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By employing refined commutator estimates, the existence and uniqueness of global strong solutions are proved for small initial data $(Q_0,u_0)\\in H^{s+1}\\times H^s$ $(s\\geq 2)$ with activity $c>c_\\star$, which improves a previous result in \\cite{active-limit}. 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By employing refined commutator estimates, the existence and uniqueness of global strong solutions are proved for small initial data $(Q_0,u_0)\\in H^{s+1}\\times H^s$ $(s\\geq 2)$ with activity $c>c_\\star$, which improves a previous result in \\cite{active-limit}. In addition, if the initial data further b"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Existence and uniqueness of global strong solutions for small initial data (Q0,u0) in H^{s+1} x H^s (s>=2) when activity c > c_star, together with a mixing decay estimate on partial^k Q(t) that combines exponential decay at rate proportional to (c - c_star) Gamma and the optimal algebraic heat-kernel rate for k <= s-1.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The initial data must be sufficiently small in the indicated Sobolev norms and the activity must exceed the critical threshold c_star; the proof relies on this smallness to close the a priori estimates via refined commutator bounds.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Global well-posedness for small data and activity-dependent decay rates are established for the 3D Beris-Edwards active liquid crystal system using commutator estimates and Green's functions.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Global strong solutions exist for the 3D active liquid crystal system when initial data are small and activity exceeds a critical threshold.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"b63712d7f4041f7545fd95b22d3e4427deb12acfb081b7a2566c29c93fc45ede"},"source":{"id":"2605.04625","kind":"arxiv","version":2},"verdict":{"id":"125550d8-6c9c-4876-ab93-c8be90d42ff6","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T17:51:43.849802Z","strongest_claim":"Existence and uniqueness of global strong solutions for small initial data (Q0,u0) in H^{s+1} x H^s (s>=2) when activity c > c_star, together with a mixing decay estimate on partial^k Q(t) that combines exponential decay at rate proportional to (c - c_star) Gamma and the optimal algebraic heat-kernel rate for k <= s-1.","one_line_summary":"Global well-posedness for small data and activity-dependent decay rates are established for the 3D Beris-Edwards active liquid crystal system using commutator estimates and Green's functions.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The initial data must be sufficiently small in the indicated Sobolev norms and the activity must exceed the critical threshold c_star; the proof relies on this smallness to close the a priori estimates via refined commutator bounds.","pith_extraction_headline":"Global strong solutions exist for the 3D active liquid crystal system when initial data are small and activity exceeds a critical threshold."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.04625/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T22:31:19.957041Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T14:18:02.735892Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"bbbc4a59ab60a6c4ad458d4ec46453250e84785ca431e4bfa92bc3928bb5d506"},"references":{"count":69,"sample":[{"doi":"","year":2014,"title":"H. 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