{"id":"W2054384161","doi":"10.4064/aa123-2-5","title":"On the number of integers represented by systems of Abelian norm forms","year":2006,"lang":"en","type":"article","venue":"Acta Arithmetica","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"Aurora College; University of Toronto","funders":"","keywords":"Mathematics; Abelian group; Norm (philosophy); Pure mathematics; Algebra over a field","routes":{"ca_aff":true,"ca_fund":false,"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":[0.001017927,0.0001562103,0.0003741385,0.00007578253,0.00005777016,0.00002462091,0.0005047263,0.00009465552,0.0005494317],"category_scores_gemma":[0.001050418,0.00009448658,0.0001328045,0.000363011,0.0003456193,0.00005911456,0.0001145763,0.0002458775,0.00006683294],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004965165,"about_ca_system_score_gemma":0.00003828181,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000691436,"about_ca_topic_score_gemma":0.00001601544,"domain_scores_codex":[0.9981071,0.0001521516,0.0005560832,0.0002152877,0.0006580438,0.0003113236],"domain_scores_gemma":[0.9963246,0.002282283,0.0002507676,0.000873983,0.00020994,0.00005842965],"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":[0.00007907079,0.0004594758,0.002464073,0.000183827,0.0001684274,0.000004248861,0.0001319935,0.000003606117,0.004050524,0.9102908,0.08207344,0.00009048736],"study_design_scores_gemma":[0.001395391,0.0002547723,0.0005229139,0.0005772883,0.0002226286,0.00005433646,0.002331489,0.004895664,0.05903754,0.9242175,0.005993571,0.0004969583],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7743832,0.00003307481,0.001626262,0.001270496,0.00007537851,0.0005982888,0.00007151473,0.00004743843,0.2218943],"genre_scores_gemma":[0.992345,0.00000547014,0.0003846402,0.00002293433,0.00002497106,0.00002265004,0.000007918678,0.00003207909,0.007154356],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2179618,"threshold_uncertainty_score":0.6015892,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02648636760733062,"score_gpt":0.3214157156034311,"score_spread":0.2949293479961004,"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."}}