{"id":"W4411720755","doi":"10.61091/ars163-05","title":"Primitive normal pairs with prescribed traces over finite fields","year":2025,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"Finite Group Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Department of Science and Technology, Ministry of Science and Technology, India","keywords":"Mathematics; Finite field; Pure mathematics; Combinatorics","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005535539,0.0002188856,0.0003007867,0.000171071,0.0001588664,0.00008159841,0.0004075638,0.0001654578,0.0002852279],"category_scores_gemma":[0.000753519,0.0001837691,0.00008035148,0.000482921,0.000155994,0.0002191366,0.0001741018,0.0004620925,0.000040349],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006987042,"about_ca_system_score_gemma":0.0001408351,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002989031,"about_ca_topic_score_gemma":0.00003564136,"domain_scores_codex":[0.998346,0.0002074028,0.0002736846,0.0003240212,0.0004032848,0.0004456031],"domain_scores_gemma":[0.9969425,0.00216466,0.00008200596,0.0005546335,0.0001675569,0.00008860299],"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":[0.0003056649,0.0002993537,0.00476881,0.0001514178,0.0001501302,0.00003900397,0.001153965,0.000006298366,0.00008873935,0.9820744,0.01043874,0.0005234355],"study_design_scores_gemma":[0.002254512,0.0003782665,0.006358291,0.0001842383,0.00006541821,0.000002805293,0.0003203576,0.0004221765,0.003847682,0.9835845,0.002303403,0.0002783103],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9305643,0.00008766817,0.0003731681,0.0003999452,0.00060515,0.0005369716,0.00001194632,0.0001788648,0.06724194],"genre_scores_gemma":[0.9925931,0.000008853785,0.0007397372,0.00016258,0.000009386985,0.00008286984,0.000006833014,0.00003124975,0.006365405],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.06202875,"threshold_uncertainty_score":0.7493888,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02606999920521546,"score_gpt":0.300264648577068,"score_spread":0.2741946493718526,"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."}}