{"id":"W2962941749","doi":"10.4153/cjm-2017-022-1","title":"A New Proof of the Hansen—Mullen Irreducibility Conjecture","year":2017,"lang":"en","type":"article","venue":"Canadian Journal of Mathematics","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"Carleton University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Irreducibility; Mathematics; Conjecture; Elementary proof; Pure mathematics; Connection (principal bundle); Finite field; Function (biology); Algebra over a field; Discrete mathematics; Geometry","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002696912,0.0005218675,0.001029034,0.001464973,0.001460027,0.002042614,0.001277122,0.001155204,0.01072368],"category_scores_gemma":[0.008263582,0.0004376916,0.001140361,0.0008966445,0.004510638,0.005808157,0.004702432,0.004264092,0.0008478553],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001071714,"about_ca_system_score_gemma":0.0008080343,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004153299,"about_ca_topic_score_gemma":0.0004497768,"domain_scores_codex":[0.9986993,0.000210714,0.0000884326,0.0002891665,0.0005123914,0.0001999599],"domain_scores_gemma":[0.9947498,0.003060242,0.0003875066,0.0008232121,0.000603255,0.0003759728],"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":[0.00002762639,0.00003555209,0.0003514975,0.00007760517,0.000008139885,0.0003005041,0.0002185211,0.0007240658,0.001123909,0.9895505,0.00187735,0.005704761],"study_design_scores_gemma":[0.00002504841,0.00004446469,0.0003708748,0.00004464192,0.000009907006,0.0003014969,0.00008580239,0.005392182,0.001431761,0.9807077,0.0115685,0.00001758305],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2374216,0.004366369,0.4909899,0.01744068,0.002997838,0.0001517679,0.00107267,0.001266691,0.2442925],"genre_scores_gemma":[0.9328416,0.001493685,0.04988412,0.001936826,0.001466044,0.0001088253,0.0003602601,0.0002007898,0.01170794],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01072368,"threshold_uncertainty_score":0.03587431,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0548129407464084,"score_gpt":0.311301671536611,"score_spread":0.2564887307902026,"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."}}