{"id":"W2082276217","doi":"10.1016/j.aim.2008.12.004","title":"On the nontrivial projection problem","year":2009,"lang":"en","type":"article","venue":"Advances in Mathematics","topic":"Advanced Banach Space Theory","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Alberta","funders":"","keywords":"Mathematics; Projection (relational algebra); Bounded function; Dimension (graph theory); Rank (graph theory); Regular polygon; Logarithm; Normed vector space; Convex body; Product (mathematics); Pure mathematics; Space (punctuation); Combinatorics; Mathematical analysis; Geometry; Convex hull","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":[0.001018696,0.0007370344,0.0008785396,0.0008704541,0.001563078,0.00258406,0.0008620396,0.001678096,0.009461296],"category_scores_gemma":[0.004185534,0.0003409251,0.0006285273,0.0009805168,0.003466936,0.004858692,0.003995508,0.004128444,0.0007448103],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001170913,"about_ca_system_score_gemma":0.001154401,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008026827,"about_ca_topic_score_gemma":0.0005247556,"domain_scores_codex":[0.999456,0.0002126476,0.00001979931,0.00008472908,0.0001513043,0.0000755204],"domain_scores_gemma":[0.9985435,0.0008929663,0.00009098763,0.0001108738,0.0001587173,0.0002030349],"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":[0.00001332393,0.000006752892,0.00004379771,0.00002222235,0.000004138231,0.00002711098,0.00003831353,0.0005584677,0.0001247737,0.9959825,0.001446949,0.00173173],"study_design_scores_gemma":[0.000007065814,0.000002854368,0.0000425907,0.000004300314,0.000001459489,0.00002137129,0.00002557694,0.003061001,0.00004677583,0.9957619,0.001023011,0.000002168031],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.2593781,0.004596245,0.2758984,0.04211757,0.001636469,0.0000785623,0.0004882044,0.0002504323,0.415556],"genre_scores_gemma":[0.8800547,0.003242258,0.03635673,0.001727138,0.001878635,0.0001558256,0.000702076,0.0001745024,0.07570812],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.009461296,"threshold_uncertainty_score":0.03165114,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02031707532634389,"score_gpt":0.3279451495534351,"score_spread":0.3076280742270912,"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."}}