1.0"},"canonical_sha256":"333ca41aca7fe5c667a5850b807552e1490131ef784cfadda6aaae772765cc0e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:41.170788Z","signature_b64":"F8BsME6yyq0RWCqqepLms24sXHb/v08/BlhXdNX1j+Fnq69+37KWqUdMfjlIeQqBiHbNtg561lLsvVfpegdkAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"333ca41aca7fe5c667a5850b807552e1490131ef784cfadda6aaae772765cc0e","last_reissued_at":"2026-05-18T03:26:41.170231Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:41.170231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.2185","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:26:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bX9YrfCEt9Ri5PUHufYqOeeQD1r1jMOrXcl0yKfYURKSxEMLM8Vu8mdVT+3Z6ZSLiyJd3klHogg1f9HZZ2V+Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:04:32.175270Z"},"content_sha256":"291f9c30c380fe3dc950d371453621b74a012b88718bbccec8e791301665d673","schema_version":"1.0","event_id":"sha256:291f9c30c380fe3dc950d371453621b74a012b88718bbccec8e791301665d673"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:GM6KIGWKP7S4MZ5FQUFYA5KS4F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Efficient Dimensionality Reduction for Canonical Correlation Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"cs.DS","authors_text":"Anastasios Zouzias, Christos Boutsidis, Haim Avron, Sivan Toledo","submitted_at":"2012-09-11T00:32:56Z","abstract_excerpt":"We present a fast algorithm for approximate Canonical Correlation Analysis (CCA). Given a pair of tall-and-thin matrices, the proposed algorithm first employs a randomized dimensionality reduction transform to reduce the size of the input matrices, and then applies any CCA algorithm to the new pair of matrices. The algorithm computes an approximate CCA to the original pair of matrices with provable guarantees, while requiring asymptotically less operations than the state-of-the-art exact algorithms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2185","kind":"arxiv","version":4},"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":"2026-05-18T03:26:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xt5AEyFlA+fI9LKcKpchi4qgEeHiTMVlOXS7LJq73XlyvRbayxE2B8iZ9yK+Q7SYIsXsewKIBtspu8skarHHCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:04:32.176050Z"},"content_sha256":"344fb49627ab1be3f3cf089fd782197e1fc56db1b2b15e34bf8dbf4a724ba48c","schema_version":"1.0","event_id":"sha256:344fb49627ab1be3f3cf089fd782197e1fc56db1b2b15e34bf8dbf4a724ba48c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GM6KIGWKP7S4MZ5FQUFYA5KS4F/bundle.json","state_url":"https://pith.science/pith/GM6KIGWKP7S4MZ5FQUFYA5KS4F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GM6KIGWKP7S4MZ5FQUFYA5KS4F/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":"2026-06-07T17:04:32Z","links":{"resolver":"https://pith.science/pith/GM6KIGWKP7S4MZ5FQUFYA5KS4F","bundle":"https://pith.science/pith/GM6KIGWKP7S4MZ5FQUFYA5KS4F/bundle.json","state":"https://pith.science/pith/GM6KIGWKP7S4MZ5FQUFYA5KS4F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GM6KIGWKP7S4MZ5FQUFYA5KS4F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:GM6KIGWKP7S4MZ5FQUFYA5KS4F","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":"cc29b4f6169b2a64eadd68f55398b46bee31b50d9dcb96023ea1106d5bbcdef6","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-09-11T00:32:56Z","title_canon_sha256":"5ef171be6a9c7fc6872b7a00eab3f6353ecfdc693d83ae9909b6273f53efeb1f"},"schema_version":"1.0","source":{"id":"1209.2185","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.2185","created_at":"2026-05-18T03:26:41Z"},{"alias_kind":"arxiv_version","alias_value":"1209.2185v4","created_at":"2026-05-18T03:26:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.2185","created_at":"2026-05-18T03:26:41Z"},{"alias_kind":"pith_short_12","alias_value":"GM6KIGWKP7S4","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GM6KIGWKP7S4MZ5F","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GM6KIGWK","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:344fb49627ab1be3f3cf089fd782197e1fc56db1b2b15e34bf8dbf4a724ba48c","target":"graph","created_at":"2026-05-18T03:26:41Z","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":"We present a fast algorithm for approximate Canonical Correlation Analysis (CCA). Given a pair of tall-and-thin matrices, the proposed algorithm first employs a randomized dimensionality reduction transform to reduce the size of the input matrices, and then applies any CCA algorithm to the new pair of matrices. The algorithm computes an approximate CCA to the original pair of matrices with provable guarantees, while requiring asymptotically less operations than the state-of-the-art exact algorithms.","authors_text":"Anastasios Zouzias, Christos Boutsidis, Haim Avron, Sivan Toledo","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-09-11T00:32:56Z","title":"Efficient Dimensionality Reduction for Canonical Correlation Analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2185","kind":"arxiv","version":4},"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":"sha256:291f9c30c380fe3dc950d371453621b74a012b88718bbccec8e791301665d673","target":"record","created_at":"2026-05-18T03:26:41Z","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":"cc29b4f6169b2a64eadd68f55398b46bee31b50d9dcb96023ea1106d5bbcdef6","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-09-11T00:32:56Z","title_canon_sha256":"5ef171be6a9c7fc6872b7a00eab3f6353ecfdc693d83ae9909b6273f53efeb1f"},"schema_version":"1.0","source":{"id":"1209.2185","kind":"arxiv","version":4}},"canonical_sha256":"333ca41aca7fe5c667a5850b807552e1490131ef784cfadda6aaae772765cc0e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"333ca41aca7fe5c667a5850b807552e1490131ef784cfadda6aaae772765cc0e","first_computed_at":"2026-05-18T03:26:41.170231Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:41.170231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F8BsME6yyq0RWCqqepLms24sXHb/v08/BlhXdNX1j+Fnq69+37KWqUdMfjlIeQqBiHbNtg561lLsvVfpegdkAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:41.170788Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.2185","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:291f9c30c380fe3dc950d371453621b74a012b88718bbccec8e791301665d673","sha256:344fb49627ab1be3f3cf089fd782197e1fc56db1b2b15e34bf8dbf4a724ba48c"],"state_sha256":"a323ea3467d7a799fb2d474a738691cca1b1edf522ba4194a8a222dc6e59cb93"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x+v80miAzCvBvVY9F+xmx5+fVb7TvleXLcCVB67tYfL6HjsWl1rkhGE1WY0jOeOcAQ/KhKf9A4dalKCwY9PlCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T17:04:32.180174Z","bundle_sha256":"1bf161e1edd2afebbcf81a235c7aee95267368666732e68a3e4ebb1d6ed62724"}}