{"id":"W1858499400","doi":"10.37236/1975","title":"Rank–Three Matroids are Rayleigh","year":2005,"lang":"en","type":"article","venue":"The Electronic Journal of Combinatorics","topic":"Graph theory and applications","field":"Mathematics","cited_by":16,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Matroid; Mathematics; Combinatorics; Rank (graph theory); Monotonic function; Set (abstract data type); Graphic matroid; Property (philosophy); Discrete mathematics; Mathematical analysis; Computer science","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0007171945,0.000572099,0.0005453403,0.0007287592,0.0009852645,0.003241775,0.0006421378,0.0006724605,0.007848541],"category_scores_gemma":[0.002989918,0.0004262095,0.0006081513,0.0007643368,0.002075534,0.003171989,0.00145901,0.001421766,0.001420195],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008911781,"about_ca_system_score_gemma":0.0006423028,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001972587,"about_ca_topic_score_gemma":0.002475669,"domain_scores_codex":[0.9989927,0.0002175914,0.00006578475,0.000190695,0.0002997091,0.0002334882],"domain_scores_gemma":[0.9964306,0.001191672,0.0006621059,0.0005817168,0.0007160989,0.0004178734],"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":[0.0002439865,0.00003903565,0.00230793,0.0001536159,0.00003998453,0.000423754,0.0004455937,0.01225331,0.01661731,0.9299113,0.00588007,0.03168404],"study_design_scores_gemma":[0.0000386517,0.0001165026,0.002480892,0.00004615295,0.00003777777,0.001664003,0.0006551132,0.07666318,0.02357086,0.8672996,0.02734249,0.00008472028],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5708283,0.0007784521,0.2957903,0.001990559,0.0001137915,0.0001000302,0.001562038,0.001054139,0.1277824],"genre_scores_gemma":[0.9659931,0.0002398549,0.02431375,0.0001989239,0.00005076037,0.00004625744,0.000412434,0.00007013801,0.008674813],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007848541,"threshold_uncertainty_score":0.02625597,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02527666300095133,"score_gpt":0.2897159135556395,"score_spread":0.2644392505546882,"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."}}