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The proof relies on a decomposition of the action into virtually conformal subspaces and a Berry-Esseen type estimate for the random walk towards these subspaces."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove that the Lyapunov exponents are pointwise log-Hölder continuous with respect to the Wasserstein distance, at semisimple probability measures with one-point Lyapunov spectrum.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The probability measures under consideration admit a decomposition of the linear action into virtually conformal subspaces for which a Berry-Esseen type estimate holds for the associated random walk (as invoked in the proof strategy described in the abstract).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Lyapunov exponents are pointwise log-Hölder continuous w.r.t. 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