{"id":"W4403245098","doi":"10.1112/blms.13165","title":"Herglotz's representation and Carathéodory's approximation","year":2024,"lang":"en","type":"article","venue":"Bulletin of the London Mathematical Society","topic":"Holomorphic and Operator Theory","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Manitoba","funders":"Science and Engineering Research Board; Department of Science and Technology, Ministry of Science and Technology, India; Ministry of Education, India; Pacific Institute for the Mathematical Sciences","keywords":"Mathematics; Holomorphic function; Representation (politics); Representation theorem; Domain (mathematical analysis); Scaling; Pure mathematics; Mathematical analysis; Geometry","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0008816209,0.0001486603,0.0002639106,0.00001358857,0.0001106598,0.00006289046,0.0001925298,0.0001259067,0.0005815445],"category_scores_gemma":[0.0004356563,0.00009320743,0.0002699621,0.0001507293,0.0002599776,0.00003183196,0.0001435101,0.0002095829,0.00008411403],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003373354,"about_ca_system_score_gemma":0.00002315079,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00000671653,"about_ca_topic_score_gemma":3.581624e-7,"domain_scores_codex":[0.9987541,0.0001374918,0.000373779,0.0002388215,0.0003269134,0.0001689345],"domain_scores_gemma":[0.9986107,0.0008308741,0.00008438466,0.0003701686,0.000050765,0.00005305962],"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":[0.00001315473,0.0001168678,0.00004016389,0.001609746,0.0001221358,0.000003069178,0.003598193,0.000004536196,0.00257954,0.8913298,0.09918504,0.001397724],"study_design_scores_gemma":[0.0004094822,0.00004098742,0.0001138808,0.0005272317,0.0001847459,0.00007611817,0.001291325,0.005297109,0.008531329,0.9657518,0.01753687,0.0002391319],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8963832,0.001959104,0.05031925,0.01927805,0.000539435,0.001669762,0.00003442058,0.0005053291,0.02931149],"genre_scores_gemma":[0.9422167,0.0001269921,0.04687388,0.0004017614,0.0001446844,0.0000702885,0.000003471608,0.00006995618,0.01009225],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.08164818,"threshold_uncertainty_score":0.6367505,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02914830638041536,"score_gpt":0.2902814131888142,"score_spread":0.2611331068083988,"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."}}