{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:PEV3KVREZCWOS3SAK65EUX2BWP","short_pith_number":"pith:PEV3KVRE","schema_version":"1.0","canonical_sha256":"792bb55624c8ace96e4057ba4a5f41b3d57cf7167722f08e120211ef50c19c5a","source":{"kind":"arxiv","id":"math/0702609","version":1},"attestation_state":"computed","paper":{"title":"Local functional principal component analysis","license":"","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Andr\\'e Mas (I3M)","submitted_at":"2007-02-21T10:40:30Z","abstract_excerpt":"Covariance operators of random functions are crucial tools to study the way random elements concentrate over their support. The principal component analysis of a random function X is well-known from a theoretical viewpoint and extensively used in practical situations. In this work we focus on local covariance operators. They provide some pieces of information about the distribution of X around a fixed point of the space x&#8320;. A description of the asymptotic behaviour of the theoretical and empirical counterparts is carried out. Asymptotic developments are given under assumptions on the loc"},"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/0702609","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.ST","submitted_at":"2007-02-21T10:40:30Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"2771ec3d7471e9c9c940d31b37a91ebf7fbdef21761829e64d4bffed960dd22a","abstract_canon_sha256":"51931e4201f90493c8adc7c60a2724371140763e0bce80170cf9dbf8ddef4616"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:15.420691Z","signature_b64":"r6k6oNqNJ1NDOrRxTptJd+n1YP483Z64NaY/ej/A7lBTgPfnaFTmG7yPmHFRerJ05Wcqp4vyyhG3sSWL8njpDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"792bb55624c8ace96e4057ba4a5f41b3d57cf7167722f08e120211ef50c19c5a","last_reissued_at":"2026-05-18T01:09:15.419895Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:15.419895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local functional principal component analysis","license":"","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Andr\\'e Mas (I3M)","submitted_at":"2007-02-21T10:40:30Z","abstract_excerpt":"Covariance operators of random functions are crucial tools to study the way random elements concentrate over their support. The principal component analysis of a random function X is well-known from a theoretical viewpoint and extensively used in practical situations. In this work we focus on local covariance operators. They provide some pieces of information about the distribution of X around a fixed point of the space x&#8320;. A description of the asymptotic behaviour of the theoretical and empirical counterparts is carried out. Asymptotic developments are given under assumptions on the loc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0702609","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/0702609","created_at":"2026-05-18T01:09:15.420016+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0702609v1","created_at":"2026-05-18T01:09:15.420016+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0702609","created_at":"2026-05-18T01:09:15.420016+00:00"},{"alias_kind":"pith_short_12","alias_value":"PEV3KVREZCWO","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"PEV3KVREZCWOS3SA","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"PEV3KVRE","created_at":"2026-05-18T12:25:55.427421+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/PEV3KVREZCWOS3SAK65EUX2BWP","json":"https://pith.science/pith/PEV3KVREZCWOS3SAK65EUX2BWP.json","graph_json":"https://pith.science/api/pith-number/PEV3KVREZCWOS3SAK65EUX2BWP/graph.json","events_json":"https://pith.science/api/pith-number/PEV3KVREZCWOS3SAK65EUX2BWP/events.json","paper":"https://pith.science/paper/PEV3KVRE"},"agent_actions":{"view_html":"https://pith.science/pith/PEV3KVREZCWOS3SAK65EUX2BWP","download_json":"https://pith.science/pith/PEV3KVREZCWOS3SAK65EUX2BWP.json","view_paper":"https://pith.science/paper/PEV3KVRE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0702609&json=true","fetch_graph":"https://pith.science/api/pith-number/PEV3KVREZCWOS3SAK65EUX2BWP/graph.json","fetch_events":"https://pith.science/api/pith-number/PEV3KVREZCWOS3SAK65EUX2BWP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PEV3KVREZCWOS3SAK65EUX2BWP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PEV3KVREZCWOS3SAK65EUX2BWP/action/storage_attestation","attest_author":"https://pith.science/pith/PEV3KVREZCWOS3SAK65EUX2BWP/action/author_attestation","sign_citation":"https://pith.science/pith/PEV3KVREZCWOS3SAK65EUX2BWP/action/citation_signature","submit_replication":"https://pith.science/pith/PEV3KVREZCWOS3SAK65EUX2BWP/action/replication_record"}},"created_at":"2026-05-18T01:09:15.420016+00:00","updated_at":"2026-05-18T01:09:15.420016+00:00"}