{"id":"W2950490117","doi":"10.48550/arxiv.1602.06040","title":"The geometry of homothetic covering and illumination","year":2016,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Point processes and geometric inequalities","field":"Mathematics","cited_by":13,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Calgary","funders":"","keywords":"Homothetic transformation; Conjecture; Discrete geometry; Regular polygon; Convex body; Boundary (topology); Geometry; Convex geometry; Mathematics; Computer science; Convex analysis; Pure mathematics; Convex hull; Mathematical analysis; Convex optimization","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":[0.0004557555,0.0001606248,0.0002586367,0.000246861,0.0001260468,0.0000327665,0.0003218521,0.0001499211,0.00002332887],"category_scores_gemma":[0.0005163362,0.0001183873,0.00009777604,0.0003132063,0.0002062681,0.00009328427,0.0005438045,0.0001764305,0.000004766957],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006377424,"about_ca_system_score_gemma":0.00005491739,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002537445,"about_ca_topic_score_gemma":0.00001340546,"domain_scores_codex":[0.9991711,0.00005513001,0.0002116261,0.0002913957,0.0000822182,0.0001885593],"domain_scores_gemma":[0.9980864,0.0009174576,0.000347579,0.0004265502,0.0001767923,0.00004522178],"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":[0.00003669438,0.00004352584,0.000820214,0.0009820268,0.0001226072,0.00001310153,0.0004232658,0.0001940169,0.00002760268,0.99505,0.0001550983,0.002131872],"study_design_scores_gemma":[0.0003307465,0.00004361769,0.0003514905,0.0002782379,0.0001091917,0.000003649045,0.0007297466,0.002346775,0.0004906316,0.9943221,0.0007660529,0.0002277693],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9391449,0.0002928702,0.05535491,0.0000792172,0.0001923014,0.0001678216,0.00004345125,0.00004302412,0.004681473],"genre_scores_gemma":[0.9940171,0.001024435,0.0001000169,0.000006856165,0.00003994313,5.907237e-7,0.000001834395,0.00001533839,0.004793911],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.05525489,"threshold_uncertainty_score":0.4827692,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.09422324462206105,"score_gpt":0.2182565211572305,"score_spread":0.1240332765351695,"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."}}