{"id":"W1993585122","doi":"10.1016/j.comgeo.2010.09.009","title":"Almost all Delaunay triangulations have stretch factor greater than <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si1.gif\" overflow=\"scroll\"><mml:mi>π</mml:mi><mml:mo stretchy=\"false\">/</mml:mo><mml:mn>2</mml:mn></mml:math>","year":2010,"lang":"en","type":"article","venue":"Computational Geometry","topic":"Computational Geometry and Mesh Generation","field":"Computer Science","cited_by":38,"is_retracted":false,"has_abstract":false,"ca_institutions":"McGill University; Carleton University","funders":"","keywords":"Mathematics; Delaunay triangulation; Combinatorics; Euclidean geometry; General position; Position (finance); Regular polygon; 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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow","scholarly_communication","insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.0008343204,0.0005312177,0.0002889267,0.000623508,0.0009580643,0.001046038,0.001212016,0.0007101602,0.001008925],"category_scores_gemma":[0.0005321436,0.0007413338,0.0006433728,0.00119495,0.0003227961,0.00124836,0.0008272646,0.00084541,0.001148631],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003250383,"about_ca_system_score_gemma":0.0007459706,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002380544,"about_ca_topic_score_gemma":0.0001883603,"domain_scores_codex":[0.9949619,0.0001742568,0.001034176,0.001214902,0.001688867,0.0009259699],"domain_scores_gemma":[0.996301,0.001121589,0.0007705338,0.000905946,0.0003669539,0.000533998],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.0001319877,0.0002362235,0.0001945711,0.0001071658,0.0004445166,0.0001239303,0.001086517,0.05250164,0.0008030392,0.9303261,0.006020718,0.00802361],"study_design_scores_gemma":[0.001307281,0.0004332155,0.003777497,0.0001198199,0.0001788267,0.0003963154,0.0001640303,0.9533073,0.0237491,0.01186308,0.003859616,0.000843933],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.938401,0.0001938902,0.05689917,0.0006881708,0.001922833,0.00009846698,0.0003455406,0.0002537208,0.001197192],"genre_scores_gemma":[0.9717915,0.00003248525,0.02390409,0.001028376,0.001176196,0.000177024,0.001593911,0.0001266949,0.0001697448],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.918463,"threshold_uncertainty_score":0.999991,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02276252827696297,"score_gpt":0.2540179107705189,"score_spread":0.231255382493556,"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."}}