{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:PMQJTDX2TZ6ZRTF4EH3JBEG62Z","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":"ee809bccdb33819b0cd153a3640987fffa2a96a90fc8eb93aa60cb6bb2ec3a45","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2022-11-23T12:41:36Z","title_canon_sha256":"7608de153e1a607c65a31c174cdb1cadfc69b18c6e0f8623242d2fb572d892e8"},"schema_version":"1.0","source":{"id":"2211.12918","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.12918","created_at":"2026-07-05T05:18:56Z"},{"alias_kind":"arxiv_version","alias_value":"2211.12918v1","created_at":"2026-07-05T05:18:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.12918","created_at":"2026-07-05T05:18:56Z"},{"alias_kind":"pith_short_12","alias_value":"PMQJTDX2TZ6Z","created_at":"2026-07-05T05:18:56Z"},{"alias_kind":"pith_short_16","alias_value":"PMQJTDX2TZ6ZRTF4","created_at":"2026-07-05T05:18:56Z"},{"alias_kind":"pith_short_8","alias_value":"PMQJTDX2","created_at":"2026-07-05T05:18:56Z"}],"graph_snapshots":[{"event_id":"sha256:d73ee17fdd65a91a649baf44e2f7fb3346c794baf3ddff9f969a3be9737929e5","target":"graph","created_at":"2026-07-05T05:18:56Z","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/2211.12918/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Since Kolmogorov's theory, turbulence has been studied using various methods, many of which could be now be understood in a probabilistic framework. Herein, a comprehensive review of the advances made on stochastic theory of turbulence since Kolmogorov has been provided. It has been suggested that stochastic theory would be able to provide a natural foundation for a unified theory of turbulence as a wide range of problems related to turbulence could be treated using stochastic methods. At first, the mathematical theory of stochastic hydrodynamics has been studied and the results such as well-P","authors_text":"Ali Bozorg, Ali Pourjamal, Ali Poursina","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2022-11-23T12:41:36Z","title":"Stochastic Approach to Turbulence: A Comprehensive Review"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.12918","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:a082e2734c5095cdfa8b1e45b81a7db557d4b215624866a136f3ac7a8b2b6ac3","target":"record","created_at":"2026-07-05T05:18:56Z","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":"ee809bccdb33819b0cd153a3640987fffa2a96a90fc8eb93aa60cb6bb2ec3a45","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2022-11-23T12:41:36Z","title_canon_sha256":"7608de153e1a607c65a31c174cdb1cadfc69b18c6e0f8623242d2fb572d892e8"},"schema_version":"1.0","source":{"id":"2211.12918","kind":"arxiv","version":1}},"canonical_sha256":"7b20998efa9e7d98ccbc21f69090ded664c6c3160fd0cd6749b260d78d9dad2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7b20998efa9e7d98ccbc21f69090ded664c6c3160fd0cd6749b260d78d9dad2d","first_computed_at":"2026-07-05T05:18:56.422904Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:18:56.422904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RbGPvGeWlkY45tskVH0qOypSL/14N10YhqZnMdNSxQy46iZxQBe2fORp5t1IUREjgOnmZuA02zIloyaEJW2TAg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:18:56.423323Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.12918","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a082e2734c5095cdfa8b1e45b81a7db557d4b215624866a136f3ac7a8b2b6ac3","sha256:d73ee17fdd65a91a649baf44e2f7fb3346c794baf3ddff9f969a3be9737929e5"],"state_sha256":"1d89a88665eab17169708d295d906a8da39c602b0190e35c7b1d870f8f4d5932"}