{"id":"W3204184250","doi":"10.5802/alco.263","title":"Lagrangian combinatorics of matroids","year":2023,"lang":"en","type":"article","venue":"Algebraic Combinatorics","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Simons Institute for the Theory of Computing, University of California Berkeley; Natural Sciences and Engineering Research Council of Canada; Sorbonne Université; Università di Bologna; Division of Mathematical Sciences; National Science Foundation","keywords":"Matroid; Mathematics; Lagrangian; Piecewise linear function; Combinatorics; Regular polygon; Conjecture; Piecewise; Pure mathematics; Geometry; Mathematical analysis","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":[0.0007488614,0.0007436451,0.0005991474,0.002606186,0.002022125,0.004430838,0.0009762839,0.0007457432,0.01243676],"category_scores_gemma":[0.001652754,0.0004752535,0.0009277751,0.001546224,0.003324262,0.005289205,0.002317137,0.001816603,0.001889824],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.003383095,"about_ca_system_score_gemma":0.0007770001,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001895081,"about_ca_topic_score_gemma":0.002139668,"domain_scores_codex":[0.9986191,0.0003261903,0.00007282928,0.0002710342,0.0004512201,0.0002596638],"domain_scores_gemma":[0.9988686,0.0002612289,0.0001924389,0.000166665,0.000229546,0.0002814241],"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":[0.00001102433,0.000008186306,0.000124495,0.00001920154,0.00000244136,0.0000456035,0.0001227814,0.0005953189,0.0002769222,0.9941704,0.001457617,0.003165998],"study_design_scores_gemma":[0.00001288801,0.00001870403,0.00029514,0.00002351196,0.000004421754,0.0001605993,0.000164153,0.004819442,0.0005085379,0.9695852,0.02439248,0.00001485753],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.2581339,0.003602783,0.2239912,0.005763988,0.0006861405,0.0001228323,0.001583615,0.0008981295,0.5052174],"genre_scores_gemma":[0.8948972,0.001578311,0.03051707,0.0008068054,0.0008021297,0.0001292763,0.001249705,0.0002981895,0.06972128],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01243676,"threshold_uncertainty_score":0.04160506,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04117453944594158,"score_gpt":0.3190658641472122,"score_spread":0.2778913247012706,"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."}}