{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001268236,0.0004724316,0.0004029152,0.001076953,0.0007848529,0.001241034,0.0005851921,0.0005401096,0.002635532],"category_scores_gemma":[0.002572815,0.0002708464,0.0005788901,0.0004272576,0.001969555,0.001618903,0.002119113,0.0009944708,0.0002185798],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007754464,"about_ca_system_score_gemma":0.0004170714,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006513942,"about_ca_topic_score_gemma":0.0005433353,"domain_scores_codex":[0.9994948,0.0001256019,0.00002172122,0.00007478648,0.000181777,0.000101319],"domain_scores_gemma":[0.9989176,0.0003063668,0.000187887,0.00008992816,0.0002098382,0.0002884543],"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":[0.00003931533,0.00001690322,0.0005532654,0.00003274822,0.00001114114,0.00009732457,0.0001292026,0.003762762,0.005634202,0.9864119,0.000300895,0.003010211],"study_design_scores_gemma":[0.00003373771,0.0001157284,0.001623444,0.00003368479,0.00001862988,0.0003491077,0.0002895579,0.0921314,0.004665565,0.8970268,0.003677309,0.00003509679],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7398086,0.0007871161,0.2220099,0.0005351172,0.000116976,0.00004738649,0.00008567012,0.0001226148,0.0364866],"genre_scores_gemma":[0.9734788,0.0002974782,0.01869957,0.00008851156,0.00008571343,0.00005001671,0.00006607598,0.00002718708,0.007206643],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002635532,"threshold_uncertainty_score":0.008816779,"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."}}