{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:UHHOJ47JERMUG4PHKGEBGL6VZ3","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":"e5a1fb6e997bd65a77addfd17e43ea06fd784ae3c25a220a9cfce08696f82c60","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-07-08T12:58:22Z","title_canon_sha256":"1c259bb74fd39651dac24304afdac8664bb036932113c92573eaf9b5d07688b3"},"schema_version":"1.0","source":{"id":"1007.1363","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.1363","created_at":"2026-05-18T04:42:43Z"},{"alias_kind":"arxiv_version","alias_value":"1007.1363v1","created_at":"2026-05-18T04:42:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.1363","created_at":"2026-05-18T04:42:43Z"},{"alias_kind":"pith_short_12","alias_value":"UHHOJ47JERMU","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"UHHOJ47JERMUG4PH","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"UHHOJ47J","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:541ab795e19773921bc287d80801f3efcb47de1b43a96906108e71c275c25fc9","target":"graph","created_at":"2026-05-18T04:42:43Z","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":"We use nowdays classical theory of generalized moment problems by Krein-Nudelman [1977] to define a special class of stochastic Gaussian processes. The class contains, of course, stationary Gaussian processes. We obtain a spectral representation for the processes from this class and we solve the corresponding prediction problem. The orthogonal rational functions on the unit circle lead to a class of Gaussian processes providing an example for the above construction.","authors_text":"L. Baratchart, L. Golinskii, S. Kupin","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-07-08T12:58:22Z","title":"Multipoint Schur algorithm, II: generalized moment problems, Gaussian processes and prediction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.1363","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":"sha256:4cb9af7c1983aa518007a9b698d75238f0c56386d70fa4e93ad6df28183c1edf","target":"record","created_at":"2026-05-18T04:42:43Z","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":"e5a1fb6e997bd65a77addfd17e43ea06fd784ae3c25a220a9cfce08696f82c60","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-07-08T12:58:22Z","title_canon_sha256":"1c259bb74fd39651dac24304afdac8664bb036932113c92573eaf9b5d07688b3"},"schema_version":"1.0","source":{"id":"1007.1363","kind":"arxiv","version":1}},"canonical_sha256":"a1cee4f3e924594371e75188132fd5cee9a0e6a799398214c0be6a95eccede19","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a1cee4f3e924594371e75188132fd5cee9a0e6a799398214c0be6a95eccede19","first_computed_at":"2026-05-18T04:42:43.135610Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:43.135610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l0B9hTOChZzIiKeGlcXmPwEJlHwZAdsqWAYxcBPuCa8gTOZA6afgkpNjm6Y91gTFwQiyYUxgk0II5TlUzpNyBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:43.136016Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.1363","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4cb9af7c1983aa518007a9b698d75238f0c56386d70fa4e93ad6df28183c1edf","sha256:541ab795e19773921bc287d80801f3efcb47de1b43a96906108e71c275c25fc9"],"state_sha256":"b0abd08066e6ad8337251bd755649eacba1ba0658025ce4688c4bda0c0b4df66"}