{"id":"W2050554783","doi":"10.1007/s000140300008","title":"SAGBI bases in rings of multiplicative invariants","year":2003,"lang":"en","type":"article","venue":"Commentarii Mathematici Helvetici","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":11,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"","keywords":"Mathematics; Multiplicative function; Ring (chemistry); Multiplicative group; Combinatorics; Finite field; Field (mathematics); Pure mathematics; Mathematical analysis; Chemistry","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":["metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001345212,0.000301573,0.0006657182,0.0002349776,0.00008078474,0.00001805199,0.0003881705,0.0001149718,0.001451134],"category_scores_gemma":[0.001947889,0.0002768705,0.0001305933,0.0004818939,0.0001803322,0.0001432102,0.0001300288,0.0002597701,0.00009653992],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001021896,"about_ca_system_score_gemma":0.00004628627,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00007274829,"about_ca_topic_score_gemma":0.00005094719,"domain_scores_codex":[0.9977059,0.0003144826,0.0008964324,0.0003253333,0.0003249994,0.0004327915],"domain_scores_gemma":[0.9960996,0.002597042,0.0003885173,0.0007289333,0.00007358783,0.0001123442],"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":[0.00005472559,0.002126449,0.007678907,0.0007203949,0.0001529332,0.00001587185,0.008328073,0.000003712729,0.001861588,0.9765134,0.002146381,0.0003975981],"study_design_scores_gemma":[0.00168599,0.000117339,0.0009798616,0.0004566005,0.00008770792,0.00003251841,0.004161797,0.0001150096,0.06346732,0.9275293,0.0009887319,0.0003777987],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9527662,0.0001101259,0.008363763,0.0003936709,0.0001078839,0.0008469646,0.00001790977,0.00007433711,0.03731908],"genre_scores_gemma":[0.9703047,0.00001292713,0.02860325,0.0004503119,0.0000134205,0.00008783094,0.000004783111,0.0000454382,0.0004772941],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.06160574,"threshold_uncertainty_score":0.9999683,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06379215026209464,"score_gpt":0.3244592707036333,"score_spread":0.2606671204415386,"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."}}