{"id":"W4311471621","doi":"10.4153/s0008439522000728","title":"Magnitude and Holmes–Thompson intrinsic volumes of convex bodies","year":2022,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Point processes and geometric inequalities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"University of Oxford; Simons Foundation","keywords":"Mathematics; Mathematical proof; Conjecture; Regular polygon; Invariant (physics); Normed vector space; Magnitude (astronomy); Euclidean geometry; Euclidean space; Mixed volume; Convex body; Pure mathematics; Space (punctuation); Metric space; Convex geometry; Metric (unit); Combinatorics; Convex analysis; Geometry; Convex hull; Mathematical physics; Convex optimization","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0009708202,0.0003537366,0.0004447003,0.003052082,0.0006789248,0.001843877,0.0007976678,0.0004295527,0.004223093],"category_scores_gemma":[0.005560327,0.0002592564,0.0004528161,0.0008484304,0.003862151,0.003370572,0.002076954,0.001393753,0.000292189],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001074806,"about_ca_system_score_gemma":0.000225377,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000534325,"about_ca_topic_score_gemma":0.000484588,"domain_scores_codex":[0.9991722,0.0001373506,0.00004034549,0.0001772365,0.0003533185,0.0001195934],"domain_scores_gemma":[0.996428,0.00177671,0.0006571521,0.0002549038,0.0004303063,0.0004529642],"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":[0.00002110271,0.000006473384,0.00103114,0.00002881702,0.000006843557,0.00004029473,0.0001299877,0.002616242,0.002495876,0.9893376,0.0003238095,0.003961845],"study_design_scores_gemma":[0.000006804586,0.00005981657,0.005619113,0.00003319485,0.00001184337,0.0002943882,0.0001785987,0.02920414,0.003600127,0.9559028,0.005057983,0.00003121411],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6448022,0.001550788,0.2717251,0.001269471,0.0002050189,0.00003813075,0.0003574381,0.0002039312,0.07984797],"genre_scores_gemma":[0.9866051,0.0002291852,0.008955772,0.00004939844,0.0001661724,0.00002683025,0.00009332191,0.00003144004,0.003842796],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004223093,"threshold_uncertainty_score":0.01412761,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03161588016204299,"score_gpt":0.2599802964192297,"score_spread":0.2283644162571867,"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."}}