{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:UFXDK7HAAVVASLUZJNWNKJCUWR","short_pith_number":"pith:UFXDK7HA","schema_version":"1.0","canonical_sha256":"a16e357ce0056a092e994b6cd52454b46ea032456050ca482d30657a806b7917","source":{"kind":"arxiv","id":"2407.07996","version":2},"attestation_state":"computed","paper":{"title":"Gradual changes in functional time series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Holger Dette, Patrick Bastian","submitted_at":"2024-07-10T19:00:53Z","abstract_excerpt":"We consider the problem of detecting gradual changes in the sequence of mean functions from a not necessarily stationary functional time series. Our approach is based on the maximum deviation (calculated over a given time interval) between a benchmark function and the mean functions at different time points. We speak of a gradual change of size $\\Delta $, if this quantity exceeds a given threshold $\\Delta>0$. For example, the benchmark function could represent an average of yearly temperature curves from the pre-industrial time, and we are interested in the question if the yearly temperature c"},"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":"2407.07996","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-07-10T19:00:53Z","cross_cats_sorted":["stat.ME","stat.TH"],"title_canon_sha256":"6b244aec6f97bec1eeb5da749e88388abceb11c59b986207a49ef6a71bac62df","abstract_canon_sha256":"c23d46e40d86ecdccb215473b4aa0fa26423b0ca096da3e9177530ed7b9c67f1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:59:17.351755Z","signature_b64":"7EaOg0+u0JT5ayoSx3t0xRjMXo9r0RyzAuoIIw7cDODCphp20t2IQ2LR4qqo+DIT7Z8qVLYNzLFGuy8fUz6JAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a16e357ce0056a092e994b6cd52454b46ea032456050ca482d30657a806b7917","last_reissued_at":"2026-07-05T09:59:17.351309Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:59:17.351309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gradual changes in functional time series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Holger Dette, Patrick Bastian","submitted_at":"2024-07-10T19:00:53Z","abstract_excerpt":"We consider the problem of detecting gradual changes in the sequence of mean functions from a not necessarily stationary functional time series. Our approach is based on the maximum deviation (calculated over a given time interval) between a benchmark function and the mean functions at different time points. We speak of a gradual change of size $\\Delta $, if this quantity exceeds a given threshold $\\Delta>0$. For example, the benchmark function could represent an average of yearly temperature curves from the pre-industrial time, and we are interested in the question if the yearly temperature c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.07996","kind":"arxiv","version":2},"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/2407.07996/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":"2407.07996","created_at":"2026-07-05T09:59:17.351376+00:00"},{"alias_kind":"arxiv_version","alias_value":"2407.07996v2","created_at":"2026-07-05T09:59:17.351376+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.07996","created_at":"2026-07-05T09:59:17.351376+00:00"},{"alias_kind":"pith_short_12","alias_value":"UFXDK7HAAVVA","created_at":"2026-07-05T09:59:17.351376+00:00"},{"alias_kind":"pith_short_16","alias_value":"UFXDK7HAAVVASLUZ","created_at":"2026-07-05T09:59:17.351376+00:00"},{"alias_kind":"pith_short_8","alias_value":"UFXDK7HA","created_at":"2026-07-05T09:59:17.351376+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/UFXDK7HAAVVASLUZJNWNKJCUWR","json":"https://pith.science/pith/UFXDK7HAAVVASLUZJNWNKJCUWR.json","graph_json":"https://pith.science/api/pith-number/UFXDK7HAAVVASLUZJNWNKJCUWR/graph.json","events_json":"https://pith.science/api/pith-number/UFXDK7HAAVVASLUZJNWNKJCUWR/events.json","paper":"https://pith.science/paper/UFXDK7HA"},"agent_actions":{"view_html":"https://pith.science/pith/UFXDK7HAAVVASLUZJNWNKJCUWR","download_json":"https://pith.science/pith/UFXDK7HAAVVASLUZJNWNKJCUWR.json","view_paper":"https://pith.science/paper/UFXDK7HA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2407.07996&json=true","fetch_graph":"https://pith.science/api/pith-number/UFXDK7HAAVVASLUZJNWNKJCUWR/graph.json","fetch_events":"https://pith.science/api/pith-number/UFXDK7HAAVVASLUZJNWNKJCUWR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UFXDK7HAAVVASLUZJNWNKJCUWR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UFXDK7HAAVVASLUZJNWNKJCUWR/action/storage_attestation","attest_author":"https://pith.science/pith/UFXDK7HAAVVASLUZJNWNKJCUWR/action/author_attestation","sign_citation":"https://pith.science/pith/UFXDK7HAAVVASLUZJNWNKJCUWR/action/citation_signature","submit_replication":"https://pith.science/pith/UFXDK7HAAVVASLUZJNWNKJCUWR/action/replication_record"}},"created_at":"2026-07-05T09:59:17.351376+00:00","updated_at":"2026-07-05T09:59:17.351376+00:00"}