{"id":"W4391103088","doi":"10.3390/math12020352","title":"The Augmented Weak Sharpness of Solution Sets in Equilibrium Problems","year":2024,"lang":"en","type":"article","venue":"Mathematics","topic":"Optimization and Variational Analysis","field":"Computer Science","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Alberta","funders":"Natural Science Foundation of Shandong Province; Natural Sciences and Engineering Research Council of Canada; National Natural Science Foundation of China; University of Alberta","keywords":"Mathematical optimization; Degenerate energy levels; Degeneracy (biology); Solution set; Solution concept; Premise; Variational inequality; Mathematics; Set (abstract data type); Finite set; Regular polygon; Optimization problem; Computer science; Applied 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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004003303,0.00005135957,0.00008001451,0.00007854367,0.00003320043,0.00012711,0.0002836336,0.00002221323,0.00001662063],"category_scores_gemma":[0.00004097065,0.00003390566,0.00003951735,0.0005919052,0.00001641065,0.0001728345,0.00009427803,0.00004374566,0.00002857931],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002498406,"about_ca_system_score_gemma":0.00003701812,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000007800025,"about_ca_topic_score_gemma":0.00001306801,"domain_scores_codex":[0.9993385,0.00002456164,0.0002480962,0.0001042066,0.0001917175,0.00009290729],"domain_scores_gemma":[0.9995419,0.0001440727,0.00005451307,0.0001928287,0.00005075168,0.00001595399],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[9.114796e-7,0.0001428017,0.00008721025,0.000304697,0.00004935071,0.000001458222,0.002932874,0.0137735,0.001049708,0.976155,0.001214984,0.004287452],"study_design_scores_gemma":[0.00004661408,0.00000685107,0.000116046,0.00006540478,0.000005756561,0.000001659845,0.00002725074,0.964992,0.0001519345,0.03389487,0.0006524984,0.0000390507],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.002237604,0.0002054101,0.9917142,0.002819557,0.0001498105,0.0001240243,0.000002584071,0.00007439531,0.002672417],"genre_scores_gemma":[0.8973265,0.00005502624,0.09990264,0.00005335908,0.0000294462,0.00003813984,0.00001147364,0.00001372274,0.002569651],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.9512185,"threshold_uncertainty_score":0.1382633,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02156666159529515,"score_gpt":0.2622413077359841,"score_spread":0.240674646140689,"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."}}