{"id":"W2136428261","doi":"10.1155/s0161171204311312","title":"On the Putnam‐Fuglede theorem","year":2004,"lang":"en","type":"article","venue":"International Journal of Mathematics and Mathematical Sciences","topic":"Mathematics and Applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Lakehead University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Discrete mathematics; Pure mathematics; Algebra over a field","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":[],"consensus_categories":[],"category_scores_codex":[0.002425646,0.0001978604,0.0003395839,0.0001501103,0.0002372302,0.0002684725,0.001083234,0.000059678,0.0002869703],"category_scores_gemma":[0.002436539,0.0001006916,0.0001698767,0.0001879259,0.0005137358,0.0001517418,0.0001399889,0.0002319719,0.00004340543],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005025719,"about_ca_system_score_gemma":0.00009119073,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001583917,"about_ca_topic_score_gemma":0.000001638458,"domain_scores_codex":[0.9975559,0.00003167367,0.0008345349,0.0001668711,0.001184992,0.0002260674],"domain_scores_gemma":[0.9959863,0.002701254,0.0006572836,0.000241348,0.0002882134,0.0001255296],"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":[0.000004384483,0.0004914561,0.000002325318,0.00003670687,0.00006514623,0.000009109867,0.0009501975,0.00002161407,0.0002643169,0.9961947,0.001477794,0.000482221],"study_design_scores_gemma":[0.0003537505,0.0001448702,0.000005036949,0.0003792932,0.00003913675,0.0003569478,0.001211263,0.0006379754,0.00102063,0.9952505,0.0004773474,0.0001232202],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.724687,0.0001104871,0.193472,0.03557358,0.0004483461,0.0006280253,0.00001575911,0.00006057681,0.04500421],"genre_scores_gemma":[0.8059253,0.00007161683,0.1931404,0.0004830816,0.0001888654,0.00001906138,2.8243e-7,0.00002222194,0.0001491224],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.08123834,"threshold_uncertainty_score":0.4106085,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06156151179183818,"score_gpt":0.3594038514746388,"score_spread":0.2978423396828007,"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."}}