{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:NP4UXMLMOSLOZQZ4VE5HIWKWMA","short_pith_number":"pith:NP4UXMLM","canonical_record":{"source":{"id":"1409.8565","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-09-30T14:36:15Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"869535c2f5a3b0ce7b2a992f280f11169262118793bbc4e1e7684f8027f02783","abstract_canon_sha256":"edde101e17b375de396d69a5828263b186983e68e2740a68f45f34d08ceffff0"},"schema_version":"1.0"},"canonical_sha256":"6bf94bb16c7496ecc33ca93a745956602868ad42dc54c9a84a4a9e8edf731a6e","source":{"kind":"arxiv","id":"1409.8565","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.8565","created_at":"2026-05-18T01:17:53Z"},{"alias_kind":"arxiv_version","alias_value":"1409.8565v4","created_at":"2026-05-18T01:17:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.8565","created_at":"2026-05-18T01:17:53Z"},{"alias_kind":"pith_short_12","alias_value":"NP4UXMLMOSLO","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NP4UXMLMOSLOZQZ4","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NP4UXMLM","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:NP4UXMLMOSLOZQZ4VE5HIWKWMA","target":"record","payload":{"canonical_record":{"source":{"id":"1409.8565","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-09-30T14:36:15Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"869535c2f5a3b0ce7b2a992f280f11169262118793bbc4e1e7684f8027f02783","abstract_canon_sha256":"edde101e17b375de396d69a5828263b186983e68e2740a68f45f34d08ceffff0"},"schema_version":"1.0"},"canonical_sha256":"6bf94bb16c7496ecc33ca93a745956602868ad42dc54c9a84a4a9e8edf731a6e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:53.248014Z","signature_b64":"B59u+qNfn+DezAptpnH/j+ioHtENB4GfF16rxSm5cu6AOF++sdw21L7T4IWOYmoFrPoLFUoiPqnCmM54Em8oDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6bf94bb16c7496ecc33ca93a745956602868ad42dc54c9a84a4a9e8edf731a6e","last_reissued_at":"2026-05-18T01:17:53.247341Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:53.247341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.8565","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":"2026-05-18T01:17:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZpniQfZicC/pjcQ2tBaK2MU+7f/zcLO33xoDhC1sZBS1CIPqCW/UiCr2fc9RNmcXD5dXPqiNz5jMGTrLnzqIBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T13:08:34.011652Z"},"content_sha256":"33501c44d7219d785e6b9895d963e67091b1d391cd40f41531ec581af8dab1f3","schema_version":"1.0","event_id":"sha256:33501c44d7219d785e6b9895d963e67091b1d391cd40f41531ec581af8dab1f3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:NP4UXMLMOSLOZQZ4VE5HIWKWMA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sparse CCA: Adaptive Estimation and Computational Barriers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"stat.ME","authors_text":"Chao Gao, Harrison H. Zhou, Zongming Ma","submitted_at":"2014-09-30T14:36:15Z","abstract_excerpt":"Canonical correlation analysis is a classical technique for exploring the relationship between two sets of variables. It has important applications in analyzing high dimensional datasets originated from genomics, imaging and other fields. This paper considers adaptive minimax and computationally tractable estimation of leading sparse canonical coefficient vectors in high dimensions. First, we establish separate minimax estimation rates for canonical coefficient vectors of each set of random variables under no structural assumption on marginal covariance matrices. Second, we propose a computati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.8565","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":"2026-05-18T01:17:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4oM90SR4+omo8NupSNQh72n3R9GwFUjKK4LOj0ovZu+KtKYw1cWItycWOEbIsx67JT2DjH7p3FmDT+U1iNIlCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T13:08:34.012375Z"},"content_sha256":"109180deb264f7b390b9f4aff4f3696ef60b89a9dc6594e4e086da083cd7b221","schema_version":"1.0","event_id":"sha256:109180deb264f7b390b9f4aff4f3696ef60b89a9dc6594e4e086da083cd7b221"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NP4UXMLMOSLOZQZ4VE5HIWKWMA/bundle.json","state_url":"https