{"id":"W3154583678","doi":"10.1112/jlms.12856","title":"Gröbner bases, symmetric matrices, and type C Kazhdan–Lusztig varieties","year":2024,"lang":"en","type":"article","venue":"Journal of the London Mathematical Society","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"McMaster University","funders":"Natural Sciences and Engineering Research Council of Canada; European Commission; National Science Foundation","keywords":"Mathematics; Variety (cybernetics); Ideal (ethics); Class (philosophy); Pure mathematics; Type (biology); Hilbert–Poincaré series; Combinatorics; Hilbert scheme; Matrix (chemical analysis); Prime ideal; Schubert variety; Polynomial; Boolean prime ideal theorem; Prime (order theory); Algebra over a field; Mathematical analysis; Computer science","routes":{"ca_aff":true,"ca_fund":true,"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":[0.001767487,0.0003272822,0.0007031124,0.0001015034,0.0001970118,0.0002571514,0.0006113444,0.0002187764,0.0001468637],"category_scores_gemma":[0.002791838,0.0001886147,0.0006383493,0.001090524,0.0002303443,0.0003314759,0.0003356534,0.0008777226,0.00003769526],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000205438,"about_ca_system_score_gemma":0.0001557504,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001177638,"about_ca_topic_score_gemma":2.613093e-7,"domain_scores_codex":[0.9972311,0.0001438376,0.00104863,0.0002248945,0.0009753707,0.0003761503],"domain_scores_gemma":[0.9951485,0.003365536,0.0005124388,0.0004832183,0.0003061683,0.0001841727],"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":[0.00002399152,0.0002430394,0.00003605013,0.002376944,0.0003598973,0.00002653496,0.001485766,0.000007959814,0.0004494252,0.9564659,0.0373194,0.001205112],"study_design_scores_gemma":[0.0004025578,0.0001292846,0.00001849448,0.0007009896,0.0004399223,0.0005662643,0.0003122345,0.002942548,0.0005907439,0.9841587,0.009510982,0.0002272819],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5695475,0.04501849,0.3361323,0.0156491,0.01476365,0.002974693,0.00004976663,0.0009696863,0.01489487],"genre_scores_gemma":[0.5215772,0.002426095,0.4646773,0.0007764373,0.002103251,0.00002240318,0.000001130827,0.0003492062,0.008066995],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.128545,"threshold_uncertainty_score":0.7691483,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02732214632728516,"score_gpt":0.3026542148050216,"score_spread":0.2753320684777365,"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."}}