{"id":"W1848120893","doi":"10.1090/s0002-9947-02-03129-x","title":"Maximal functions with polynomial densities in lacunary directions","year":2002,"lang":"en","type":"article","venue":"Transactions of the American Mathematical Society","topic":"Advanced Harmonic Analysis Research","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Lacunary function; Mathematics; Polynomial; Bounded function; Combinatorics; Degree (music); Operator (biology); Discrete mathematics; Mathematical analysis; Physics","routes":{"ca_aff":true,"ca_fund":true,"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":[0.002262495,0.001163958,0.000981327,0.002598094,0.002427269,0.004968234,0.001474871,0.001284955,0.01622991],"category_scores_gemma":[0.01206129,0.0008386249,0.001795135,0.001885934,0.004680691,0.009048802,0.004424558,0.003757177,0.005255246],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.003662369,"about_ca_system_score_gemma":0.001617256,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.004067734,"about_ca_topic_score_gemma":0.003940541,"domain_scores_codex":[0.9977958,0.0004743348,0.0001021267,0.0005341903,0.0005469167,0.0005465975],"domain_scores_gemma":[0.9948831,0.00277052,0.0002985852,0.0005118003,0.001004219,0.0005318162],"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":[0.00006031918,0.00001310888,0.0002138466,0.00006585849,0.000006776033,0.00008017664,0.000225741,0.000948919,0.000390085,0.9872174,0.002721195,0.008056602],"study_design_scores_gemma":[0.00002315355,0.00002033644,0.000250909,0.00003718527,0.00001574215,0.0001281421,0.0001719256,0.005756542,0.001389347,0.9809057,0.01127511,0.0000259261],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1654039,0.001744943,0.6007735,0.004307692,0.0006000458,0.00009890532,0.001329231,0.002722777,0.2230191],"genre_scores_gemma":[0.8378148,0.001169235,0.07558069,0.0009052394,0.0005324357,0.0001998342,0.00123042,0.001501404,0.08106594],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01622991,"threshold_uncertainty_score":0.05429441,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03908640324672785,"score_gpt":0.3004772205186382,"score_spread":0.2613908172719103,"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."}}