{"id":"W2964216498","doi":"10.4007/annals.2010.171.533","title":"Essential dimension, spinor groups, and quadratic forms","year":2010,"lang":"en","type":"article","venue":"Scuola Normale Superiore di Pisa","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":45,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"Banff International Research Station for Mathematical Innovation and Discovery","keywords":"Mathematics; Spinor; Dimension (graph theory); Pure mathematics; Quadratic equation; Algebra over a field; Geometry; Mathematical physics","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":["metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0005642699,0.0003145953,0.000389034,0.0001217856,0.0003434147,0.0001047692,0.0002614539,0.0002245655,0.001169793],"category_scores_gemma":[0.0003838805,0.0002538517,0.0001323378,0.0002390356,0.0003219367,0.0005231148,0.0002005072,0.00050349,0.000164895],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001332163,"about_ca_system_score_gemma":0.0000486439,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002994978,"about_ca_topic_score_gemma":0.0001288788,"domain_scores_codex":[0.9982896,0.00006098591,0.0004237999,0.0003923138,0.0003193567,0.0005139528],"domain_scores_gemma":[0.9987479,0.0002355662,0.00009439155,0.0005951184,0.00008438291,0.0002426584],"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":[0.0003423662,0.0008974455,0.1741462,0.001272471,0.0003246569,0.000196695,0.01247755,0.000001356675,0.1442085,0.6537176,0.002262519,0.01015266],"study_design_scores_gemma":[0.006327991,0.000816155,0.1383328,0.0003224655,0.0006070572,0.001988606,0.009304871,0.0006864097,0.1082415,0.7181072,0.01172567,0.003539299],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9954678,0.00009814085,0.000521924,0.0001730487,0.0007234354,0.0003240818,0.00001380499,0.0001565738,0.002521143],"genre_scores_gemma":[0.9967348,0.00001447773,0.001814128,0.0001549737,0.0003120631,0.00002858075,0.00002044284,0.00005109838,0.0008694669],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.06438953,"threshold_uncertainty_score":0.9999914,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.009187150440232494,"score_gpt":0.2543758612735568,"score_spread":0.2451887108333243,"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."}}