{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:SHKDC757C7QZX5ZAD6TP4OX3EY","short_pith_number":"pith:SHKDC757","schema_version":"1.0","canonical_sha256":"91d4317fbf17e19bf7201fa6fe3afb2613db4c9574bea319115d87a4ff52e471","source":{"kind":"arxiv","id":"2503.23097","version":1},"attestation_state":"computed","paper":{"title":"Tracy-Widom, Gaussian, and Bootstrap: Approximations for Leading Eigenvalues in High-Dimensional PCA","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Miles E. Lopes, Nina D\\\"ornemann","submitted_at":"2025-03-29T14:30:20Z","abstract_excerpt":"Under certain conditions, the largest eigenvalue of a sample covariance matrix undergoes a well-known phase transition when the sample size $n$ and data dimension $p$ diverge proportionally. In the subcritical regime, this eigenvalue has fluctuations of order $n^{-2/3}$ that can be approximated by a Tracy-Widom distribution, while in the supercritical regime, it has fluctuations of order $n^{-1/2}$ that can be approximated with a Gaussian distribution. However, the statistical problem of determining which regime underlies a given dataset is far from resolved. We develop a new testing framework"},"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":"2503.23097","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2025-03-29T14:30:20Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"c86d797dfa6d6c9f1828bbc8975af7039b7ff1fcdd7ba9de76f4f8afef023665","abstract_canon_sha256":"6e66a395f5ba8271ca3af7111088045be7bf5629f9fb875e21dc64fe3a783c22"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:41:30.656212Z","signature_b64":"TKA06EnuV9WdFEpFu412lNMQZu6CSX51ERAPfZxn+Kgr9q2pXNlMGm9NOxbzcoG3UU479QZ0lwfdDJA3q8HBBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"91d4317fbf17e19bf7201fa6fe3afb2613db4c9574bea319115d87a4ff52e471","last_reissued_at":"2026-07-05T10:41:30.655712Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:41:30.655712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tracy-Widom, Gaussian, and Bootstrap: Approximations for Leading Eigenvalues in High-Dimensional PCA","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Miles E. Lopes, Nina D\\\"ornemann","submitted_at":"2025-03-29T14:30:20Z","abstract_excerpt":"Under certain conditions, the largest eigenvalue of a sample covariance matrix undergoes a well-known phase transition when the sample size $n$ and data dimension $p$ diverge proportionally. In the subcritical regime, this eigenvalue has fluctuations of order $n^{-2/3}$ that can be approximated by a Tracy-Widom distribution, while in the supercritical regime, it has fluctuations of order $n^{-1/2}$ that can be approximated with a Gaussian distribution. However, the statistical problem of determining which regime underlies a given dataset is far from resolved. We develop a new testing framework"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.23097","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.23097/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2503.23097","created_at":"2026-07-05T10:41:30.655772+00:00"},{"alias_kind":"arxiv_version","alias_value":"2503.23097v1","created_at":"2026-07-05T10:41:30.655772+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.23097","created_at":"2026-07-05T10:41:30.655772+00:00"},{"alias_kind":"pith_short_12","alias_value":"SHKDC757C7QZ","created_at":"2026-07-05T10:41:30.655772+00:00"},{"alias_kind":"pith_short_16","alias_value":"SHKDC757C7QZX5ZA","created_at":"2026-07-05T10:41:30.655772+00:00"},{"alias_kind":"pith_short_8","alias_value":"SHKDC757","created_at":"2026-07-05T10:41:30.655772+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.21844","citing_title":"Does PCA Work for Rough Functional Data?","ref_index":9,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SHKDC757C7QZX5ZAD6TP4OX3EY","json":"https://pith.science/pith/SHKDC757C7QZX5ZAD6TP4OX3EY.json","graph_json":"https://pith.science/api/pith-number/SHKDC757C7QZX5ZAD6TP4OX3EY/graph.json","events_json":"https://pith.science/api/pith-number/SHKDC757C7QZX5ZAD6TP4OX3EY/events.json","paper":"https://pith.science/paper/SHKDC757"},"agent_actions":{"view_html":"https://pith.science/pith/SHKDC757C7QZX5ZAD6TP4OX3EY","download_json":"https://pith.science/pith/SHKDC757C7QZX5ZAD6TP4OX3EY.json","view_paper":"https://pith.science/paper/SHKDC757","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2503.23097&json=true","fetch_graph":"https://pith.science/api/pith-number/SHKDC757C7QZX5ZAD6TP4OX3EY/graph.json","fetch_events":"https://pith.science/api/pith-number/SHKDC757C7QZX5ZAD6TP4OX3EY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SHKDC757C7QZX5ZAD6TP4OX3EY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SHKDC757C7QZX5ZAD6TP4OX3EY/action/storage_attestation","attest_author":"https://pith.science/pith/SHKDC757C7QZX5ZAD6TP4OX3EY/action/author_attestation","sign_citation":"https://pith.science/pith/SHKDC757C7QZX5ZAD6TP4OX3EY/action/citation_signature","submit_replication":"https://pith.science/pith/SHKDC757C7QZX5ZAD6TP4OX3EY/action/replication_record"}},"created_at":"2026-07-05T10:41:30.655772+00:00","updated_at":"2026-07-05T10:41:30.655772+00:00"}