{"id":"W2024611132","doi":"10.1016/j.jmaa.2007.04.011","title":"On a conjecture on the symmetric means","year":2007,"lang":"en","type":"article","venue":"Journal of Mathematical Analysis and Applications","topic":"Mathematical Inequalities and Applications","field":"Mathematics","cited_by":13,"is_retracted":false,"has_abstract":false,"ca_institutions":"The Scarborough Hospital; University of Toronto","funders":"Université de Montréal; Centre de Recherches Mathématiques","keywords":"Mathematics; Conjecture; Pure mathematics; Collatz conjecture; Combinatorics","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":[0.00539283,0.000849531,0.00198999,0.001650447,0.00365151,0.004096512,0.002660857,0.004749397,0.01532998],"category_scores_gemma":[0.02873498,0.0006443267,0.002269026,0.001964762,0.008705979,0.01551851,0.004951386,0.007891529,0.001738234],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001986587,"about_ca_system_score_gemma":0.00143166,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001522488,"about_ca_topic_score_gemma":0.0008637655,"domain_scores_codex":[0.9975326,0.0007047012,0.0001524529,0.0007178857,0.0005276342,0.0003647425],"domain_scores_gemma":[0.9822319,0.01106428,0.001194454,0.002579042,0.002025493,0.000904948],"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":[0.00003967836,0.00001338509,0.0001646207,0.00002581836,0.000006219413,0.00003222009,0.0001339538,0.0003686516,0.0001377445,0.9931002,0.003642905,0.002334736],"study_design_scores_gemma":[0.00001418519,0.000008480704,0.00009618567,0.000008706876,0.000003394115,0.00003205294,0.00003070505,0.001183037,0.00005392507,0.9971614,0.001400916,0.00000703703],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.3151133,0.004339991,0.3096177,0.1407995,0.009146736,0.0001072252,0.001326874,0.0006348554,0.2189137],"genre_scores_gemma":[0.9111155,0.002251323,0.03684416,0.009121059,0.00910764,0.0001787961,0.0008679578,0.0003130608,0.03020052],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01532998,"threshold_uncertainty_score":0.0512839,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05094030570812233,"score_gpt":0.3400531423879915,"score_spread":0.2891128366798692,"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."}}