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This property permits the unraveling of fine details of fluid-particle interactions at microscales defined by its non-equilibrium properties from the analysis of a single Brownian trajectory and to connect them to the hydrodynamics of the solvent fluid, simply considering the lower-order (second) moments of particle position in trapped conditions. In this way, the acceleration "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Owing to the Chapman-Kolmogorov equation for Markovian dynamics, any equilibrium trajectory of a Brownian particle in a solvent fluid can be viewed as the superposition of an uncountable number of non-equilibrium states, permitting the unraveling of fine details of fluid-particle interactions at microscales from the analysis of a single Brownian trajectory by considering the lower-order (second) moments of particle position in trapped conditions.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The particle dynamics are strictly Markovian so that the Chapman-Kolmogorov equation applies directly to the equilibrium trajectory and allows its decomposition into non-equilibrium components (stated in the opening sentence of the abstract).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Equilibrium Brownian trajectories encode non-equilibrium hydrodynamic information through displacement moments, confirming a t^{5/2} scaling from fluid inertia and suggesting a possible t^4 scaling at shorter times due to velocity regularity.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Any equilibrium Brownian trajectory decomposes into a superposition of non-equilibrium states via the Chapman-Kolmogorov equation.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"c00ce0e98f37b414d343ec1980f3a4a3b189b6696393be3c145b7a83a6e14f99"},"source":{"id":"2605.16247","kind":"arxiv","version":1},"verdict":{"id":"5088fff4-8eae-415a-af5a-1af3751f9c9a","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T18:31:00.118073Z","strongest_claim":"Owing to the Chapman-Kolmogorov equation for Markovian dynamics, any equilibrium trajectory of a Brownian particle in a solvent fluid can be viewed as the superposition of an uncountable number of non-equilibrium states, permitting the unraveling of fine details of fluid-particle interactions at microscales from the analysis of a single Brownian trajectory by considering the lower-order (second) moments of particle position in trapped conditions.","one_line_summary":"Equilibrium Brownian trajectories encode non-equilibrium hydrodynamic information through displacement moments, confirming a t^{5/2} scaling from fluid inertia and suggesting a possible t^4 scaling at shorter times due to velocity regularity.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The particle dynamics are strictly Markovian so that the Chapman-Kolmogorov equation applies directly to the equilibrium trajectory and allows its decomposition into non-equilibrium components (stated in the opening sentence of the abstract).","pith_extraction_headline":"Any equilibrium Brownian trajectory decomposes into a superposition of non-equilibrium states via the Chapman-Kolmogorov equation."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16247/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T19:01:18.874053Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T18:40:52.987630Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"shingle_duplication","ran_at":"2026-05-19T17:49:42.181526Z","status":"skipped","version":"0.1.0","findings_count":0},{"name":"citation_quote_validity","ran_at":"2026-05-19T17:49:41.792340Z","status":"skipped","version":"0.1.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:23.092759Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"external_links","ran_at":"2026-05-19T17:31:24.989746Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T17:01:55.602583Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"cited_work_retraction","ran_at":"2026-05-19T16:51:56.780943Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"cfa39a8a272320f9a07849171623ac9467f767b7198ea6550beb6896280a9298"},"references":{"count":63,"sample":[{"doi":"","year":null,"title":"001 0 . 01 0 . 1 1 10 100 1000 mxx(t) 1 10 t5 FIG. 2. mxx(t) = ⟨x2(t)|v(0) = 0 , R (0) = 0 ⟩ vs t expressed by eq. 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