{"id":"W1964432551","doi":"10.1007/bf01237472","title":"Each convex body inE 3 symmetric about a plane can be illuminated by 8 directions","year":2000,"lang":"en","type":"article","venue":"Journal of Geometry","topic":"Mathematical Approximation and Integration","field":"Mathematics","cited_by":11,"is_retracted":false,"has_abstract":false,"ca_institutions":"Mount Allison University","funders":"","keywords":"Convex body; Mathematics; Regular polygon; Plane (geometry); Geometry; Pure mathematics; Mixed volume; Combinatorics; Mathematical analysis; 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":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.000666842,0.0001586198,0.0004228927,0.0005464084,0.00009535305,0.00006268307,0.0001790422,0.0001238849,0.009197415],"category_scores_gemma":[0.001223018,0.0001183822,0.0001419553,0.001116441,0.000053973,0.0001745326,0.00001139719,0.0003941407,0.00007018863],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001007983,"about_ca_system_score_gemma":0.00004699549,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002111887,"about_ca_topic_score_gemma":0.000004966043,"domain_scores_codex":[0.9982751,0.00008071739,0.0008220872,0.0001120427,0.0005063654,0.0002036806],"domain_scores_gemma":[0.9985379,0.0004196935,0.0004187269,0.0001699299,0.0002807896,0.0001729339],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"not_applicable","study_design_gemma":"not_applicable","study_design_scores_codex":[0.0003258146,0.005489215,0.0006875103,0.0009460925,0.0009520207,0.00008875896,0.003296722,0.000006381655,0.01220172,0.126367,0.7393271,0.1103117],"study_design_scores_gemma":[0.00701376,0.002664808,0.00288227,0.001063581,0.000851865,0.002399433,0.002586645,0.01036554,0.05591426,0.1511447,0.7615424,0.001570716],"study_design_candidate":"not_applicable","study_design_consensus":"not_applicable","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9576497,0.0003589126,0.004136595,0.001894652,0.0002340423,0.0002316887,0.00006407363,0.00007167805,0.03535867],"genre_scores_gemma":[0.9594921,0.0004041455,0.0122399,0.000606436,0.0002753438,0.00001023893,0.00004077226,0.00004754603,0.02688355],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.108741,"threshold_uncertainty_score":0.9917083,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02079439559484243,"score_gpt":0.2877273113088029,"score_spread":0.2669329157139604,"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."}}