{"id":"W2042949782","doi":"10.1002/mana.200610830","title":"Directional maximal operators with smooth densities","year":2009,"lang":"en","type":"article","venue":"Mathematische Nachrichten","topic":"Advanced Harmonic Analysis Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Mathematics; Bounded function; Operator (biology); Order (exchange); Function (biology); Mathematical analysis; Type (biology); Set (abstract data type); Combinatorics; Pure mathematics; Discrete mathematics","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":[],"consensus_categories":[],"category_scores_codex":[0.0004831865,0.0003146262,0.000516349,0.0002173416,0.000256139,0.0001026183,0.0003418253,0.0001036129,0.0006230164],"category_scores_gemma":[0.0003052649,0.0002263125,0.0001313065,0.0005870305,0.0001159475,0.000324498,0.00006863151,0.0003612156,0.0001904869],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001188633,"about_ca_system_score_gemma":0.0001022359,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000009066202,"about_ca_topic_score_gemma":0.00001355425,"domain_scores_codex":[0.9976569,0.00009557323,0.0003974766,0.0004210943,0.0008990763,0.0005299214],"domain_scores_gemma":[0.9985693,0.0003440335,0.0001558498,0.0005249034,0.0002400958,0.0001658394],"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":[0.0005577684,0.002058286,0.001852101,0.0003814132,0.00129029,0.0005217397,0.00466906,0.0004230564,0.01297685,0.8971745,0.04547307,0.03262191],"study_design_scores_gemma":[0.004480931,0.001371006,0.005626238,0.0005098607,0.0007574233,0.0008300377,0.003299583,0.01135209,0.0234749,0.9252799,0.02036659,0.002651501],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4477472,0.001139999,0.4059548,0.002668878,0.0001024771,0.001310084,0.00003776518,0.001224493,0.1398143],"genre_scores_gemma":[0.8441234,0.00002514503,0.1476273,0.0001926388,0.00014684,0.00005217087,0.000009790484,0.00006155439,0.007761186],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3963762,"threshold_uncertainty_score":0.9228756,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04034117963036024,"score_gpt":0.32964681449098,"score_spread":0.2893056348606198,"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."}}