{"id":"W2002007546","doi":"10.1007/bf01237176","title":"Depth of modular invariant rings","year":2000,"lang":"en","type":"article","venue":"Transformation Groups","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":20,"is_retracted":false,"has_abstract":false,"ca_institutions":"Royal Military College of Canada; Queen's University","funders":"","keywords":"Mathematics; Modular design; Invariant (physics); Pure mathematics; Ring (chemistry); Dimension (graph theory); Algebra over a field; Simple (philosophy); Modular representation theory; Modular form; Representation (politics); Modular invariance; Invariant theory; Representation theory; 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":[0.0009249701,0.0004719837,0.0006284162,0.001952098,0.0009846893,0.002643734,0.0006849803,0.0004903096,0.006617173],"category_scores_gemma":[0.002131805,0.0004405208,0.000466023,0.001042091,0.002514747,0.00736158,0.002075314,0.001715276,0.0007034751],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001142551,"about_ca_system_score_gemma":0.0004156074,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004855162,"about_ca_topic_score_gemma":0.0004746083,"domain_scores_codex":[0.9994155,0.0001219802,0.00002320825,0.00009430869,0.0001857026,0.000159262],"domain_scores_gemma":[0.9988851,0.0004896259,0.0001752411,0.0001000223,0.0001110994,0.0002389307],"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":[0.00008775641,0.00002731894,0.0008329006,0.00004719309,0.000008851848,0.0000663364,0.000557786,0.0006777795,0.001783232,0.9859251,0.0008962352,0.009089646],"study_design_scores_gemma":[0.00003034391,0.00003405625,0.001125504,0.00001276517,0.00002510006,0.0001396359,0.00016896,0.002434595,0.001302348,0.990837,0.003875659,0.00001404594],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.799713,0.002048502,0.0602592,0.001657314,0.0001224096,0.00006568341,0.0004667298,0.0003215687,0.1353457],"genre_scores_gemma":[0.9790614,0.0006858131,0.004888162,0.0001179286,0.0002394655,0.00002552193,0.0001771685,0.00004909189,0.01475535],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006617173,"threshold_uncertainty_score":0.02213663,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0274644998122572,"score_gpt":0.2536711531469028,"score_spread":0.2262066533346456,"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."}}