{"id":"W2795186926","doi":"10.1016/j.aam.2018.08.003","title":"On contact graphs of totally separable packings in low dimensions","year":2018,"lang":"en","type":"preprint","venue":"Advances in Applied Mathematics","topic":"Point processes and geometric inequalities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Calgary","funders":"Nemzeti Kutatási Fejlesztési és Innovációs Hivatal; Emberi Eroforrások Minisztériuma; Natural Sciences and Engineering Research Council of Canada; Magyar Tudományos Akadémia","keywords":"Combinatorics; Mathematics; Isoperimetric inequality; Separable space; Hyperplane; Regular polygon; Convexity; Disjoint sets; Vertex (graph theory); Convex body; Euclidean space; Graph; Convex hull; Geometry; Mathematical analysis","routes":{"ca_aff":true,"ca_fund":true,"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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.001051314,0.0005463754,0.001420279,0.0008787568,0.00004655554,0.0000371993,0.0005883381,0.0003964103,0.00008382861],"category_scores_gemma":[0.00132258,0.0004912523,0.0001703248,0.0008147938,0.0001544432,0.0001091056,0.0004855969,0.0007429082,0.00002549635],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001384645,"about_ca_system_score_gemma":0.0001268894,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002080692,"about_ca_topic_score_gemma":0.000109723,"domain_scores_codex":[0.9966698,0.00003294247,0.001545748,0.0005705685,0.000631752,0.0005491801],"domain_scores_gemma":[0.994689,0.003035807,0.001103579,0.0009661019,0.0001338224,0.00007164069],"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":[0.00006353176,0.0008922045,0.00006254789,0.009719601,0.0000341395,0.00001001737,0.002458662,0.0006885474,0.00004852723,0.9854348,0.0001746912,0.000412744],"study_design_scores_gemma":[0.0006708795,0.0001104099,0.00002293614,0.003867283,0.00003790483,0.000003036341,0.0008457395,0.0008146756,0.002173245,0.9908224,0.0001489789,0.0004825395],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7638829,0.001801322,0.01620048,0.00004289847,0.0006906192,0.002420001,0.0001718626,0.0001899961,0.2145999],"genre_scores_gemma":[0.9145943,0.001092197,0.0836555,0.00006807681,0.00004448084,0.0002666102,0.00002403894,0.0000868158,0.0001679862],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2144319,"threshold_uncertainty_score":0.9997539,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02833486342297087,"score_gpt":0.3268931210890578,"score_spread":0.2985582576660869,"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."}}