{"id":"W2024380745","doi":"10.1007/s00031-005-1114-5","title":"Motivic decomposition of projective homogeneous varieties and the Krull-Schmidt theorem","year":2006,"lang":"en","type":"article","venue":"Transformation Groups","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":72,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Alberta","funders":"","keywords":"Mathematics; Subcategory; Abelian category; Algebraically closed field; Pure mathematics; Homogeneous; Tensor product; Abelian group; Projective test; Combinatorics","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":[0.0007317843,0.0001258889,0.0002074467,0.00007960355,0.0001642264,0.00002561762,0.00009432157,0.00006959505,0.0000594488],"category_scores_gemma":[0.00002650872,0.00008386213,0.000080324,0.0001800739,0.0002782316,0.0002326214,0.00001106582,0.0001073181,0.000007912391],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000173543,"about_ca_system_score_gemma":0.00001223875,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00003558809,"about_ca_topic_score_gemma":0.00001103616,"domain_scores_codex":[0.999042,0.0001811984,0.0003500735,0.00009952953,0.0001925313,0.0001346062],"domain_scores_gemma":[0.9991412,0.0004899348,0.0001314576,0.0001466018,0.00007257125,0.00001821947],"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":[0.0002475262,0.00007580227,0.00005623926,0.0001464831,0.00003724336,4.257867e-7,0.008272126,0.00002399143,0.0003069551,0.9895234,0.00004008075,0.001269741],"study_design_scores_gemma":[0.001407272,0.00005670625,0.0011586,0.00002350197,0.00008298271,0.00004030249,0.001640316,0.000647436,0.01168606,0.9830976,0.0000517218,0.0001075526],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8322426,0.0001368328,0.1451666,0.0002792276,0.00004774723,0.0005412604,0.0000108171,0.00006271007,0.0215122],"genre_scores_gemma":[0.9988411,0.00002137416,0.0008968383,0.00003393534,0.00004326333,0.00003573985,0.00001726186,0.0000113867,0.00009911382],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1665985,"threshold_uncertainty_score":0.3419798,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.00943912393561476,"score_gpt":0.2479558382447754,"score_spread":0.2385167143091606,"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."}}