{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001087721,0.0009250049,0.001151028,0.00111275,0.001692113,0.003703665,0.001944532,0.0008608276,0.009677086],"category_scores_gemma":[0.01002131,0.001266054,0.00111593,0.001924952,0.002964285,0.004107968,0.004544131,0.003273136,0.002310177],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009792779,"about_ca_system_score_gemma":0.0006065189,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001352176,"about_ca_topic_score_gemma":0.001724904,"domain_scores_codex":[0.9974169,0.0004781399,0.0001630952,0.0004929372,0.0008670386,0.0005819065],"domain_scores_gemma":[0.9918666,0.005054712,0.000782895,0.001319499,0.0005408406,0.0004354999],"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":[0.001176527,0.0002200827,0.004800498,0.0007475741,0.0001226458,0.001307423,0.0007939745,0.1094227,0.01114421,0.7783701,0.0112713,0.08062298],"study_design_scores_gemma":[0.0001139948,0.0001743638,0.001084725,0.0001790646,0.00007378185,0.001107058,0.0006394325,0.1415355,0.01454654,0.8204904,0.0199955,0.00005969859],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"other","genre_scores_codex":[0.4500265,0.001915692,0.4602745,0.001303324,0.0002941423,0.0001886262,0.001355645,0.0009782223,0.08366328],"genre_scores_gemma":[0.8167126,0.001333371,0.1630628,0.0005181085,0.0001460695,0.0002236694,0.002104245,0.0004877387,0.01541144],"genre_candidate":"other","genre_consensus":null,"teacher_disagreement_score":0.009677086,"threshold_uncertainty_score":0.03237307,"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."}}