{"id":"W4391211282","doi":"10.4153/s0008414x24000099","title":"Tracial oscillation zero and stable rank one","year":2024,"lang":"en","type":"article","venue":"Canadian Journal of Mathematics","topic":"Advanced Operator Algebra Research","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Mathematics; Surjective function; Rank (graph theory); Separable space; Zero (linguistics); Converse; Crossed product; Simple (philosophy); Pure mathematics; Semigroup; Banach space; Affine transformation; Combinatorics; Algebra over a field; 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":[],"consensus_categories":[],"category_scores_codex":[0.0009091336,0.0001248097,0.000291669,0.0003557114,0.0001203537,0.0002230723,0.0001579445,0.00008303735,0.0004941262],"category_scores_gemma":[0.0009994549,0.000109191,0.00006798597,0.0002503472,0.0000949969,0.0003206048,0.00001309096,0.0003417199,0.00004541283],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001910005,"about_ca_system_score_gemma":0.0009169833,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000668104,"about_ca_topic_score_gemma":0.001563341,"domain_scores_codex":[0.9987382,0.00004061619,0.0004769699,0.0001068914,0.0003354127,0.0003019075],"domain_scores_gemma":[0.9985859,0.0004497035,0.0001046064,0.0001561744,0.0002143904,0.0004891641],"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":[0.00002738203,0.0001659353,0.0004491697,0.003938476,0.000541747,0.001224431,0.01557487,0.0001212572,0.003117519,0.917863,0.02583158,0.03114462],"study_design_scores_gemma":[0.0005896538,0.0002029766,0.00009900201,0.001115771,0.0001571055,0.0008313741,0.0009043906,0.00383182,0.001202568,0.9698416,0.02089265,0.0003310821],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8765169,0.004586654,0.1084541,0.001672449,0.0005640447,0.0005050334,0.00005928393,0.00005418747,0.007587328],"genre_scores_gemma":[0.9147643,0.00006990377,0.08291551,0.00003210159,0.0002888825,0.000003090484,0.000001122468,0.00006892633,0.001856099],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.05197859,"threshold_uncertainty_score":0.5410335,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06308011263660174,"score_gpt":0.325979084187693,"score_spread":0.2628989715510913,"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."}}