{"id":"W2004261989","doi":"10.1006/jabr.2001.8840","title":"The Depth of Invariant Rings and Cohomology","year":2001,"lang":"en","type":"article","venue":"Journal of Algebra","topic":"Finite Group Theory Research","field":"Mathematics","cited_by":22,"is_retracted":false,"has_abstract":false,"ca_institutions":"Queen's University","funders":"","keywords":"Mathematics; Pure mathematics; Invariant (physics); Cohomology; Mathematical physics","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":[],"consensus_categories":[],"category_scores_codex":[0.00193762,0.00006278773,0.000208806,0.00008715147,0.00006794802,0.00002338568,0.0002503493,0.00004939965,0.00006629616],"category_scores_gemma":[0.001314923,0.00003707074,0.00005667822,0.0001145572,0.0001863018,0.00007957668,0.00008024309,0.000264848,0.000004792957],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001835238,"about_ca_system_score_gemma":0.00005504534,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004403503,"about_ca_topic_score_gemma":0.00001761408,"domain_scores_codex":[0.9989749,0.0001563022,0.0003959308,0.00005219313,0.0002546396,0.0001660776],"domain_scores_gemma":[0.9976097,0.001658751,0.0003295089,0.0001585305,0.0001747748,0.00006874585],"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":[0.0007262257,0.0002103219,0.02575423,0.00009308069,0.0003182252,0.0004144093,0.001800105,0.00000163725,0.006401533,0.9483443,0.004975288,0.0109606],"study_design_scores_gemma":[0.0009019722,0.0005470905,0.01842524,0.00006480577,0.00004417322,0.002716773,0.0004659783,0.00005843545,0.002005039,0.9713597,0.003335648,0.00007515031],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9943445,0.0003969716,0.0005245452,0.001053843,0.00007378487,0.00006159157,5.091067e-7,0.000003554365,0.00354066],"genre_scores_gemma":[0.9972317,0.0003508944,0.001893043,0.00004821248,0.00008693618,6.983115e-7,6.034977e-8,0.00001175917,0.0003767077],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.02301534,"threshold_uncertainty_score":0.1574181,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05478183459676571,"score_gpt":0.3330708725227793,"score_spread":0.2782890379260136,"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."}}