{"id":"W2080199983","doi":"10.1016/j.disc.2008.02.005","title":"A criterion for the half-plane property","year":2008,"lang":"en","type":"article","venue":"Discrete Mathematics","topic":"Polynomial and algebraic computation","field":"Computer Science","cited_by":37,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Mathematics; Matroid; Property (philosophy); Homogeneous; Plane (geometry); Polynomial; Combinatorics; Pure mathematics; Discrete mathematics; 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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0001414738,0.00009071428,0.0001068507,0.0000227575,0.0002607454,0.00007775753,0.0004779838,0.00002324959,0.000006543212],"category_scores_gemma":[0.00005469053,0.00004300915,0.00006334386,0.0001032171,0.0000446995,0.0001598938,0.000100381,0.00004732893,0.00003464547],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001133316,"about_ca_system_score_gemma":0.00003216977,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001326122,"about_ca_topic_score_gemma":0.000002715761,"domain_scores_codex":[0.9993665,0.00001249355,0.0001685763,0.0001449608,0.0001464747,0.0001610047],"domain_scores_gemma":[0.9993367,0.0002052771,0.0000652125,0.0003165703,0.0000396576,0.0000366098],"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":[0.00004552571,0.0004859187,0.0001005834,0.0006247868,0.0001766316,0.00005201484,0.04764957,0.0005468047,0.005167771,0.690624,0.04970787,0.2048185],"study_design_scores_gemma":[0.000408028,0.0001171798,0.0003714754,0.00004393505,0.00001547931,0.000165186,0.00009879072,0.9316841,0.001682809,0.03777875,0.02739768,0.000236545],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.008826504,0.00007144611,0.9862446,0.003170509,0.0002052967,0.0003528052,0.00000336246,0.0001108004,0.001014664],"genre_scores_gemma":[0.826785,0.00002507416,0.1693697,0.0005336578,0.0002084776,0.0001089072,0.000008449119,0.00001660816,0.002944086],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.9311373,"threshold_uncertainty_score":0.200547,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03454349146865929,"score_gpt":0.2535597875582731,"score_spread":0.2190162960896138,"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."}}