{"id":"W2178583511","doi":"10.46298/dmtcs.2852","title":"Criteria for rational smoothness of some symmetric orbit closures","year":2010,"lang":"en","type":"article","venue":"Discrete Mathematics & Theoretical Computer Science","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"Toronto Metropolitan University","funders":"","keywords":"Mathematics; Combinatorics; Bruhat order; Weyl group; Algebraic group; Orbit (dynamics); Schubert variety; Reductive group; Algebraic number; Mathematical analysis","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":[0.001230472,0.0005313409,0.0007351779,0.00337808,0.001808998,0.002848853,0.0008860497,0.001198497,0.002998085],"category_scores_gemma":[0.008384979,0.0006239149,0.001012026,0.0007422369,0.004325405,0.00300104,0.002908711,0.001902149,0.0002849569],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001248217,"about_ca_system_score_gemma":0.0004988413,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001213616,"about_ca_topic_score_gemma":0.0007145359,"domain_scores_codex":[0.9987432,0.0001332625,0.00008488032,0.0002900567,0.0004178848,0.0003306454],"domain_scores_gemma":[0.9950473,0.001853082,0.0008675583,0.0005128445,0.0006218867,0.001097292],"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":[0.000461644,0.0001511453,0.02457692,0.0001346212,0.00004058864,0.0009815486,0.002034414,0.007971566,0.02335601,0.9234688,0.0007762893,0.01604646],"study_design_scores_gemma":[0.0001935664,0.0005082468,0.03657304,0.0001227887,0.00008139478,0.001959776,0.00219665,0.078605,0.01891722,0.8529322,0.007690017,0.0002201939],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9685148,0.0001856142,0.0206619,0.0002345372,0.00003200378,0.00005970124,0.0002123568,0.0001021815,0.009997005],"genre_scores_gemma":[0.993165,0.00009221099,0.004900854,0.00001934227,0.0000401434,0.00003369824,0.0002171409,0.00003123892,0.001500447],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.00337808,"threshold_uncertainty_score":0.01002961,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02304319922976767,"score_gpt":0.3294578798038308,"score_spread":0.3064146805740632,"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."}}