{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:IJD4T2WIYKMEDDWJS43LISJBM7","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":"48dd56a12b104b606a62b7a5eaa5d45bc857bb66d8a1e0cf46ae0f2f1451b66b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-18T13:00:22Z","title_canon_sha256":"500aab78a533d87bf34c5e1a1b7148cf1856a0b81f9242caca4e99ff550fc292"},"schema_version":"1.0","source":{"id":"1503.05379","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.05379","created_at":"2026-05-18T02:21:50Z"},{"alias_kind":"arxiv_version","alias_value":"1503.05379v1","created_at":"2026-05-18T02:21:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05379","created_at":"2026-05-18T02:21:50Z"},{"alias_kind":"pith_short_12","alias_value":"IJD4T2WIYKME","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IJD4T2WIYKMEDDWJ","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IJD4T2WI","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:589b87a8cb7a98042ac9f47950c1a39f5ab76970332fa9fc4297f4c6ed7384ec","target":"graph","created_at":"2026-05-18T02:21:50Z","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 consider a measurable stationary Gaussian stochastic process. A criterion for testing hypotheses about the covariance function of such a process using estimates for its norm in the space $L_p(\\mathbb {T}),\\,p\\geq1$, is constructed.","authors_text":"Viktor Troshki, Yuriy Kozachenko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-18T13:00:22Z","title":"A criterion for testing hypotheses about the covariance function of a stationary Gaussian stochastic process"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05379","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":"sha256:0ee4b5be906dcc5814956d75b093dfe34a07adc1299a27d3f5f2aa8402766a9a","target":"record","created_at":"2026-05-18T02:21:50Z","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":"48dd56a12b104b606a62b7a5eaa5d45bc857bb66d8a1e0cf46ae0f2f1451b66b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-18T13:00:22Z","title_canon_sha256":"500aab78a533d87bf34c5e1a1b7148cf1856a0b81f9242caca4e99ff550fc292"},"schema_version":"1.0","source":{"id":"1503.05379","kind":"arxiv","version":1}},"canonical_sha256":"4247c9eac8c298418ec99736b4492167cc1be7f00dacd9d39064b3b659a2bcef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4247c9eac8c298418ec99736b4492167cc1be7f00dacd9d39064b3b659a2bcef","first_computed_at":"2026-05-18T02:21:50.613651Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:50.613651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x01zg1/cIJcFLlpIcfZA5WifoqQ5KS7qXBUoAw6mlUgucxjExYmkZE3+CjCL5PvFoWeIIz5OVg6eE9G1I0tsDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:50.614059Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.05379","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ee4b5be906dcc5814956d75b093dfe34a07adc1299a27d3f5f2aa8402766a9a","sha256:589b87a8cb7a98042ac9f47950c1a39f5ab76970332fa9fc4297f4c6ed7384ec"],"state_sha256":"3c4e288f118eebb5baab1228ef664e51f0c2e8f98f05ab907fd40859174529d9"}