{"id":"W2056988106","doi":"10.1134/s0081543814060169","title":"Convex bodies and multiplicities of ideals","year":2014,"lang":"en","type":"article","venue":"Proceedings of the Steklov Institute of Mathematics","topic":"Commutative Algebra and Its Applications","field":"Mathematics","cited_by":33,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Polyhedron; Mathematics; Linear subspace; Regular polygon; Pure mathematics; Generalization; Minkowski space; Convex polytope; Mixed volume; Class (philosophy); Convex body; Combinatorics; Convex analysis; Mathematical analysis; Convex optimization; Geometry; Computer science","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":[0.000477303,0.0001555504,0.0005251923,0.00007880979,0.00008247796,0.00001245588,0.0004147361,0.00006019195,0.000007747849],"category_scores_gemma":[0.001277698,0.000107291,0.0001050152,0.0001092195,0.0006699606,0.0001593405,0.0002182278,0.00009438448,9.355066e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00000942575,"about_ca_system_score_gemma":0.0000170047,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001250173,"about_ca_topic_score_gemma":0.000006927307,"domain_scores_codex":[0.9988111,0.000006268002,0.0006557744,0.0001217555,0.0002778226,0.00012733],"domain_scores_gemma":[0.9980596,0.0004061968,0.0008658057,0.0002293662,0.0004049697,0.00003410774],"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":[0.000006435727,0.0001258385,0.00148183,0.003234032,0.00008229958,1.181794e-8,0.007113282,0.000001219003,0.02667822,0.9601507,0.0005161315,0.0006099627],"study_design_scores_gemma":[0.0004733304,0.0001007803,0.0008952257,0.0007066261,0.0001641094,0.000007100118,0.00341925,0.0006539968,0.2350294,0.7573879,0.001010407,0.0001518569],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9793621,0.00007270733,0.001025905,0.0002774496,0.00004716032,0.0004260865,0.00001701818,0.00002508925,0.01874653],"genre_scores_gemma":[0.9450595,0.00003285095,0.05451431,0.0000131811,0.00001958166,0.00002056111,3.246969e-7,0.00001722384,0.0003224423],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2083512,"threshold_uncertainty_score":0.4375199,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0339283620019442,"score_gpt":0.2830674347431591,"score_spread":0.2491390727412149,"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."}}