{"id":"W2140006841","doi":"10.1090/s0002-9947-2014-06108-4","title":"Essential normality and the decomposability of homogeneous submodules","year":2014,"lang":"en","type":"preprint","venue":"Transactions of the American Mathematical Society","topic":"Holomorphic and Operator Theory","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"Carleton University","funders":"","keywords":"Mathematics; Rank (graph theory); Homogeneous; Pure mathematics; Conjecture; Class (philosophy); Normality; Discrete mathematics; Combinatorics; Computer science","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005957366,0.0004671572,0.0004492527,0.000928331,0.0006368069,0.001084254,0.000580913,0.00027563,0.003640815],"category_scores_gemma":[0.00150812,0.0001968384,0.0008474701,0.0003249745,0.003136368,0.002913452,0.002306907,0.001273382,0.0005520292],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000698392,"about_ca_system_score_gemma":0.0004474165,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005596448,"about_ca_topic_score_gemma":0.0004949282,"domain_scores_codex":[0.9992564,0.0001017508,0.00003973504,0.0001869144,0.0002641305,0.000150989],"domain_scores_gemma":[0.9987432,0.0003414794,0.000140959,0.000249769,0.0002866569,0.0002378306],"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":[0.0000853503,0.00004862223,0.002452256,0.00007282957,0.0000254979,0.0006572407,0.001165653,0.001620585,0.02446972,0.9514127,0.0006965471,0.01729297],"study_design_scores_gemma":[0.00002185865,0.0001334428,0.002258741,0.00001468581,0.00002336349,0.0006581528,0.0004420941,0.01066091,0.0333454,0.9436975,0.008711599,0.00003241442],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7115828,0.0003315807,0.2532502,0.0004132342,0.00009041242,0.00006107619,0.0001987017,0.0003563152,0.03371574],"genre_scores_gemma":[0.9774868,0.0001341329,0.01341349,0.00008773538,0.00007680806,0.00003005874,0.0002152295,0.00007061403,0.008485179],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003640815,"threshold_uncertainty_score":0.01217967,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01648582938446116,"score_gpt":0.2861383086969128,"score_spread":0.2696524793124517,"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."}}