{"id":"W4214845636","doi":"10.1090/proc/16049","title":"Roots of the identity operator and proximal mappings: (Classical and phantom) cycles and gap vectors","year":2022,"lang":"en","type":"article","venue":"Proceedings of the American Mathematical Society","topic":"Optimization and Variational Analysis","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Okanagan University College; University of British Columbia, Okanagan Campus; University of British Columbia","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Lemma (botany); Mathematics; Conjecture; Convex set; Imaging phantom; Regular polygon; Hilbert space; Operator (biology); Pure mathematics; Duality (order theory); Identity (music); Set (abstract data type); Convex analysis; Operator theory; Normed vector space; Combinatorics; Mathematical analysis; Geometry; Computer science; Convex optimization; 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":[0.00107576,0.0005885673,0.0007863438,0.002218114,0.001235227,0.002250642,0.0008821178,0.00130129,0.005071407],"category_scores_gemma":[0.005663736,0.0004120659,0.0006011053,0.001151829,0.00408852,0.005616424,0.00294388,0.00206945,0.0004667099],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001314216,"about_ca_system_score_gemma":0.0007228223,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009156172,"about_ca_topic_score_gemma":0.0004989245,"domain_scores_codex":[0.9993362,0.0001499748,0.00002992983,0.0001700246,0.0001842989,0.0001295507],"domain_scores_gemma":[0.9983486,0.0006289498,0.0002322523,0.000131394,0.0003133145,0.0003455114],"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":[0.00001623155,0.000005351959,0.000186233,0.00001437833,0.000002424735,0.00004347307,0.0001396731,0.0007384123,0.0004115885,0.9951428,0.0002479255,0.003051584],"study_design_scores_gemma":[0.000006808591,0.00001438278,0.0001840606,0.000008385578,0.000001742016,0.00008246032,0.00009627698,0.006851114,0.0003945737,0.9910568,0.001295478,0.000007948245],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5785245,0.001750494,0.363756,0.002382611,0.0001730762,0.00008200695,0.0002787286,0.0001759786,0.05287656],"genre_scores_gemma":[0.960472,0.0005125793,0.02873981,0.0001926845,0.0001020284,0.00006812513,0.0001168479,0.00009757674,0.009698419],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005071407,"threshold_uncertainty_score":0.01696551,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01199151137471313,"score_gpt":0.2434513830502556,"score_spread":0.2314598716755425,"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."}}