{"id":"W2963635378","doi":"10.5539/ijsp.v7n1p115","title":"Statistical Distribution of Roots of a Polynomial Modulo Primes III","year":2017,"lang":"en","type":"article","venue":"International Journal of Statistics and Probability","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Combinatorics; Modulo; Prime (order theory); Distribution (mathematics); Sequence (biology); Conjecture; Integer (computer science); Polynomial; Discrete mathematics; Mathematical analysis","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.004312157,0.0004050018,0.001093471,0.001587095,0.000810419,0.0016026,0.001633101,0.0009361241,0.004134106],"category_scores_gemma":[0.03150606,0.0005054382,0.0004986535,0.001045013,0.003992183,0.00315425,0.001355267,0.001909914,0.0005251679],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001483157,"about_ca_system_score_gemma":0.0007808718,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001291066,"about_ca_topic_score_gemma":0.0006519725,"domain_scores_codex":[0.99852,0.0004561027,0.00004708476,0.0004241643,0.0003118826,0.0002407816],"domain_scores_gemma":[0.9743313,0.0176539,0.002244954,0.003126414,0.001563512,0.001079946],"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":[0.0009952621,0.0001806821,0.05007887,0.0002046532,0.0001155054,0.0008540034,0.0009137372,0.0724938,0.01157282,0.8257492,0.007948532,0.0288928],"study_design_scores_gemma":[0.0001491244,0.0003567099,0.02805548,0.00009099307,0.0000819864,0.00121935,0.0006802874,0.5597086,0.01047828,0.3944567,0.004555339,0.0001671645],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8231258,0.0006290054,0.1660448,0.001900465,0.0001299117,0.0001110634,0.0008525174,0.0005379876,0.006668414],"genre_scores_gemma":[0.9924669,0.000257174,0.004449811,0.0000971139,0.0001522156,0.00007637949,0.0004093666,0.00005340982,0.00203754],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004312157,"threshold_uncertainty_score":0.02280515,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04342555324906845,"score_gpt":0.3753228131710957,"score_spread":0.3318972599220272,"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."}}