{"id":"W2058787718","doi":"10.1137/130950422","title":"Empty Pentagons in Point Sets with Collinearities","year":2015,"lang":"en","type":"article","venue":"SIAM Journal on Discrete Mathematics","topic":"Computational Geometry and Mesh Generation","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; Grantová Agentura České Republiky; Deutsche Forschungsgemeinschaft; Fonds De La Recherche Scientifique - FNRS; Australian Government; Hungarian Scientific Research Fund; Deutscher Akademischer Austauschdienst; National Science Foundation","keywords":"Pentagon; Regular polygon; Plane (geometry); General position; Convex polytope; Point (geometry); Finite set; Convex set; Constant (computer programming)","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0006442457,0.0001268061,0.0001719871,0.0001999333,0.0000907117,0.0002937094,0.000329453,0.00003275965,0.00001592165],"category_scores_gemma":[0.00008981064,0.00009153299,0.00004300668,0.0003685321,0.0000269527,0.0004240811,0.00006580901,0.0002199452,0.00003741203],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00009452562,"about_ca_system_score_gemma":0.0002018869,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002424442,"about_ca_topic_score_gemma":0.00001336715,"domain_scores_codex":[0.9987649,0.00006367753,0.0003149981,0.0001423386,0.0005224045,0.000191675],"domain_scores_gemma":[0.9992175,0.0001032602,0.000155353,0.0002038137,0.0001480256,0.0001720375],"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":[0.0002133692,0.001554779,0.001591748,0.0001912772,0.0001678951,0.0009786561,0.03103754,0.2249168,0.0002805522,0.7114198,0.01248206,0.01516553],"study_design_scores_gemma":[0.003900116,0.001666298,0.002413621,0.000620725,0.00002823735,0.002776856,0.003433633,0.6992353,0.001966936,0.2796347,0.003500046,0.0008235176],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2132087,0.0001088437,0.7762238,0.002865089,0.0003573731,0.0002021453,0.000004629705,0.00005301952,0.006976469],"genre_scores_gemma":[0.7927102,0.00001385562,0.2065393,0.0002606041,0.00009772755,0.00000636097,0.000004320958,0.00001142451,0.000356119],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.5795016,"threshold_uncertainty_score":0.3732607,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03581181690191652,"score_gpt":0.2838631880575671,"score_spread":0.2480513711556505,"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."}}