{"id":"W7117851389","doi":"","title":"Notes on non-separable arrangements of convex bodies","year":2025,"lang":"","type":"article","venue":"ArXiv.org","topic":"Point processes and geometric inequalities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"National Research, Development and Innovation Office; Nemzeti Kutatási, Fejlesztési és Innovaciós Alap; Natural Sciences and Engineering Research Council of Canada; Nemzeti Kutatási Fejlesztési és Innovációs Hivatal","keywords":"Convex hull; Convex body; Subderivative; Hyperplane; Homothetic transformation; Convex analysis; Regular polygon; Convex set","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"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":[0.0007869619,0.000397989,0.0005809651,0.001072592,0.002097115,0.001618688,0.0007698225,0.0008741807,0.007266364],"category_scores_gemma":[0.003806787,0.0004538802,0.0007468424,0.001203859,0.003237728,0.00312473,0.00250661,0.002127261,0.000542822],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001829277,"about_ca_system_score_gemma":0.0004838198,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002379583,"about_ca_topic_score_gemma":0.00131507,"domain_scores_codex":[0.9992191,0.0001640239,0.00004098768,0.0001777106,0.0002814589,0.0001167972],"domain_scores_gemma":[0.9985184,0.000711221,0.0002071896,0.000133657,0.0002180174,0.000211473],"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":[0.00002849312,0.000009158307,0.0008096049,0.00005158635,0.000008679102,0.0001338307,0.0003382309,0.00472886,0.001247043,0.9862425,0.001519616,0.004882477],"study_design_scores_gemma":[0.00001571902,0.00006666686,0.001923243,0.00005137852,0.00001349041,0.0003266358,0.0005122026,0.02191809,0.001341641,0.9536637,0.02014298,0.00002435431],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5368925,0.00677507,0.2845765,0.007644272,0.0005534141,0.00006864771,0.0007151621,0.0001469904,0.1626274],"genre_scores_gemma":[0.9448789,0.003122729,0.02354775,0.0004120522,0.0004507661,0.0001022594,0.0004690423,0.00006305677,0.02695357],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007266364,"threshold_uncertainty_score":0.02430844,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08378647540474962,"score_gpt":0.345907663858143,"score_spread":0.2621211884533934,"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."}}