{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:WL27X55A6LGALM3JBAGUPXUQR3","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":"97b778c4d8062f0227e83f2babd6e208f5e796286c973dd398aa2b68a95f1342","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-04-23T04:09:55Z","title_canon_sha256":"0697ca75dc0bf3455450c125fd5af528e7d01d204e115fae3bc6dfd3d303ef7f"},"schema_version":"1.0","source":{"id":"2504.16401","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.16401","created_at":"2026-07-05T10:52:46Z"},{"alias_kind":"arxiv_version","alias_value":"2504.16401v1","created_at":"2026-07-05T10:52:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.16401","created_at":"2026-07-05T10:52:46Z"},{"alias_kind":"pith_short_12","alias_value":"WL27X55A6LGA","created_at":"2026-07-05T10:52:46Z"},{"alias_kind":"pith_short_16","alias_value":"WL27X55A6LGALM3J","created_at":"2026-07-05T10:52:46Z"},{"alias_kind":"pith_short_8","alias_value":"WL27X55A","created_at":"2026-07-05T10:52:46Z"}],"graph_snapshots":[{"event_id":"sha256:a6ab05c9cab68f1b10244a2667d43addacbaadd32b165f3aee6cc445a1d834f0","target":"graph","created_at":"2026-07-05T10:52:46Z","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/2504.16401/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we investigate the nonlinear stability and transition threshold for the 3D Boussinesq system in Sobolev space under the high Reynolds number and small thermal diffusion in $\\mathbb{T}\\times\\mathbb{R}\\times\\mathbb{T} $. It is proved that if the initial velocity $v_{\\rm in}$ and the initial temperature $ \\theta_{\\rm in} $ satisfy $ \\|v_{\\rm in}-(y,0,0)\\|_{H^{2}}\\leq \\varepsilon\\nu, \\|\\theta_{\\rm in}\\|_{H^{2}}\\leq \\varepsilon\\nu^{2} $, respectively for some $ \\varepsilon>0 $ independent of the Reynolds number or thermal diffusion, then the solutions of 3D Boussinesq system are glob","authors_text":"Lili Wang, Shikun Cui, Wendong Wang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-04-23T04:09:55Z","title":"Stability threshold of Couette flow for 3D Boussinesq system in Sobolev spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.16401","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":"sha256:7a650faa7fe9854af12ecf285139616c3cef322ea77e5f593e9db2b50f881c82","target":"record","created_at":"2026-07-05T10:52:46Z","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":"97b778c4d8062f0227e83f2babd6e208f5e796286c973dd398aa2b68a95f1342","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-04-23T04:09:55Z","title_canon_sha256":"0697ca75dc0bf3455450c125fd5af528e7d01d204e115fae3bc6dfd3d303ef7f"},"schema_version":"1.0","source":{"id":"2504.16401","kind":"arxiv","version":1}},"canonical_sha256":"b2f5fbf7a0f2cc05b369080d47de908ef6434fbbde849d4738495b3382fe57a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2f5fbf7a0f2cc05b369080d47de908ef6434fbbde849d4738495b3382fe57a9","first_computed_at":"2026-07-05T10:52:46.224253Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:52:46.224253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pqxE0q26NMLYuZmSmB5UOX9KtmysDNwFaTEGr9FSKlv998/JJMc7uvyD1SpU6CiY86RfhbHDOBVy6U7R0vjRAw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:52:46.224617Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.16401","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a650faa7fe9854af12ecf285139616c3cef322ea77e5f593e9db2b50f881c82","sha256:a6ab05c9cab68f1b10244a2667d43addacbaadd32b165f3aee6cc445a1d834f0"],"state_sha256":"296845b6490117a1e267312bfb417864357141a5c8a5d8384d727fc44e98e0c8"}