{"id":"W2113848637","doi":"10.1007/978-3-0348-0142-3_16","title":"Borcea’s Variance Conjectures on the Critical Points of Polynomials","year":2011,"lang":"en","type":"preprint","venue":"","topic":"Advanced Mathematical Theories and Applications","field":"Physics and Astronomy","cited_by":13,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Guelph","funders":"","keywords":"Conjecture; Mathematics; Simple (philosophy); Rank (graph theory); Variance (accounting); Polynomial; Matrix (chemical analysis); Pure mathematics; Combinatorics; Mathematical analysis","routes":{"ca_aff":true,"ca_fund":false,"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":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0001384831,0.0001809863,0.0003041223,0.0000143874,0.00007605861,0.00002287768,0.0003535633,0.00006678289,0.004716571],"category_scores_gemma":[0.00006981251,0.0001067724,0.0001555633,0.000035445,0.0002351538,0.00001622977,0.0002703315,0.0003133068,0.00007369161],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000006248567,"about_ca_system_score_gemma":0.00004300847,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00005700135,"about_ca_topic_score_gemma":2.920223e-7,"domain_scores_codex":[0.999157,0.00004162738,0.0002889986,0.0002443079,0.0001023883,0.0001656367],"domain_scores_gemma":[0.9982727,0.0008169062,0.0001305114,0.0006574591,0.00007012321,0.00005235838],"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":[0.00000811053,0.0001031445,0.000007768985,0.00002420749,0.0000405397,6.141482e-8,0.00009504262,0.00002000085,0.00009134478,0.997877,0.001219006,0.0005137842],"study_design_scores_gemma":[0.00005139552,0.00001482312,0.00002521307,0.00006478478,0.00002922715,9.619615e-8,0.0001216122,0.00004597392,0.0119432,0.9859279,0.001655201,0.0001205471],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.003358803,0.00002809541,0.4815185,0.002619688,0.0001712343,0.0005236068,0.0002423545,0.00003506751,0.5115026],"genre_scores_gemma":[0.9898465,0.000002252957,0.008455021,0.0002581593,0.0002352159,0.0001375166,0.00001137413,0.00001818209,0.001035819],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.9864876,"threshold_uncertainty_score":0.9961932,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0349429025034424,"score_gpt":0.3158979637973607,"score_spread":0.2809550612939183,"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."}}