{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:BDA6RWH3R3QDCOMBUZ46SSQGI7","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":"4f648cc580a4c60d12d06b1f617400eca74bfa17e9ed8cdd9c92be9dcdb530b4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"stat.AP","submitted_at":"2021-05-24T16:59:13Z","title_canon_sha256":"bfd1c30671f91699563a3cd0d117b4956026e0673c943b1148ead45b762ebc40"},"schema_version":"1.0","source":{"id":"2105.11409","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.11409","created_at":"2026-07-05T03:38:07Z"},{"alias_kind":"arxiv_version","alias_value":"2105.11409v3","created_at":"2026-07-05T03:38:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.11409","created_at":"2026-07-05T03:38:07Z"},{"alias_kind":"pith_short_12","alias_value":"BDA6RWH3R3QD","created_at":"2026-07-05T03:38:07Z"},{"alias_kind":"pith_short_16","alias_value":"BDA6RWH3R3QDCOMB","created_at":"2026-07-05T03:38:07Z"},{"alias_kind":"pith_short_8","alias_value":"BDA6RWH3","created_at":"2026-07-05T03:38:07Z"}],"graph_snapshots":[{"event_id":"sha256:7e8cf4d2805704bc1166a48ffec7c219ad07ea15e12a3846883b9809d494d89a","target":"graph","created_at":"2026-07-05T03:38:07Z","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/2105.11409/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Sequential methods for synthetic realisation of random processes have a number of advantages compared with spectral methods. In this article, the determination of optimal autoregressive (AR) models for reproducing a predefined target autocovariance function of a random process is addressed. To this end, a novel formulation of the problem is developed. This formulation is linear and generalises the well-known Yule-Walker (Y-W) equations and a recent approach based on restricted AR models (Krenk-Moller approach, K-M). Two main features characterise the introduced formulation: (i) flexibility in ","authors_text":"Alvaro Cuerva-Tejero, Cristobal Gallego-Castillo, Mohanad Elagamy, Oscar Lopez-Garcia, Sergio Avila-Sanchez","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"stat.AP","submitted_at":"2021-05-24T16:59:13Z","title":"A tutorial on reproducing a predefined autocovariance function through AR models: Application to stationary homogeneous isotropic turbulence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.11409","kind":"arxiv","version":3},"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":"sha256:54ed94f053e370c2301df3ed9a7ca536aa9de4fde6f871e9ec3624ce440ce77b","target":"record","created_at":"2026-07-05T03:38:07Z","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":"4f648cc580a4c60d12d06b1f617400eca74bfa17e9ed8cdd9c92be9dcdb530b4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"stat.AP","submitted_at":"2021-05-24T16:59:13Z","title_canon_sha256":"bfd1c30671f91699563a3cd0d117b4956026e0673c943b1148ead45b762ebc40"},"schema_version":"1.0","source":{"id":"2105.11409","kind":"arxiv","version":3}},"canonical_sha256":"08c1e8d8fb8ee0313981a679e94a0647c5fae963a8c83bfe520b8eb0db8b2c86","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08c1e8d8fb8ee0313981a679e94a0647c5fae963a8c83bfe520b8eb0db8b2c86","first_computed_at":"2026-07-05T03:38:07.726921Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:38:07.726921Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oVwrb3/ApuMHGnQ0+3eImaPkgukHD41PS6h7TimoTwl+kuDSulv6zihAjh6RlG8IZmUWLpDtCFqSADxZJWDfCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:38:07.727261Z","signed_message":"canonical_sha256_bytes"},"source_id":"2105.11409","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:54ed94f053e370c2301df3ed9a7ca536aa9de4fde6f871e9ec3624ce440ce77b","sha256:7e8cf4d2805704bc1166a48ffec7c219ad07ea15e12a3846883b9809d494d89a"],"state_sha256":"5d612ec01fbf371455dbd6abb063fc0d45ed50d79f83dc0d2d8652c564c079f8"}