{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UUZX6FTNRJYYE2SMWGBCID4XY4","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":"6e724105b059a7adf261ef66c875ef42aa23e8091a4148f5fcf0ca950e530563","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-09-29T09:39:42Z","title_canon_sha256":"c244fadf501df59c7fa24589c7c461e46b949ac41449f31ae409f236ee9e00ef"},"schema_version":"1.0","source":{"id":"1609.09272","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.09272","created_at":"2026-05-18T01:03:38Z"},{"alias_kind":"arxiv_version","alias_value":"1609.09272v1","created_at":"2026-05-18T01:03:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.09272","created_at":"2026-05-18T01:03:38Z"},{"alias_kind":"pith_short_12","alias_value":"UUZX6FTNRJYY","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UUZX6FTNRJYYE2SM","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UUZX6FTN","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:7d46fe8a39a9d40de529385c2c4cd63d454a9518df039995fbbd935265f821e1","target":"graph","created_at":"2026-05-18T01:03:38Z","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"},"paper":{"abstract_excerpt":"The partial stochastic realization of periodic processes from finite covariance data has recently been solved by Lindquist and Picci based on convex optimization of a generalized entropy functional. The meaning and the role of this criterion have an unclear origin. In this paper we propose a solution based on a nonlinear generalization of the classical Yule-Walker type equations and on a new iterative algorithm which is shown to converge to the same (unique) solution of the variational problem. This provides a conceptual link to the variational principles and at the same time yields a robust a","authors_text":"Bin Zhu, Giorgio Picci","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-09-29T09:39:42Z","title":"A New Algorithm for Circulant Rational Covariance Extension and Applications to Finite-interval Smoothing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.09272","kind":"arxiv","version":1},"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":"sha256:48b00d7093e1432e082bd139a29fb3d840d0b465fd222a1ca768ef43175d792d","target":"record","created_at":"2026-05-18T01:03:38Z","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":"6e724105b059a7adf261ef66c875ef42aa23e8091a4148f5fcf0ca950e530563","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-09-29T09:39:42Z","title_canon_sha256":"c244fadf501df59c7fa24589c7c461e46b949ac41449f31ae409f236ee9e00ef"},"schema_version":"1.0","source":{"id":"1609.09272","kind":"arxiv","version":1}},"canonical_sha256":"a5337f166d8a71826a4cb182240f97c706bf742f5081dec05c49c7182c0f5d00","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5337f166d8a71826a4cb182240f97c706bf742f5081dec05c49c7182c0f5d00","first_computed_at":"2026-05-18T01:03:38.314018Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:38.314018Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wjw3v8veNyt0733KID8iufNtviCkGM39k96J1lMqvZs7vTM2LMrn7MBMdQ7JCddrCdQsbZ8t4Xq5PYZBO1feCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:38.314666Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.09272","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48b00d7093e1432e082bd139a29fb3d840d0b465fd222a1ca768ef43175d792d","sha256:7d46fe8a39a9d40de529385c2c4cd63d454a9518df039995fbbd935265f821e1"],"state_sha256":"f5566a41c1f8e6d9796cc46e4a0f9056667e849f1628e0c886cd937232ddeb4e"}