{"id":"W2061769755","doi":"10.1007/s00365-009-9041-7","title":"Positive Cubature Formulas and Marcinkiewicz–Zygmund Inequalities on Spherical Caps","year":2009,"lang":"en","type":"article","venue":"Constructive Approximation","topic":"Analytic and geometric function theory","field":"Mathematics","cited_by":21,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Alberta","funders":"","keywords":"Combinatorics; Omega; Mathematics; Unit sphere; Unit (ring theory); Bounded function; Geometry; Physics; Mathematical analysis; Quantum mechanics","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":[0.000274431,0.0001883753,0.0002742841,0.0001545788,0.0001488433,0.00004407576,0.00006949223,0.0001319788,0.000113031],"category_scores_gemma":[0.0005849585,0.0001587765,0.00006295017,0.0003335831,0.0001727571,0.0002126444,0.00002316838,0.0002159073,0.00001931795],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00009117233,"about_ca_system_score_gemma":0.00002943574,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004341243,"about_ca_topic_score_gemma":5.376147e-7,"domain_scores_codex":[0.9989415,0.00009328077,0.0002668854,0.0002617902,0.0002435961,0.0001928802],"domain_scores_gemma":[0.998917,0.0005058516,0.0001684499,0.0001872634,0.0001459668,0.00007549598],"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":[0.0001298104,0.00007182211,0.0003042073,0.00003420025,0.00004598554,0.000002820039,0.001115176,0.000002798831,0.0001182499,0.9645239,0.0008127548,0.03283825],"study_design_scores_gemma":[0.0007237562,0.0003387307,0.00581148,0.00005812969,0.0000670853,0.00004901125,0.00275971,0.001117046,0.00149054,0.9871514,0.0001953099,0.0002378454],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7423229,0.0002413365,0.196423,0.0007404545,0.0001863964,0.0006390409,0.00003694728,0.0001633865,0.05924652],"genre_scores_gemma":[0.9823938,0.00001326178,0.01594028,0.000423176,0.0001125036,0.000009883158,0.00002352026,0.00001250074,0.001071073],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2400709,"threshold_uncertainty_score":0.6474717,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02599761601653169,"score_gpt":0.2775381461667648,"score_spread":0.2515405301502331,"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."}}