{"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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0007485828,0.0004982024,0.001078698,0.0006509298,0.0002627118,0.00006571435,0.0005189136,0.0002516362,0.0009074548],"category_scores_gemma":[0.002389264,0.0004511898,0.0002962436,0.001026797,0.000248372,0.0002390248,0.000267359,0.0003437911,0.0004605168],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00008484298,"about_ca_system_score_gemma":0.0002144798,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001901768,"about_ca_topic_score_gemma":0.00002545525,"domain_scores_codex":[0.9969922,0.00008231769,0.0011994,0.0005297562,0.0005005472,0.0006957524],"domain_scores_gemma":[0.996133,0.00189937,0.0005554096,0.0008370892,0.0004814616,0.00009368154],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"observational","study_design_gemma":"bench_or_experimental","study_design_scores_codex":[0.001043663,0.004794447,0.7532497,0.030161,0.003826847,0.0000503,0.01397185,0.0001357055,0.004845305,0.1466383,0.03318393,0.008098935],"study_design_scores_gemma":[0.009575228,0.002786231,0.1043778,0.01162465,0.002193587,0.000005053408,0.01245965,0.001245022,0.617777,0.1706539,0.06450605,0.002795816],"study_design_candidate":"observational","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9330173,0.002477732,0.002591891,0.001100565,0.001157289,0.0005690299,0.00008464144,0.0000543241,0.0589472],"genre_scores_gemma":[0.9692886,0.001214672,0.0003760453,0.0007420233,0.0001380065,0.00004844156,0.00001016191,0.00003662463,0.02814536],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.6488719,"threshold_uncertainty_score":0.999794,"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."}}