{"id":"W1512882170","doi":"10.48550/arxiv.0906.2924","title":"Lower Bounds for Pinning Lines by Balls","year":2009,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Computational Geometry and Mesh Generation","field":"Computer Science","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"Kootenay Association for Science & Technology","funders":"","keywords":"Disjoint sets; Combinatorics; Transversal (combinatorics); Subfamily; Line (geometry); Regular polygon; Mathematics; Pairwise comparison; Unit (ring theory); Integer (computer science); Property (philosophy); Discrete mathematics; Computer science; Geometry; Mathematical analysis; Statistics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.004732935,0.003331775,0.003618524,0.006380638,0.003848308,0.006735528,0.008201831,0.003497255,0.03290532],"category_scores_gemma":[0.03751772,0.001926294,0.003017659,0.005158453,0.004735452,0.01724943,0.01017224,0.008787016,0.005147632],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.004570275,"about_ca_system_score_gemma":0.0009390604,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002125864,"about_ca_topic_score_gemma":0.00209786,"domain_scores_codex":[0.9937831,0.00130018,0.0002575622,0.001193574,0.001940302,0.001525422],"domain_scores_gemma":[0.9645469,0.02489135,0.001920265,0.003790536,0.00218991,0.002661037],"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":[0.0008422732,0.0002223082,0.005483592,0.001352378,0.0002115601,0.0004369314,0.001015097,0.05869894,0.007140898,0.8306545,0.02725367,0.0666879],"study_design_scores_gemma":[0.00008336818,0.0003252915,0.002226412,0.0004468054,0.0002186246,0.0008191315,0.0003863905,0.2355105,0.004480238,0.723147,0.03223788,0.0001184717],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.172744,0.02323543,0.6015781,0.008956659,0.001382572,0.000348888,0.002259694,0.002652876,0.1868417],"genre_scores_gemma":[0.7751732,0.01254862,0.1560789,0.002401899,0.002516133,0.001050874,0.004563788,0.00243292,0.04323361],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.03290532,"threshold_uncertainty_score":0.1100792,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04073148470873926,"score_gpt":0.2931617187817571,"score_spread":0.2524302340730178,"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."}}