{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:PPVSXINVLUUL5XCJKDC77JM43N","short_pith_number":"pith:PPVSXINV","schema_version":"1.0","canonical_sha256":"7beb2ba1b55d28bedc4950c5ffa59cdb4b8371dbf95d9aa2b2dcbd271216a248","source":{"kind":"arxiv","id":"math/0608025","version":1},"attestation_state":"computed","paper":{"title":"Assessing extrema of empirical principal component functions","license":"","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"C\\'eline Vial, Peter Hall","submitted_at":"2006-08-01T13:13:00Z","abstract_excerpt":"The difficulties of estimating and representing the distributions of functional data mean that principal component methods play a substantially greater role in functional data analysis than in more conventional finite-dimensional settings. Local maxima and minima in principal component functions are of direct importance; they indicate places in the domain of a random function where influence on the function value tends to be relatively strong but of opposite sign. We explore statistical properties of the relationship between extrema of empirical principal component functions, and their counter"},"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":"math/0608025","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.ST","submitted_at":"2006-08-01T13:13:00Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"42a4d84971b649b194beaef617d09269e6fd8551bad6259cdccdd526eaef297f","abstract_canon_sha256":"d46321ba13c57477ab4d25ea5fdbc662f9ac106a585b519241593059bdc9bcd4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:49.829127Z","signature_b64":"KVm5ZGBGE8Otu9c6PBlLr36xEUa1RpylScNELZF0c/zMjft+rUv7a42hoB3v+7tr/o81iidUGUjiN3EyRMK+Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7beb2ba1b55d28bedc4950c5ffa59cdb4b8371dbf95d9aa2b2dcbd271216a248","last_reissued_at":"2026-05-18T01:08:49.828480Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:49.828480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Assessing extrema of empirical principal component functions","license":"","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"C\\'eline Vial, Peter Hall","submitted_at":"2006-08-01T13:13:00Z","abstract_excerpt":"The difficulties of estimating and representing the distributions of functional data mean that principal component methods play a substantially greater role in functional data analysis than in more conventional finite-dimensional settings. Local maxima and minima in principal component functions are of direct importance; they indicate places in the domain of a random function where influence on the function value tends to be relatively strong but of opposite sign. We explore statistical properties of the relationship between extrema of empirical principal component functions, and their counter"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0608025","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":""},"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":"math/0608025","created_at":"2026-05-18T01:08:49.828583+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0608025v1","created_at":"2026-05-18T01:08:49.828583+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0608025","created_at":"2026-05-18T01:08:49.828583+00:00"},{"alias_kind":"pith_short_12","alias_value":"PPVSXINVLUUL","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"PPVSXINVLUUL5XCJ","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"PPVSXINV","created_at":"2026-05-18T12:25:54.717736+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/PPVSXINVLUUL5XCJKDC77JM43N","json":"https://pith.science/pith/PPVSXINVLUUL5XCJKDC77JM43N.json","graph_json":"https://pith.science/api/pith-number/PPVSXINVLUUL5XCJKDC77JM43N/graph.json","events_json":"https://pith.science/api/pith-number/PPVSXINVLUUL5XCJKDC77JM43N/events.json","paper":"https://pith.science/paper/PPVSXINV"},"agent_actions":{"view_html":"https://pith.science/pith/PPVSXINVLUUL5XCJKDC77JM43N","download_json":"https://pith.science/pith/PPVSXINVLUUL5XCJKDC77JM43N.json","view_paper":"https://pith.science/paper/PPVSXINV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0608025&json=true","fetch_graph":"https://pith.science/api/pith-number/PPVSXINVLUUL5XCJKDC77JM43N/graph.json","fetch_events":"https://pith.science/api/pith-number/PPVSXINVLUUL5XCJKDC77JM43N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PPVSXINVLUUL5XCJKDC77JM43N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PPVSXINVLUUL5XCJKDC77JM43N/action/storage_attestation","attest_author":"https://pith.science/pith/PPVSXINVLUUL5XCJKDC77JM43N/action/author_attestation","sign_citation":"https://pith.science/pith/PPVSXINVLUUL5XCJKDC77JM43N/action/citation_signature","submit_replication":"https://pith.science/pith/PPVSXINVLUUL5XCJKDC77JM43N/action/replication_record"}},"created_at":"2026-05-18T01:08:49.828583+00:00","updated_at":"2026-05-18T01:08:49.828583+00:00"}