{"id":"W1966201024","doi":"10.1016/j.jfa.2009.10.003","title":"Linear maps preserving the minimum and reduced minimum moduli","year":2009,"lang":"en","type":"article","venue":"Journal of Functional Analysis","topic":"Advanced Topics in Algebra","field":"Mathematics","cited_by":21,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université Laval","funders":"","keywords":"Mathematics; Moduli; Modulus; Linear algebra; Mathematical analysis; Pure mathematics; Combinatorics; Geometry","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0006930032,0.0006877728,0.0008486668,0.002865616,0.001309888,0.003157483,0.00102343,0.001383246,0.008562976],"category_scores_gemma":[0.002930823,0.0005376025,0.0008643211,0.0008984901,0.002391865,0.006868721,0.002487712,0.003454233,0.00117691],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009101766,"about_ca_system_score_gemma":0.0004942978,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000295437,"about_ca_topic_score_gemma":0.0003255696,"domain_scores_codex":[0.9994513,0.00009568496,0.00003141813,0.00011543,0.0001697583,0.0001363279],"domain_scores_gemma":[0.9989879,0.000233719,0.0001843786,0.0002056941,0.0001673941,0.0002209871],"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":[0.000056034,0.00001951037,0.0001178139,0.00002395421,0.00000813659,0.00007227698,0.0001302967,0.0003097017,0.002539095,0.9911302,0.0004809529,0.005111984],"study_design_scores_gemma":[0.00002583854,0.000036158,0.0003462085,0.00001247515,0.00001244285,0.0002716398,0.0001268785,0.00333996,0.002546385,0.9907761,0.002489579,0.00001627625],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7071053,0.0008662754,0.1366473,0.003263702,0.0004670525,0.00008731759,0.0003745688,0.0005789192,0.1506095],"genre_scores_gemma":[0.9489051,0.0004680827,0.01553749,0.0003441371,0.0005017835,0.00007308009,0.0002628214,0.0003425213,0.03356498],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.008562976,"threshold_uncertainty_score":0.02864605,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04429955226996397,"score_gpt":0.3096151232359166,"score_spread":0.2653155709659527,"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."}}