{"id":"W2032887129","doi":"10.1215/00127094-1345644","title":"Maximal operators and differentiation theorems for sparse sets","year":2011,"lang":"en","type":"article","venue":"Duke Mathematical Journal","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"","keywords":"Bounded function; Dimension (graph theory); Hausdorff space; Probabilistic logic; Euclidean geometry; Hausdorff dimension; Hausdorff distance; Hausdorff measure","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001123693,0.0002715102,0.0005120955,0.0001073809,0.0002357799,0.0001786891,0.0002391346,0.0001520743,0.001130038],"category_scores_gemma":[0.001110565,0.0001882282,0.0001933156,0.00007959673,0.0001312381,0.0001989264,0.00008782598,0.0002888294,0.0000400778],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000331552,"about_ca_system_score_gemma":0.00002680698,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":5.25842e-7,"about_ca_topic_score_gemma":9.595315e-7,"domain_scores_codex":[0.9981583,0.00007741949,0.0007710413,0.0002298793,0.0003352139,0.00042818],"domain_scores_gemma":[0.9982643,0.0007257627,0.0002668412,0.0002647653,0.0001504524,0.0003279362],"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":[0.00004855153,0.00040594,0.00009647179,0.0002912391,0.00008635967,0.00001324114,0.001426526,1.082446e-7,0.0002662912,0.9945507,0.0004918036,0.002322735],"study_design_scores_gemma":[0.000688612,0.0001506455,0.0002410227,0.0001372076,0.0001297048,0.0004032625,0.0002580853,0.01463024,0.0004019765,0.9825966,0.0001160948,0.0002465151],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4821525,0.00003877992,0.503188,0.0002005233,0.0001655759,0.0005840955,0.00002396577,0.00006924596,0.01357736],"genre_scores_gemma":[0.8163077,0.00002357235,0.182995,0.00009777999,0.0001283677,0.00004517375,0.000003482328,0.00006522301,0.0003337173],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.3341552,"threshold_uncertainty_score":0.999783,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.071018228090228,"score_gpt":0.3005851617874843,"score_spread":0.2295669336972563,"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."}}