{"id":"W4380153802","doi":"10.1007/s00025-023-01938-y","title":"On a Characterization of Shifts of Haar Distributions on Compact Open Subgroups of a Compact Abelian Group","year":2023,"lang":"en","type":"article","venue":"Results in Mathematics","topic":"advanced mathematical theories","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Mathematics; Abelian group; Compact group; Locally compact space; Haar measure; Real line; Random variable; Distribution (mathematics); Group (periodic table); Automorphism; Characterization (materials science); Elementary abelian group; Locally compact group; Pure mathematics; Haar; Discrete mathematics; Mathematical analysis; Lie group; Statistics","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.001636874,0.0003120989,0.001208451,0.0003659248,0.00005654628,0.00002364882,0.0007305307,0.0001441154,0.00003405457],"category_scores_gemma":[0.005236023,0.000260466,0.0001580041,0.0012499,0.0002673899,0.0001762959,0.0001569713,0.0002313639,0.00003149103],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00009670039,"about_ca_system_score_gemma":0.00004466201,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001213356,"about_ca_topic_score_gemma":0.00001039331,"domain_scores_codex":[0.9967325,0.0001557414,0.001818027,0.000297836,0.0006342258,0.0003616078],"domain_scores_gemma":[0.9930946,0.004321612,0.00131595,0.001018442,0.0001587172,0.00009072122],"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":[0.000384001,0.002160155,0.00004695038,0.001877745,0.00007006618,0.000005513662,0.003065669,0.000131539,0.01666689,0.9751867,0.0002837305,0.0001210096],"study_design_scores_gemma":[0.001773278,0.0005255034,0.00258409,0.00321671,0.00004898099,0.000002123981,0.0005130293,0.002914209,0.03222899,0.9559076,0.00003625205,0.0002491768],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9762067,0.00000370362,0.01136198,0.0002742285,0.00008713271,0.001540056,0.002043511,0.0001119914,0.008370657],"genre_scores_gemma":[0.9893422,0.00002246614,0.01010467,0.000008802526,0.00001610873,0.00001852329,0.0002151581,0.00005803294,0.0002141116],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01927907,"threshold_uncertainty_score":0.9999847,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07372719914894549,"score_gpt":0.3682286073595424,"score_spread":0.2945014082105969,"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."}}