{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:3SWGRF4XJP45NQVZXIFQV2SRNZ","short_pith_number":"pith:3SWGRF4X","schema_version":"1.0","canonical_sha256":"dcac6897974bf9d6c2b9ba0b0aea516e5fa351a38d95d5a64fe971e1dfdbb90e","source":{"kind":"arxiv","id":"1211.2671","version":6},"attestation_state":"computed","paper":{"title":"A General Framework For Consistency of Principal Component Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Dan Shen, Haipeng Shen, J. S. Marron","submitted_at":"2012-11-12T16:02:28Z","abstract_excerpt":"A general asymptotic framework is developed for studying consis- tency properties of principal component analysis (PCA). Our frame- work includes several previously studied domains of asymptotics as special cases and allows one to investigate interesting connections and transitions among the various domains. More importantly, it enables us to investigate asymptotic scenarios that have not been considered before, and gain new insights into the consistency, subspace consistency and strong inconsistency regions of PCA and the boundaries among them. We also establish the corresponding convergence "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1211.2671","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-11-12T16:02:28Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"b276ccf46b33a516a4c1f5904f4a0c8f6aa6c7743e9070ce9b4bab33baf3c885","abstract_canon_sha256":"52054b988c28f93cbeda1df4580178d78c96387cb5173ea44861b9145c0cedf3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:52.338704Z","signature_b64":"CnWjZ+pdazSKMZbgQDyepRB3ZDqXa5KF62OFB3qKSnvOMNxroQBK9nhinygOgcnaCMMLUjFavmb2M8sozgVgDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dcac6897974bf9d6c2b9ba0b0aea516e5fa351a38d95d5a64fe971e1dfdbb90e","last_reissued_at":"2026-05-18T00:56:52.338172Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:52.338172Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A General Framework For Consistency of Principal Component Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Dan Shen, Haipeng Shen, J. S. Marron","submitted_at":"2012-11-12T16:02:28Z","abstract_excerpt":"A general asymptotic framework is developed for studying consis- tency properties of principal component analysis (PCA). Our frame- work includes several previously studied domains of asymptotics as special cases and allows one to investigate interesting connections and transitions among the various domains. More importantly, it enables us to investigate asymptotic scenarios that have not been considered before, and gain new insights into the consistency, subspace consistency and strong inconsistency regions of PCA and the boundaries among them. We also establish the corresponding convergence "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2671","kind":"arxiv","version":6},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1211.2671","created_at":"2026-05-18T00:56:52.338246+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.2671v6","created_at":"2026-05-18T00:56:52.338246+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.2671","created_at":"2026-05-18T00:56:52.338246+00:00"},{"alias_kind":"pith_short_12","alias_value":"3SWGRF4XJP45","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_16","alias_value":"3SWGRF4XJP45NQVZ","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_8","alias_value":"3SWGRF4X","created_at":"2026-05-18T12:26:53.410803+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3SWGRF4XJP45NQVZXIFQV2SRNZ","json":"https://pith.science/pith/3SWGRF4XJP45NQVZXIFQV2SRNZ.json","graph_json":"https://pith.science/api/pith-number/3SWGRF4XJP45NQVZXIFQV2SRNZ/graph.json","events_json":"https://pith.science/api/pith-number/3SWGRF4XJP45NQVZXIFQV2SRNZ/events.json","paper":"https://pith.science/paper/3SWGRF4X"},"agent_actions":{"view_html":"https://pith.science/pith/3SWGRF4XJP45NQVZXIFQV2SRNZ","download_json":"https://pith.science/pith/3SWGRF4XJP45NQVZXIFQV2SRNZ.json","view_paper":"https://pith.science/paper/3SWGRF4X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.2671&json=true","fetch_graph":"https://pith.science/api/pith-number/3SWGRF4XJP45NQVZXIFQV2SRNZ/graph.json","fetch_events":"https://pith.science/api/pith-number/3SWGRF4XJP45NQVZXIFQV2SRNZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3SWGRF4XJP45NQVZXIFQV2SRNZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3SWGRF4XJP45NQVZXIFQV2SRNZ/action/storage_attestation","attest_author":"https://pith.science/pith/3SWGRF4XJP45NQVZXIFQV2SRNZ/action/author_attestation","sign_citation":"https://pith.science/pith/3SWGRF4XJP45NQVZXIFQV2SRNZ/action/citation_signature","submit_replication":"https://pith.science/pith/3SWGRF4XJP45NQVZXIFQV2SRNZ/action/replication_record"}},"created_at":"2026-05-18T00:56:52.338246+00:00","updated_at":"2026-05-18T00:56:52.338246+00:00"}