{"id":"W206532914","doi":"10.1006/jfan.1999.3500","title":"Brownian Motion Penetrating Fractals","year":2000,"lang":"en","type":"article","venue":"Journal of Functional Analysis","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":55,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"University of British Columbia","keywords":"Mathematics; Hausdorff dimension; Brownian motion; Fractal; Fractional Brownian motion; Besov space; Diffusion process; Dirichlet form; Lipschitz continuity; Space (punctuation); Pure mathematics; Motion (physics); Mathematical analysis; Order (exchange); Sierpinski carpet; Fractal dimension; Dirichlet distribution; Sierpinski triangle; Interpolation space; Classical mechanics; Physics","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0007987824,0.0001200607,0.0004214325,0.000311258,0.00009887702,0.00006094207,0.0001193371,0.00007148799,0.01446852],"category_scores_gemma":[0.0003224464,0.00008937916,0.0006296324,0.000636333,0.00002584823,0.0002312303,0.000009220629,0.0002124,0.00005530279],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004686491,"about_ca_system_score_gemma":0.00002800178,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000005444225,"about_ca_topic_score_gemma":0.00000814996,"domain_scores_codex":[0.9982835,0.00006355164,0.0007945406,0.0001128009,0.0005999589,0.0001456485],"domain_scores_gemma":[0.9985468,0.0004373402,0.0004791603,0.0001494982,0.0002677905,0.0001193702],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.001346195,0.008535799,0.07203886,0.000732287,0.04659794,0.0004744495,0.002329557,0.08232474,0.02603168,0.3716921,0.03266875,0.3552276],"study_design_scores_gemma":[0.001178761,0.0003341331,0.09615941,0.00009809275,0.007251184,0.0003267617,0.0002815288,0.1353533,0.0002764378,0.7547159,0.003429618,0.0005949277],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8155336,0.00006399537,0.1693864,0.0006369017,0.00009483651,0.00005339347,0.00000943659,0.00001731073,0.01420411],"genre_scores_gemma":[0.9866965,0.00002325541,0.009706485,0.0001103442,0.0003065552,0.000001283289,0.000006978325,0.00001126737,0.003137346],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3830237,"threshold_uncertainty_score":0.9864324,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03544004754254408,"score_gpt":0.2862862805696174,"score_spread":0.2508462330270733,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}