{"id":"W4382492057","doi":"10.48550/arxiv.2306.15556","title":"The Primitive Eulerian polynomial","year":2023,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Eulerian path; Mathematics; Combinatorics; Interpretation (philosophy); Polynomial; Reflection (computer programming); Hyperplane; Connection (principal bundle); Type (biology); Simplicial complex; Pure mathematics; Geometry; Mathematical analysis; Lagrangian; Computer science","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":[0.0004762466,0.0004370314,0.0005019127,0.0001274723,0.0004371416,0.0001103274,0.001358184,0.0003995885,0.0000224996],"category_scores_gemma":[0.001051583,0.000397527,0.0003239662,0.0003820655,0.0002651756,0.0001104258,0.001979606,0.0009136754,0.0002987721],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0004206879,"about_ca_system_score_gemma":0.000230231,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00003120913,"about_ca_topic_score_gemma":0.00007517906,"domain_scores_codex":[0.9979987,0.0001893873,0.0003659156,0.0007656072,0.0001531406,0.0005272858],"domain_scores_gemma":[0.9956865,0.0018699,0.0005369966,0.001543163,0.0002069817,0.0001563975],"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":[0.00007995642,0.00008875379,0.00006281643,0.0001565229,0.0002339718,0.0001748526,0.000357695,0.00218311,0.00002111324,0.9909016,0.00562522,0.0001143314],"study_design_scores_gemma":[0.000507115,0.00003783918,0.00007808912,0.0001525712,0.000186158,0.000002482847,0.0005322307,0.006179283,0.0001396159,0.9896635,0.002070314,0.000450829],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7963842,0.0001041238,0.151862,0.0009469637,0.01494733,0.003707283,0.0002101634,0.003116379,0.02872157],"genre_scores_gemma":[0.9814757,0.0001852301,0.001402601,0.00002082599,0.0004407226,0.000006588297,0.00001161486,0.0001359937,0.01632078],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1850914,"threshold_uncertainty_score":0.9998477,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2032207103135161,"score_gpt":0.2456350857291479,"score_spread":0.04241437541563178,"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."}}