{"id":"W4402219439","doi":"10.1090/proc/16931","title":"A generalization of Darboux-Froda theorem and its applications","year":2024,"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":"Western University","funders":"Natural Sciences and Engineering Research Council of Canada; National Natural Science Foundation of China","keywords":"Uncountable set; Countable set; Mathematics; Monotone polygon; Lemma (botany); Generalization; Classification of discontinuities; Discrete mathematics; Jump; Pure mathematics; Mathematical analysis","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":[0.0002300512,0.00006922086,0.0001588439,0.00002621627,0.00006179905,0.00006581547,0.0003563911,0.00001792722,0.0000117996],"category_scores_gemma":[0.00006580458,0.00004489364,0.0001327839,0.001007444,0.0001391713,0.0001713191,0.0001770256,0.00005108477,0.00000291793],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001479062,"about_ca_system_score_gemma":0.00002342834,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002415179,"about_ca_topic_score_gemma":3.648648e-8,"domain_scores_codex":[0.9993016,0.000005479072,0.0002160707,0.0001680842,0.000229869,0.00007896053],"domain_scores_gemma":[0.9994295,0.00009481023,0.000173143,0.0000873145,0.000181701,0.00003356514],"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":[4.928608e-7,0.00002888321,0.0000801859,0.0001592556,0.00004788382,5.638408e-9,0.0007461476,0.00004501858,0.003833508,0.9939839,0.0001946883,0.0008800655],"study_design_scores_gemma":[0.00003780095,0.00001542711,0.000295129,0.00004218257,0.00004798933,0.000002544007,0.000145579,0.7524431,0.003245716,0.243399,0.0002568184,0.00006864152],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.03507948,0.0002299747,0.9548303,0.005438073,0.0000201271,0.0002864798,0.000007514206,0.0001078245,0.004000179],"genre_scores_gemma":[0.9050048,0.0001030332,0.09447559,0.0002099497,0.00002608882,0.00002868478,6.289167e-7,0.000007040358,0.0001442123],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.8699253,"threshold_uncertainty_score":0.1830709,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.00847304478455699,"score_gpt":0.2463466814574323,"score_spread":0.2378736366728753,"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."}}