{"id":"W2981854879","doi":"10.1093/imrn/rnaa231","title":"Lebesgue Decomposition of Non-Commutative Measures","year":2020,"lang":"en","type":"preprint","venue":"International Mathematics Research Notices","topic":"Holomorphic and Operator Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Manitoba","funders":"National Science Foundation","keywords":"Mathematics; Lebesgue integration; Norm (philosophy); Closure (psychology); Commutative property; Borel measure; Pure mathematics; Discrete mathematics; Algebra over a field; Probability measure","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.003365297,0.0003594376,0.0007789792,0.0004994872,0.0001381026,0.0002160575,0.001975834,0.0003425166,0.0004259423],"category_scores_gemma":[0.004156726,0.0003216953,0.0002724018,0.0002189267,0.0004995963,0.0001646438,0.001760488,0.001684437,0.0001818922],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002505885,"about_ca_system_score_gemma":0.0003877684,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00008315093,"about_ca_topic_score_gemma":0.00003676449,"domain_scores_codex":[0.9950496,0.0005228625,0.001043711,0.0005190434,0.002481295,0.0003834843],"domain_scores_gemma":[0.992722,0.003831981,0.0006235007,0.0006932105,0.001947467,0.0001817843],"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":[0.0004852678,0.003557788,0.0002755015,0.00949478,0.00352055,0.0002566625,0.0478244,0.001397856,0.02535061,0.886048,0.01847065,0.003317971],"study_design_scores_gemma":[0.0004867835,0.0001432512,0.00009856942,0.001889271,0.00009423605,0.000008900032,0.002786982,0.0337933,0.02320593,0.9366461,0.0004722427,0.0003744377],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7370707,0.0003741616,0.114505,0.006907972,0.001809601,0.003057885,0.001008131,0.0002702856,0.1349963],"genre_scores_gemma":[0.9268712,0.0000793171,0.07196108,0.00004680925,0.0003406734,0.0001397269,0.00008844357,0.00008039167,0.0003923167],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1898005,"threshold_uncertainty_score":0.9999235,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.3101742238677619,"score_gpt":0.5155230671996653,"score_spread":0.2053488433319035,"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."}}