{"id":"W4400196807","doi":"10.5070/c64163853","title":"The primitive Eulerian polynomial","year":2024,"lang":"en","type":"article","venue":"Combinatorial Theory","topic":"Mathematics and Applications","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université du Québec à Montréal","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Eulerian path; Polynomial; Mathematics; Computer science; Pure mathematics; Mathematical analysis","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":[0.001067518,0.0001190829,0.0001265205,0.00002869363,0.0003153545,0.0002155085,0.0002970897,0.00006473114,0.0001391504],"category_scores_gemma":[0.0004680839,0.00007659719,0.0001006905,0.0001452738,0.0001267618,0.00004826974,0.000087727,0.0001718234,0.0001643581],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004334948,"about_ca_system_score_gemma":0.00007190527,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001119623,"about_ca_topic_score_gemma":7.125366e-7,"domain_scores_codex":[0.9991466,0.00009793371,0.0002240762,0.0001713504,0.0001631784,0.0001968557],"domain_scores_gemma":[0.9969672,0.002492632,0.00004535105,0.0003947145,0.00004266053,0.00005743696],"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":[0.00001193959,0.00003861017,3.130736e-7,0.00002513934,0.00003641403,0.000001977431,0.0003442224,2.61491e-8,0.0003049586,0.9041572,0.09249324,0.00258598],"study_design_scores_gemma":[0.0001205123,0.00001700356,0.000002223293,0.00003086977,0.00002595086,0.000004149162,0.0001299476,0.00005717239,0.001037027,0.7795784,0.2189154,0.00008124387],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.131318,0.003146795,0.0186558,0.005464684,0.03065394,0.002820083,0.00008582047,0.001988256,0.8058666],"genre_scores_gemma":[0.9909736,0.00003488042,0.0005768045,0.0000343264,0.001242157,0.0001468991,0.000002774454,0.0000465431,0.006942017],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.8596556,"threshold_uncertainty_score":0.3123543,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03012577469032673,"score_gpt":0.3274828436840979,"score_spread":0.2973570689937712,"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."}}