{"id":"W3203715069","doi":"10.1007/s11117-022-00928-8","title":"A four-mean theorem and its application to pseudospectra","year":2022,"lang":"en","type":"article","venue":"Positivity","topic":"Mathematical Inequalities and Applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université Laval","funders":"Fonds de recherche du Québec – Nature et technologies; Natural Sciences and Engineering Research Council of Canada; Canada Research Chairs","keywords":"Combinatorics; Mathematics; Integer (computer science); Polynomial; Zero (linguistics); Potential theory; Physics; 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":[0.0004872835,0.00009258955,0.0001459004,0.00003209482,0.0002946513,0.00002326388,0.0001244164,0.00001858174,0.0002291537],"category_scores_gemma":[0.00007372129,0.00008966781,0.00003691041,0.0001636025,0.00001523599,0.00003754069,0.000189309,0.00011537,0.00003256668],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004636357,"about_ca_system_score_gemma":0.000008592711,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001894023,"about_ca_topic_score_gemma":0.00001271948,"domain_scores_codex":[0.9991868,0.00008066275,0.0001612952,0.0002122423,0.0001931896,0.0001658618],"domain_scores_gemma":[0.9991653,0.0003991846,0.00005574413,0.0002558956,0.00002767363,0.00009622432],"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":[0.000007126376,0.0001246788,0.00001979475,0.00003982656,0.000008327021,9.4492e-7,0.0009026969,0.000003383988,0.005750501,0.9911482,0.0003723741,0.001622183],"study_design_scores_gemma":[0.000137834,0.00006864247,0.0003933229,0.000006981199,0.00002622648,0.00003365383,0.0002564761,0.004333227,0.003343137,0.9886917,0.002532137,0.0001766468],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8687054,0.00002714466,0.1094162,0.004149693,0.000026169,0.001020873,0.0001256296,0.0001717582,0.01635717],"genre_scores_gemma":[0.9940112,0.000001440407,0.004371068,0.0003475538,0.0000445144,0.0006275081,0.000004936457,0.00001693572,0.0005748632],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1253058,"threshold_uncertainty_score":0.3656547,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05647830301065556,"score_gpt":0.3254280200908226,"score_spread":0.2689497170801671,"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."}}