{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:2RN57BWJAYYOBAMQ4Q3PKMSRE3","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"df7667b4b2a9bfb337ded130df6bc7404677852dd65035b14d2d68f8500a107a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2022-01-24T21:42:37Z","title_canon_sha256":"9ea0c6142c260e02e2f93081796263756735a39e2195a0a1ca719462c38a96a7"},"schema_version":"1.0","source":{"id":"2201.09970","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2201.09970","created_at":"2026-07-05T04:14:41Z"},{"alias_kind":"arxiv_version","alias_value":"2201.09970v2","created_at":"2026-07-05T04:14:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.09970","created_at":"2026-07-05T04:14:41Z"},{"alias_kind":"pith_short_12","alias_value":"2RN57BWJAYYO","created_at":"2026-07-05T04:14:41Z"},{"alias_kind":"pith_short_16","alias_value":"2RN57BWJAYYOBAMQ","created_at":"2026-07-05T04:14:41Z"},{"alias_kind":"pith_short_8","alias_value":"2RN57BWJ","created_at":"2026-07-05T04:14:41Z"}],"graph_snapshots":[{"event_id":"sha256:9ce714e4dd64f58f6d021cec7d7620a59f6eac214b14c10bb156f21d582ee293","target":"graph","created_at":"2026-07-05T04:14:41Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2201.09970/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Time warping function provides a mathematical representation to measure phase variability in functional data. Recent studies have developed various approaches to estimate optimal warping between functions and provide non-Euclidean models. However, a principled, linear, generative model on time warping functions is still under-explored. This is a highly challenging problem because the space of warping functions is non-linear with the conventional Euclidean metric. To address this problem, we propose a stochastic process model for time warping functions, where the key is to define a linear, inne","authors_text":"Wei Wu, Xinyu Zhou, Yijia Ma","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2022-01-24T21:42:37Z","title":"A Stochastic Process Model for Time Warping Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.09970","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6f31959566fbafeb3be7e0528713f0f441df04b27ae0fd16f2f49897271264d0","target":"record","created_at":"2026-07-05T04:14:41Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"df7667b4b2a9bfb337ded130df6bc7404677852dd65035b14d2d68f8500a107a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2022-01-24T21:42:37Z","title_canon_sha256":"9ea0c6142c260e02e2f93081796263756735a39e2195a0a1ca719462c38a96a7"},"schema_version":"1.0","source":{"id":"2201.09970","kind":"arxiv","version":2}},"canonical_sha256":"d45bdf86c90630e08190e436f5325126f84353761702de1e9c86ddcd5693b864","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d45bdf86c90630e08190e436f5325126f84353761702de1e9c86ddcd5693b864","first_computed_at":"2026-07-05T04:14:41.511495Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:14:41.511495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hdty1ksaH41PT8GKMXtLdTfdTZy7GN8XBkIbZAJWphysZpzHD+SoQaVpDpeCrBWKjLu18vqgku0RhAVfN0mGCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:14:41.511963Z","signed_message":"canonical_sha256_bytes"},"source_id":"2201.09970","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f31959566fbafeb3be7e0528713f0f441df04b27ae0fd16f2f49897271264d0","sha256:9ce714e4dd64f58f6d021cec7d7620a59f6eac214b14c10bb156f21d582ee293"],"state_sha256":"88db34319709ff67a76ed8b521000423d5e6fd5bca7c4fd767f88d1731486a86"}