{"id":"W2043041545","doi":"10.1016/j.jfa.2003.09.014","title":"A new proof of Poltoratskii's theorem","year":2004,"lang":"en","type":"article","venue":"Journal of Functional Analysis","topic":"Spectral Theory in Mathematical Physics","field":"Mathematics","cited_by":24,"is_retracted":false,"has_abstract":false,"ca_institutions":"McGill University","funders":"Natural Sciences and Engineering Research Council of Canada; Israel Science Foundation","keywords":"Mathematics; Borel measure; Lebesgue measure; Measure (data warehouse); Simple (philosophy); Discrete mathematics; Pure mathematics; Lebesgue integration; Combinatorics; Probability measure","routes":{"ca_aff":true,"ca_fund":true,"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":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0006814261,0.0001435251,0.0006240435,0.0003784976,0.00004056135,0.00001865162,0.000226394,0.00006007191,0.00101337],"category_scores_gemma":[0.0005714992,0.0001014081,0.0008780397,0.001206435,0.00007007152,0.0001884996,0.00002608346,0.0002186467,0.00001094539],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001161739,"about_ca_system_score_gemma":0.0002079436,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000008270286,"about_ca_topic_score_gemma":0.000004991493,"domain_scores_codex":[0.9981018,0.00005718638,0.0008279354,0.0001060828,0.0007596574,0.0001473499],"domain_scores_gemma":[0.9978563,0.000462407,0.0008666895,0.000235853,0.0004372956,0.0001414435],"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":[0.0001681104,0.0004578028,0.0001718538,0.0000427544,0.003385137,0.00001027693,0.0002470365,0.009480505,0.003326002,0.9812499,0.0009297912,0.0005307915],"study_design_scores_gemma":[0.0005271576,0.0001768882,0.0004869617,0.00003897084,0.002179515,0.00003733808,0.0001061602,0.00008709783,0.01288813,0.9833274,0.00004728534,0.00009702609],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1647361,0.00009263383,0.8301866,0.0008001886,0.0001481175,0.00007792447,0.000005643526,0.00001419808,0.00393858],"genre_scores_gemma":[0.9480575,0.000003574567,0.05100911,0.0000500543,0.0004473815,8.227472e-7,0.000001439767,0.00001543308,0.000414684],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.7833214,"threshold_uncertainty_score":0.9998999,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03440021059056465,"score_gpt":0.2994054370128814,"score_spread":0.2650052264223168,"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."}}