{"id":"W2013749589","doi":"10.4153/cmb-2011-016-6","title":"The Saddle-Point Method and the Li Coefficients","year":2011,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Saddle point; Saddle; Point (geometry); Applied mathematics; Geometry; Mathematical optimization","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.005340131,0.0002091843,0.0003483824,0.00007204136,0.0006335754,0.0001335481,0.00068498,0.0001032919,0.01028388],"category_scores_gemma":[0.00518987,0.0001061197,0.0001227253,0.0001786474,0.001083728,0.00001878456,0.0001570419,0.0003935355,0.004372354],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001002251,"about_ca_system_score_gemma":0.0001528765,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001143265,"about_ca_topic_score_gemma":0.001298018,"domain_scores_codex":[0.9975866,0.0006008474,0.0004359754,0.0002765604,0.0003828851,0.0007171133],"domain_scores_gemma":[0.9929568,0.005447774,0.00008846061,0.0007946357,0.0001150489,0.0005972413],"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":[0.00004387471,0.00003023036,0.00001013977,0.00004543597,0.00006333904,0.0000216946,0.001978515,1.259553e-7,9.842236e-7,0.9730285,0.02299922,0.001777927],"study_design_scores_gemma":[0.0006114781,0.00002379868,0.00001968519,0.00004870861,0.00006681142,0.0000874121,0.001234929,0.001267152,0.00003986435,0.9546645,0.04178074,0.0001549799],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.01496927,0.0005223247,0.2137223,0.04512411,0.000228202,0.003012084,0.0000365157,0.0001754104,0.7222098],"genre_scores_gemma":[0.9002764,0.00005583674,0.03410785,0.002739436,0.0001997976,0.0003176355,0.000002565137,0.0001761641,0.06212436],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.8853071,"threshold_uncertainty_score":0.9964029,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06296597995323638,"score_gpt":0.3158357938399637,"score_spread":0.2528698138867274,"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."}}