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More precisely, we prove that if the initial velocity and initial temperature satisfies$$||u_{0}-(1-y^2,0) ||_{H^{\\frac{7}{2}+}}\\leq c_0\\min\\left\\lbrace \\mu,\\nu\\right\\rbrace ^{\\frac{2}{3}}$$ and $$ ||\\theta_{0}||_{H^1}+|||D_x|^{\\frac{1}{8}}\\theta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.11787","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.11787/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2405.11787","created_at":"2026-07-05T08:20:55.815892+00:00"},{"alias_kind":"arxiv_version","alias_value":"2405.11787v1","created_at":"2026-07-05T08:20:55.815892+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.11787","created_at":"2026-07-05T08:20:55.815892+00:00"},{"alias_kind":"pith_short_12","alias_value":"HLIYQVE3CFOJ","created_at":"2026-07-05T08:20:55.815892+00:00"},{"alias_kind":"pith_short_16","alias_value":"HLIYQVE3CFOJTAMN","created_at":"2026-07-05T08:20:55.815892+00:00"},{"alias_kind":"pith_short_8","alias_value":"HLIYQVE3","created_at":"2026-07-05T08:20:55.815892+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.00690","citing_title":"Enhanced Dissipation, Taylor Dispersion, and Inviscid Damping of Couette flow in the Boussinesq system on the Plane","ref_index":29,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HLIYQVE3CFOJTAMNAKZB7556RG","json":"https://pith.science/pith/HLIYQVE3CFOJTAMNAKZB7556RG.json","graph_json":"https://pith.science/api/pith-number/HLIYQVE3CFOJTAMNAKZB7556RG/graph.json","events_json":"https://pith.science/api/pith-number/HLIYQVE3CFOJTAMNAKZB7556RG/events.json","paper":"https://pith.science/paper/HLIYQVE3"},"agent_actions":{"view_html":"https://pith.science/pith/HLIYQVE3CFOJTAMNAKZB7556RG","download_json":"https://pith.science/pith/HLIYQVE3CFOJTAMNAKZB7556RG.json","view_paper":"https://pith.science/paper/HLIYQVE3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2405.11787&json=true","fetch_graph":"https://pith.science/api/pith-number/HLIYQVE3CFOJTAMNAKZB7556RG/graph.json","fetch_events":"https://pith.science/api/pith-number/HLIYQVE3CFOJTAMNAKZB7556RG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HLIYQVE3CFOJTAMNAKZB7556RG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HLIYQVE3CFOJTAMNAKZB7556RG/action/storage_attestation","attest_author":"https://pith.science/pith/HLIYQVE3CFOJTAMNAKZB7556RG/action/author_attestation","sign_citation":"https://pith.science/pith/HLIYQVE3CFOJTAMNAKZB7556RG/action/citation_signature","submit_replication":"https://pith.science/pith/HLIYQVE3CFOJTAMNAKZB7556RG/action/replication_record"}},"created_at":"2026-07-05T08:20:55.815892+00:00","updated_at":"2026-07-05T08:20:55.815892+00:00"}