{"id":"W2568903863","doi":"10.1016/j.comgeo.2010.05.001","title":"Distance k-sectors exist","year":2010,"lang":"en","type":"article","venue":"Computational Geometry","topic":"Computational Geometry and Mesh Generation","field":"Computer Science","cited_by":12,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Mathematics; Disjoint sets; Combinatorics; Metric space; Dimension (graph theory); Integer (computer science); Euclidean space; Uniqueness; Euclidean distance; Geodesic; Discrete mathematics; Fixed point; Mathematical analysis; Geometry","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":[0.0006444633,0.00156691,0.001422931,0.002370276,0.002426337,0.004730951,0.001908989,0.002759644,0.04172573],"category_scores_gemma":[0.004407804,0.0008503704,0.001008824,0.001767166,0.00246806,0.006417945,0.00595119,0.003925871,0.02071451],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009092124,"about_ca_system_score_gemma":0.0005522049,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002935449,"about_ca_topic_score_gemma":0.0004288067,"domain_scores_codex":[0.9987754,0.0001390989,0.00009974065,0.0003597968,0.0002762561,0.000349701],"domain_scores_gemma":[0.9975724,0.0005976242,0.0002276332,0.0006786007,0.0005844807,0.0003392876],"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":[0.0003863659,0.0001063915,0.0008689889,0.0002127353,0.00002486494,0.0002354705,0.0002913318,0.00095301,0.003890727,0.9420317,0.00745797,0.04354046],"study_design_scores_gemma":[0.00005088887,0.00004573546,0.0004296844,0.00006475193,0.00002092756,0.0006124004,0.0004032479,0.004013854,0.004697049,0.9521287,0.03750616,0.00002664499],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.2054602,0.00339813,0.3109357,0.00401446,0.002600795,0.0002140693,0.001921109,0.001806257,0.4696492],"genre_scores_gemma":[0.8034885,0.001280138,0.05978546,0.00101482,0.0002585333,0.0002014786,0.001955065,0.0009132513,0.1311027],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.04172573,"threshold_uncertainty_score":0.1395864,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.009670648628013008,"score_gpt":0.2464551322304975,"score_spread":0.2367844836024845,"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."}}