{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:CN3JLV2ALZBL2RCMYG56WJNFIG","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":"632d09ae344fb0fd246841a2643bb446774ecf61d3a1f5fba515fc5cd85a52e0","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2009-01-28T02:40:50Z","title_canon_sha256":"01151a3adf41b7dff002c65948bd5a5eaa5492af5ff67c994ae86b18e5769669"},"schema_version":"1.0","source":{"id":"0901.4392","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.4392","created_at":"2026-07-04T15:36:58Z"},{"alias_kind":"arxiv_version","alias_value":"0901.4392v1","created_at":"2026-07-04T15:36:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.4392","created_at":"2026-07-04T15:36:58Z"},{"alias_kind":"pith_short_12","alias_value":"CN3JLV2ALZBL","created_at":"2026-07-04T15:36:58Z"},{"alias_kind":"pith_short_16","alias_value":"CN3JLV2ALZBL2RCM","created_at":"2026-07-04T15:36:58Z"},{"alias_kind":"pith_short_8","alias_value":"CN3JLV2A","created_at":"2026-07-04T15:36:58Z"}],"graph_snapshots":[{"event_id":"sha256:aaa887f8a4ea96e47ed26d25752bb86f8df6477970348c8a32bbae9087d937d9","target":"graph","created_at":"2026-07-04T15:36:58Z","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/0901.4392/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Principal components analysis (PCA) is a classical method for the reduction of dimensionality of data in the form of n observations (or cases) of a vector with p variables. For a simple model of factor analysis type, it is proved that ordinary PCA can produce a consistent (for n large) estimate of the principal factor if and only if p(n) is asymptotically of smaller order than n.\n  There may be a basis in which typical signals have sparse representations: most co-ordinates have small signal energies. If such a basis (e.g. wavelets) is used to represent the signals, then the variation in many c","authors_text":"Arthur Yu Lu, Iain M Johnstone","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2009-01-28T02:40:50Z","title":"Sparse Principal Components Analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.4392","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:a02d16fc3034c84b433da90e55f0008281142c00fdc79bae2dc4ad3a78a7a1cd","target":"record","created_at":"2026-07-04T15:36:58Z","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":"632d09ae344fb0fd246841a2643bb446774ecf61d3a1f5fba515fc5cd85a52e0","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2009-01-28T02:40:50Z","title_canon_sha256":"01151a3adf41b7dff002c65948bd5a5eaa5492af5ff67c994ae86b18e5769669"},"schema_version":"1.0","source":{"id":"0901.4392","kind":"arxiv","version":1}},"canonical_sha256":"137695d7405e42bd444cc1bbeb25a541b3b05f11ae5f89cf9ad68a2807415148","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"137695d7405e42bd444cc1bbeb25a541b3b05f11ae5f89cf9ad68a2807415148","first_computed_at":"2026-07-04T15:36:58.561017Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:36:58.561017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kVJ0dMqXjzoUtbPrSfRPhYWESZF5jyYlv9oKhG5Q77B69JWlhJj6eu10QhqrvVyVfC10pkbbtj7DLxFaiIZnAQ==","signature_status":"signed_v1","signed_at":"2026-07-04T15:36:58.561425Z","signed_message":"canonical_sha256_bytes"},"source_id":"0901.4392","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a02d16fc3034c84b433da90e55f0008281142c00fdc79bae2dc4ad3a78a7a1cd","sha256:aaa887f8a4ea96e47ed26d25752bb86f8df6477970348c8a32bbae9087d937d9"],"state_sha256":"19871d166742b4e1b15b3ce132a3be2cfadf0fe1cc7db91a0a844c0164efc2bc"}