{"id":"W2067961285","doi":"10.4153/cmb-2014-055-3","title":"Spectral Flows of Dilations of Fredholm Operators","year":2014,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Spectral Theory in Mathematical Physics","field":"Mathematics","cited_by":19,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Unitary state; Dilation (metric space); Contraction (grammar); Fredholm theory; Pure mathematics; Fredholm operator; Flow (mathematics); Mathematical analysis; Operator (biology); Pseudodifferential operators; Cone (formal languages); Fredholm integral equation; Compact operator; Geometry; Integral equation; Algorithm","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":["metaepi_narrow","insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.0007316772,0.0002780565,0.0007764455,0.0001948844,0.00008018752,0.00002178032,0.0005110101,0.0001606026,0.01445599],"category_scores_gemma":[0.003535794,0.0002475921,0.0002505433,0.0003215177,0.0003084421,0.00004222259,0.00004811735,0.0002405878,0.00158316],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001019461,"about_ca_system_score_gemma":0.0001499974,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002490392,"about_ca_topic_score_gemma":0.0004368853,"domain_scores_codex":[0.9977034,0.0001548659,0.0009444163,0.0002744831,0.0004040446,0.0005187964],"domain_scores_gemma":[0.9965659,0.001720188,0.0002270518,0.0008115504,0.0001650274,0.0005102173],"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":[0.00000548272,0.0001539866,0.00004186295,0.0003964442,0.00004523425,0.000002433911,0.0003498784,0.0000171964,0.0014563,0.9945927,0.002780704,0.0001577453],"study_design_scores_gemma":[0.0002776333,0.0000937377,0.00006851192,0.0002057165,0.00007712376,0.000009342856,0.0001507636,0.001728328,0.00681022,0.9885873,0.001736347,0.0002549861],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8055536,0.00002022869,0.03219406,0.00168362,0.0001153605,0.0006789083,0.00007601087,0.0001003528,0.1595779],"genre_scores_gemma":[0.9401236,0.00000127335,0.05907147,0.0001104568,0.0001057593,0.00002218968,0.000004682181,0.00006386812,0.0004966594],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1590812,"threshold_uncertainty_score":0.9999976,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02105082551620785,"score_gpt":0.2632597833097834,"score_spread":0.2422089577935756,"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."}}