{"id":"W4223630001","doi":"10.48550/arxiv.2204.04561","title":"Illuminating spiky balls and cap bodies","year":2022,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Point processes and geometric inequalities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Ball (mathematics); Convex body; Regular polygon; Convex hull; Combinatorics; Euclidean space; Euclidean geometry; Conjecture; Geometry; Mathematics; Physics","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":[0.000481019,0.0003058958,0.0004518609,0.0003938779,0.0002907788,0.00007196765,0.0004594092,0.0001814214,0.0006081521],"category_scores_gemma":[0.0005166842,0.0003494899,0.0001465398,0.0003393154,0.0001340256,0.0001491577,0.002050454,0.0006124464,0.00001100059],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001526952,"about_ca_system_score_gemma":0.0001015291,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003125099,"about_ca_topic_score_gemma":0.00007111707,"domain_scores_codex":[0.9985248,0.0001015952,0.0002532324,0.0006575079,0.0001230413,0.0003398136],"domain_scores_gemma":[0.998403,0.0005437561,0.0003231693,0.0004990745,0.0001311319,0.00009982655],"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":[0.00004590993,0.0001649002,0.003368212,0.003032648,0.0002949167,0.0004470256,0.004612548,0.002965316,0.00001047428,0.9824951,0.001897354,0.0006655462],"study_design_scores_gemma":[0.0006092464,0.0001056404,0.0004603492,0.0002133073,0.000321076,0.00001442149,0.008917619,0.009690925,0.00008763803,0.9735054,0.005153605,0.0009207757],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.968196,0.0005110337,0.007287963,0.00007941182,0.0003636531,0.0002851722,0.0001103164,0.0001965878,0.02296982],"genre_scores_gemma":[0.9793608,0.0005185736,0.0008782843,0.00005705069,0.00008466422,0.000002322349,0.00002075105,0.00003244535,0.01904517],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01116469,"threshold_uncertainty_score":0.9998957,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1677782248513865,"score_gpt":0.2374645873111618,"score_spread":0.0696863624597753,"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."}}