{"id":"W2969594755","doi":"10.1016/j.aim.2019.106772","title":"A Steiner formula in the L Brunn Minkowski theory","year":2019,"lang":"en","type":"article","venue":"Advances in Mathematics","topic":"Point processes and geometric inequalities","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Alberta","funders":"National Science Foundation","keywords":"Mathematics; Minkowski space; Affine transformation; Dual (grammatical number); Steiner tree problem; Convex body; Combinatorics; Mathematical analysis; Pure mathematics; Geometry; Regular polygon; 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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002101146,0.0002063682,0.0003924505,0.0002504063,0.00003467487,0.00004449584,0.0005398366,0.00008309963,0.0002194501],"category_scores_gemma":[0.001186651,0.0001296752,0.00007749572,0.0007997524,0.00005277591,0.000462749,0.00007817508,0.0002598979,0.000106543],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004349945,"about_ca_system_score_gemma":0.00002953208,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004847428,"about_ca_topic_score_gemma":0.00007121651,"domain_scores_codex":[0.9982815,0.00009842033,0.0006127905,0.0002071201,0.0004097575,0.0003904276],"domain_scores_gemma":[0.9957101,0.003452311,0.0002028809,0.0005620419,0.00004919016,0.00002349816],"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":[0.00001348013,0.0002542615,0.0005266874,0.001158033,0.00000738404,0.000009660309,0.007933021,0.0000491874,0.00001028821,0.9867342,0.00009771195,0.003206053],"study_design_scores_gemma":[0.0005147565,0.00005550841,0.00009018473,0.000261778,0.00001123663,0.00001916341,0.01022018,0.0005824641,0.00008954868,0.9811971,0.006760536,0.0001974976],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7386629,0.005994773,0.01403887,0.0003825991,0.0003978238,0.001550424,0.0000166207,0.0001061857,0.2388498],"genre_scores_gemma":[0.9635053,0.0005616104,0.02902167,0.0003679653,0.00008001144,0.0001106362,0.000004295979,0.00004588689,0.006302664],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2325472,"threshold_uncertainty_score":0.5288,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02496894815028604,"score_gpt":0.3293205082319822,"score_spread":0.3043515600816961,"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."}}