{"id":"W2066236747","doi":"10.1016/s0024-3795(00)00037-9","title":"Estimates for the spectrum near algebraic elements","year":2000,"lang":"en","type":"article","venue":"Linear Algebra and its Applications","topic":"Advanced Topics in Algebra","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université Laval","funders":"","keywords":"Mathematics; Banach algebra; Spectrum (functional analysis); Eigenvalues and eigenvectors; Algebraic number; Hausdorff space; Linear algebra; Degree (music); Pure mathematics; Algebra over a field; Combinatorics; Banach space; Mathematical analysis; 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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.000158129,0.0001749503,0.0001745013,0.00002393241,0.0006192392,0.00006631239,0.000286471,0.00006781508,0.0006663033],"category_scores_gemma":[0.0001140103,0.0001306956,0.00006666603,0.000180903,0.00009839187,0.0001012096,0.00004791738,0.0001397683,0.0001705679],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001686412,"about_ca_system_score_gemma":0.00002480922,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002161649,"about_ca_topic_score_gemma":0.000006538237,"domain_scores_codex":[0.9989316,0.00001171125,0.0003192767,0.0003037073,0.0001409937,0.0002926813],"domain_scores_gemma":[0.9984788,0.0008494289,0.00008499313,0.0004614901,0.00004526421,0.00008002958],"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":[0.00001002928,0.00008265665,0.00006224112,0.00004927067,0.00006101701,2.226679e-7,0.0001489799,0.00001166199,0.00009943663,0.9717398,0.001083144,0.0266515],"study_design_scores_gemma":[0.0003480838,0.00003602361,0.0001897649,0.000009642104,0.00008673128,0.000007335383,0.00003077917,0.0105278,0.001421707,0.7944919,0.1926826,0.0001676244],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3806439,0.008015616,0.5577112,0.02365815,0.0003518687,0.01379725,0.0004817351,0.001405001,0.01393523],"genre_scores_gemma":[0.4967199,0.001456407,0.4712463,0.002331622,0.001905365,0.006071473,0.0001628003,0.0002762148,0.01982992],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.1915995,"threshold_uncertainty_score":0.7295554,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03093295059607458,"score_gpt":0.3278813043029583,"score_spread":0.2969483537068837,"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."}}