{"id":"W2150037097","doi":"10.1007/s00373-010-0957-2","title":"Every Large Point Set contains Many Collinear Points or an Empty Pentagon","year":2010,"lang":"en","type":"article","venue":"Graphs and Combinatorics","topic":"Computational Geometry and Mesh Generation","field":"Computer Science","cited_by":12,"is_retracted":false,"has_abstract":false,"ca_institutions":"Carleton University","funders":"","keywords":"Pentagon; Conjecture; Integer (computer science); Set (abstract data type); Plane (geometry); Point (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":[],"consensus_categories":[],"category_scores_codex":[0.0004361593,0.000149416,0.0001540456,0.0001556925,0.0003106427,0.0002284448,0.0003403769,0.00008967864,0.00003971681],"category_scores_gemma":[0.00003639129,0.0001300446,0.00005034934,0.0005903863,0.00002907618,0.0005620972,0.0001576888,0.0002145451,0.000009880959],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000014589,"about_ca_system_score_gemma":0.00008530721,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000170705,"about_ca_topic_score_gemma":0.00004658676,"domain_scores_codex":[0.99885,0.00005537628,0.0002057745,0.0003635958,0.0002713485,0.0002539269],"domain_scores_gemma":[0.9991443,0.00007053357,0.00007878589,0.0003510277,0.0001619762,0.0001933465],"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":[0.00002581845,0.000295274,0.003435378,0.000013832,0.00001569981,0.00002847819,0.000403662,0.00004980485,0.0004570369,0.9919471,0.001396051,0.001931876],"study_design_scores_gemma":[0.004592326,0.001525464,0.04869743,0.00002295611,0.00003927741,0.000259251,0.000344442,0.3978825,0.003636609,0.5004374,0.04146565,0.001096612],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8759168,0.00007092629,0.1212817,0.0004888683,0.001620434,0.000200606,0.00002052505,0.0001352709,0.0002648865],"genre_scores_gemma":[0.9932167,0.00004595262,0.00568258,0.0006458363,0.00004943072,0.00001241285,0.00004043721,0.000008725425,0.0002979102],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4915096,"threshold_uncertainty_score":0.5303066,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01543672156284936,"score_gpt":0.2628801235376614,"score_spread":0.2474434019748121,"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."}}