{"id":"W2587397364","doi":"10.1016/j.aim.2017.09.028","title":"On polynomially integrable convex bodies","year":2017,"lang":"en","type":"article","venue":"Advances in Mathematics","topic":"Point processes and geometric inequalities","field":"Mathematics","cited_by":15,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Alberta","funders":"National Science Foundation of Sri Lanka; Natural Sciences and Engineering Research Council of Canada; National Science Foundation","keywords":"Mathematics; Integrable system; Regular polygon; Convex body; Ellipsoid; Degree (music); Pure mathematics; Section (typography); Combinatorics; Convex function; Mixed volume; Geometry; Convex hull","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001594388,0.001512207,0.001805285,0.00236518,0.001531104,0.002955201,0.001720958,0.002105288,0.006712467],"category_scores_gemma":[0.008667882,0.0006127963,0.001365341,0.00194503,0.007074264,0.006392838,0.003918555,0.005734084,0.0006651389],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002228093,"about_ca_system_score_gemma":0.0008183133,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.003680661,"about_ca_topic_score_gemma":0.002255787,"domain_scores_codex":[0.9989511,0.0003194637,0.00004278786,0.000212769,0.0003048001,0.0001690638],"domain_scores_gemma":[0.9952429,0.00303194,0.0005771501,0.0002386052,0.0004963899,0.0004129043],"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":[0.0000153772,0.000007735941,0.0001170154,0.00002501166,0.000006979136,0.00003820378,0.0001138799,0.003337982,0.0002526962,0.9938269,0.0003680592,0.001890238],"study_design_scores_gemma":[0.000008121858,0.000009741982,0.0001749769,0.000009943195,0.000006176939,0.0000269995,0.00004595596,0.01821858,0.000104749,0.980639,0.0007486717,0.000006974655],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2445751,0.00417032,0.6706871,0.006783457,0.0004372356,0.00003918852,0.0003642526,0.0001849687,0.07275836],"genre_scores_gemma":[0.9139189,0.003721754,0.03963317,0.0008261565,0.0008505415,0.00009843901,0.0004832364,0.0001728669,0.04029508],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.006712467,"threshold_uncertainty_score":0.02245545,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05248484546673964,"score_gpt":0.3705491602988994,"score_spread":0.3180643148321598,"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."}}