{"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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.001040029,0.0004954094,0.0009471356,0.0005336584,0.0002066389,0.00004251353,0.0009840251,0.0003090497,0.00008186633],"category_scores_gemma":[0.002111318,0.0005090094,0.0003250626,0.003606162,0.0001863721,0.0002582145,0.0004680645,0.0004554134,0.0003204204],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001913781,"about_ca_system_score_gemma":0.0001301829,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001013222,"about_ca_topic_score_gemma":0.000002302892,"domain_scores_codex":[0.9962393,0.000146514,0.001110224,0.0005219987,0.001136271,0.000845688],"domain_scores_gemma":[0.9952626,0.002036994,0.0005933889,0.001381742,0.0004622911,0.0002629978],"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":[0.00001507135,0.0004227584,0.0006271738,0.0004530945,0.00008440023,0.00003537343,0.0005914452,0.000004438209,0.0004556779,0.9859939,0.01092289,0.0003938082],"study_design_scores_gemma":[0.001541713,0.0002468859,0.0003523071,0.0001011562,0.00009852849,0.00001575295,0.0003467859,0.0002959504,0.003992085,0.9891675,0.003338328,0.0005030152],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9611396,0.000318315,0.004080306,0.0006708337,0.006649483,0.001389278,0.00004376551,0.002653145,0.02305533],"genre_scores_gemma":[0.9947914,0.0001023761,0.001592283,0.00003303986,0.00009775277,0.00007060492,0.00002247671,0.0001766498,0.003113455],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.03365181,"threshold_uncertainty_score":0.9997361,"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."}}