{"id":"W2963025361","doi":"10.1142/s1005386715000346","title":"Standard Monomial Theory of RR Varieties","year":2015,"lang":"en","type":"article","venue":"Algebra Colloquium","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"Dawson College; Champlain Regional College; Cegep de Trois-Rivieres; Cegep de Thetford","funders":"","keywords":"Monomial; Mathematics; Homogeneous; Construct (python library); Pure mathematics; Monomial basis; Algebra over a field; 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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0008040669,0.0002009638,0.0004429925,0.00013111,0.00006345185,0.00002388892,0.0002843727,0.0001257181,0.0002101003],"category_scores_gemma":[0.001009676,0.0001797214,0.0001206435,0.0003397961,0.0001910656,0.0002064171,0.0001475236,0.0001545023,0.00005014239],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007558351,"about_ca_system_score_gemma":0.0002319805,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000003017908,"about_ca_topic_score_gemma":0.000007911794,"domain_scores_codex":[0.9985094,0.0001097888,0.0004165574,0.000240567,0.0004092361,0.0003144564],"domain_scores_gemma":[0.9983656,0.0005171903,0.0002062916,0.0004874389,0.0002509056,0.0001725502],"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":[0.0004659393,0.00009779053,0.0006216067,0.00005989562,0.00008935136,0.000008116703,0.001308729,0.00001348105,0.0002431727,0.9794886,0.01533271,0.002270633],"study_design_scores_gemma":[0.001074,0.0002754446,0.0001272,0.00001901502,0.00005756854,0.000006919329,0.001566963,0.00001304448,0.01008267,0.9801893,0.006370537,0.0002173478],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9168119,0.0005081007,0.05383737,0.0002517046,0.0009213883,0.0003944964,0.00005947299,0.0001989479,0.02701663],"genre_scores_gemma":[0.9875917,0.00001190207,0.008903839,0.0001130193,0.000196004,0.00002184144,0.000005407515,0.00004239446,0.003113823],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.07077988,"threshold_uncertainty_score":0.7328826,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05103561184403476,"score_gpt":0.3037909591274975,"score_spread":0.2527553472834627,"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."}}