{"id":"W2504277986","doi":"10.1007/978-3-540-45560-8_1","title":"0. Paradoxical decompositions","year":2002,"lang":"en","type":"book-chapter","venue":"Lecture notes in mathematics","topic":"Mathematics and Applications","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Alberta","funders":"","keywords":"Mathematics; Mathematical economics; Calculus (dental); Pure mathematics; Orthodontics; Medicine","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":[0.0008690647,0.0007254104,0.0005503782,0.001164206,0.002701429,0.003534017,0.0007917574,0.001513699,0.01875918],"category_scores_gemma":[0.002772404,0.0004790481,0.000781699,0.0009367258,0.006278215,0.008293951,0.002368248,0.004920353,0.00413602],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002051995,"about_ca_system_score_gemma":0.0008130299,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001137089,"about_ca_topic_score_gemma":0.001016181,"domain_scores_codex":[0.9993725,0.0002150196,0.00002991551,0.0001320765,0.0001691727,0.00008133267],"domain_scores_gemma":[0.9992365,0.0003363451,0.00004840953,0.000160541,0.0001636716,0.0000546702],"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":[0.000004035745,0.000003519137,0.000008566094,0.00001422765,9.955105e-7,0.000007183313,0.00009900958,0.00002276096,0.00003255705,0.9917669,0.005545998,0.002494278],"study_design_scores_gemma":[0.000003332311,0.000001488922,0.00001622807,0.000009824834,0.000001128433,0.00002881473,0.0000324164,0.00005608348,0.00002506673,0.9825057,0.01731832,0.000001594989],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"methods","genre_scores_codex":[0.007483916,0.006819849,0.02925638,0.009733746,0.001941219,0.00003254963,0.0001752153,0.000154974,0.9444021],"genre_scores_gemma":[0.5623929,0.008806844,0.02861209,0.008475902,0.00406698,0.0002710258,0.0005904901,0.0004234358,0.3863603],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.01875918,"threshold_uncertainty_score":0.06275564,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05510001572685776,"score_gpt":0.3094523884149747,"score_spread":0.254352372688117,"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."}}