{"id":"W2067891397","doi":"10.1007/s12220-008-9063-6","title":"Covering Convex Bodies by Cylinders and Lattice Points by Flats","year":2009,"lang":"en","type":"article","venue":"Journal of Geometric Analysis","topic":"Point processes and geometric inequalities","field":"Mathematics","cited_by":12,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Alberta; University of Calgary","funders":"","keywords":"Regular polygon; Convex body; Combinatorics; Linear subspace; Mathematics; Connection (principal bundle); Cover (algebra); Base (topology); Euclidean space; Lattice (music); Euclidean geometry; Integer lattice; Integer (computer science); Geometry; Convex hull; Mathematical analysis; Physics; Computer science; Half-integer; Engineering","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":[],"consensus_categories":[],"category_scores_codex":[0.00145136,0.0002134282,0.0009102093,0.00308978,0.0001232518,0.0001376187,0.0002400189,0.0001116122,0.0001701985],"category_scores_gemma":[0.002702502,0.0001730711,0.0003434737,0.005497293,0.00005172408,0.0004223001,0.00003902577,0.0002801255,0.000004409732],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007727256,"about_ca_system_score_gemma":0.00003562908,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00003222983,"about_ca_topic_score_gemma":0.000003030614,"domain_scores_codex":[0.9977711,0.00006482023,0.0009127785,0.0001885583,0.0007325573,0.0003302283],"domain_scores_gemma":[0.9971473,0.001110028,0.0009372988,0.0001831126,0.0004270772,0.0001952427],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"not_applicable","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.001020204,0.003962278,0.1115781,0.001818091,0.04761047,0.0004559525,0.009102776,0.0006672835,0.002099977,0.01378697,0.6327036,0.1751943],"study_design_scores_gemma":[0.02449122,0.01082174,0.06866994,0.000992411,0.08141023,0.001437526,0.03666979,0.01535514,0.02242308,0.581005,0.148222,0.008501906],"study_design_candidate":"not_applicable","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8497699,0.01708894,0.1282981,0.001931009,0.0001106028,0.00009040978,0.00005165921,0.00003287457,0.002626484],"genre_scores_gemma":[0.9922208,0.002136886,0.003267722,0.0003963724,0.00007626401,5.076649e-7,0.000005209255,0.00001206999,0.001884173],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.5672181,"threshold_uncertainty_score":0.7057632,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02588030412208664,"score_gpt":0.3010020940134291,"score_spread":0.2751217898913425,"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."}}