{"id":"W4407625144","doi":"10.1016/j.jnt.2025.01.004","title":"Kummer theory for function fields","year":2025,"lang":"en","type":"article","venue":"Journal of Number Theory","topic":"Meromorphic and Entire Functions","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"Fonds National de la Recherche Luxembourg; Pacific Institute for the Mathematical Sciences; University of Lethbridge; Division of Mathematical Sciences; Université du Luxembourg","keywords":"Mathematics; Function field; Function (biology); Pure mathematics; Field (mathematics)","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":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001550726,0.00009057605,0.0002079311,0.000079111,0.0001072529,0.00001935781,0.0001223751,0.00009835714,0.005358589],"category_scores_gemma":[0.0009636027,0.00006841127,0.0002315594,0.0001056948,0.00004006938,0.0001013313,0.00002009521,0.0002051375,0.00003411047],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000292669,"about_ca_system_score_gemma":0.00006964481,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":4.733972e-7,"about_ca_topic_score_gemma":0.00000122659,"domain_scores_codex":[0.9991511,0.0001475345,0.000372444,0.00007486129,0.0001234955,0.0001306075],"domain_scores_gemma":[0.9972921,0.002076153,0.0002241741,0.0001661027,0.0001965937,0.0000448557],"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":[0.0003978038,0.00008650021,0.0001001022,0.0000466085,0.0001996929,0.000001960339,0.00010541,0.000002174783,0.00004311745,0.6704242,0.3220364,0.006555967],"study_design_scores_gemma":[0.0005064529,0.00007002145,0.0001405415,0.00009411618,0.0002650458,0.00003398094,0.0004316312,0.00001146374,0.0001427304,0.8838287,0.1144162,0.00005908961],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.02269021,0.0001528762,0.8869317,0.0007032372,0.002776584,0.0001520979,0.00001643485,0.00002800554,0.08654887],"genre_scores_gemma":[0.7991021,0.00004133729,0.01124578,0.002345518,0.001197838,0.00003353578,0.000007993539,0.00004107316,0.1859849],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.8756859,"threshold_uncertainty_score":0.9955506,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04148496422549003,"score_gpt":0.3362764919013411,"score_spread":0.294791527675851,"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."}}