{"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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001708594,0.0001835103,0.000336109,0.000107173,0.0002732626,0.0000404957,0.0007804202,0.00008297437,0.00008664653],"category_scores_gemma":[0.000203511,0.0001242912,0.000248075,0.0004268502,0.00008995585,0.0001473278,0.00004870815,0.0008975557,0.00006110366],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00022241,"about_ca_system_score_gemma":0.0001809828,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":9.399689e-7,"about_ca_topic_score_gemma":0.00002470933,"domain_scores_codex":[0.9982592,0.0001364214,0.0005556085,0.0001078137,0.0004129997,0.000527971],"domain_scores_gemma":[0.9979386,0.0005473382,0.0006839742,0.0004861018,0.000253122,0.0000909129],"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":[0.00004932132,0.0002426474,0.0001390638,0.00001138802,0.0001014017,0.000001263334,0.0001699408,0.00001958015,0.0003017577,0.9927999,0.005699451,0.0004643025],"study_design_scores_gemma":[0.0008336258,0.0001185724,0.0001430495,0.00002587959,0.0001368589,0.0002138883,0.00007557659,0.00002278714,0.001014492,0.9349856,0.06229921,0.0001304716],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9503221,0.003614043,0.03496797,0.007826678,0.0002409013,0.0002848323,0.000002796116,0.00006406058,0.0026766],"genre_scores_gemma":[0.9979873,0.0003268242,0.0002361023,0.0001255686,0.0002738887,0.000008206705,5.878503e-7,0.0000330795,0.001008436],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.05781429,"threshold_uncertainty_score":0.5068446,"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."}}