://pith.science/pith/NP4UXMLMOSLOZQZ4VE5HIWKWMA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NP4UXMLMOSLOZQZ4VE5HIWKWMA/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":"2026-06-06T13:08:34Z","links":{"resolver":"https://pith.science/pith/NP4UXMLMOSLOZQZ4VE5HIWKWMA","bundle":"https://pith.science/pith/NP4UXMLMOSLOZQZ4VE5HIWKWMA/bundle.json","state":"https://pith.science/pith/NP4UXMLMOSLOZQZ4VE5HIWKWMA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NP4UXMLMOSLOZQZ4VE5HIWKWMA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NP4UXMLMOSLOZQZ4VE5HIWKWMA","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":"edde101e17b375de396d69a5828263b186983e68e2740a68f45f34d08ceffff0","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-09-30T14:36:15Z","title_canon_sha256":"869535c2f5a3b0ce7b2a992f280f11169262118793bbc4e1e7684f8027f02783"},"schema_version":"1.0","source":{"id":"1409.8565","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.8565","created_at":"2026-05-18T01:17:53Z"},{"alias_kind":"arxiv_version","alias_value":"1409.8565v4","created_at":"2026-05-18T01:17:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.8565","created_at":"2026-05-18T01:17:53Z"},{"alias_kind":"pith_short_12","alias_value":"NP4UXMLMOSLO","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NP4UXMLMOSLOZQZ4","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NP4UXMLM","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:109180deb264f7b390b9f4aff4f3696ef60b89a9dc6594e4e086da083cd7b221","target":"graph","created_at":"2026-05-18T01:17:53Z","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":"Canonical correlation analysis is a classical technique for exploring the relationship between two sets of variables. It has important applications in analyzing high dimensional datasets originated from genomics, imaging and other fields. This paper considers adaptive minimax and computationally tractable estimation of leading sparse canonical coefficient vectors in high dimensions. First, we establish separate minimax estimation rates for canonical coefficient vectors of each set of random variables under no structural assumption on marginal covariance matrices. Second, we propose a computati","authors_text":"Chao Gao, Harrison H. Zhou, Zongming Ma","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-09-30T14:36:15Z","title":"Sparse CCA: Adaptive Estimation and Computational Barriers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.8565","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":"sha256:33501c44d7219d785e6b9895d963e67091b1d391cd40f41531ec581af8dab1f3","target":"record","created_at":"2026-05-18T01:17:53Z","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":"edde101e17b375de396d69a5828263b186983e68e2740a68f45f34d08ceffff0","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-09-30T14:36:15Z","title_canon_sha256":"869535c2f5a3b0ce7b2a992f280f11169262118793bbc4e1e7684f8027f02783"},"schema_version":"1.0","source":{"id":"1409.8565","kind":"arxiv","version":4}},"canonical_sha256":"6bf94bb16c7496ecc33ca93a745956602868ad42dc54c9a84a4a9e8edf731a6e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6bf94bb16c7496ecc33ca93a745956602868ad42dc54c9a84a4a9e8edf731a6e","first_computed_at":"2026-05-18T01:17:53.247341Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:53.247341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B59u+qNfn+DezAptpnH/j+ioHtENB4GfF16rxSm5cu6AOF++sdw21L7T4IWOYmoFrPoLFUoiPqnCmM54Em8oDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:53.248014Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.8565","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33501c44d7219d785e6b9895d963e67091b1d391cd40f41531ec581af8dab1f3","sha256:109180deb264f7b390b9f4aff4f3696ef60b89a9dc6594e4e086da083cd7b221"],"state_sha256":"26f8327149af853d623f91317aa922c0202d77a2e282643f4c8685548a9b2e97"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DQgLOG2xlbHXcFAvKFWNoEhmK971szqpEqU2r/hFOaDNKfufsZWUFlAQl7kar3sekgqh/GiXMSElZA0jxsPiDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T13:08:34.016165Z","bundle_sha256":"73dd291b29009b673feb0aa76d5c314d7e189560e415b3c09317a6d90ecfb787"}}