{"id":"W2053097241","doi":"10.1016/j.jnt.2013.03.001","title":"Powerful values of polynomials and a conjecture of Vojta","year":2013,"lang":"en","type":"article","venue":"Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":13,"is_retracted":false,"has_abstract":false,"ca_institutions":"Queen's University","funders":"","keywords":"Mathematics; Meromorphic function; Exponent; Square-free integer; Diophantine equation; Conjecture; Diophantine approximation; Nevanlinna theory; Geometry of numbers; Algebraic number field; Macdonald polynomials; Combinatorics; Orthogonal polynomials; Pure mathematics; Discrete mathematics; Difference polynomials","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.003781087,0.001023357,0.002466596,0.002544243,0.004705153,0.005787905,0.002013854,0.003184744,0.00808954],"category_scores_gemma":[0.01367642,0.001033384,0.001916385,0.00261183,0.01374676,0.01302209,0.007205512,0.008436471,0.001027945],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002619088,"about_ca_system_score_gemma":0.001047142,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001580649,"about_ca_topic_score_gemma":0.001051238,"domain_scores_codex":[0.9971343,0.0008745544,0.0001345989,0.0006395992,0.0005506648,0.0006662167],"domain_scores_gemma":[0.9916487,0.005959926,0.0003971518,0.0008399938,0.0005612283,0.0005929515],"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":[0.00006336543,0.00001581462,0.0001993263,0.00003346638,0.000008251687,0.0000659125,0.0003021975,0.0004588535,0.0001722359,0.9949219,0.002213419,0.001545342],"study_design_scores_gemma":[0.00001866036,0.000009379245,0.00009118274,0.000009742906,0.000006958586,0.00003642382,0.00005645092,0.0006340906,0.00008479096,0.9966942,0.002348536,0.00000948179],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.454013,0.009564457,0.1094694,0.06953175,0.005833184,0.00009437495,0.0009225098,0.0006014528,0.3499699],"genre_scores_gemma":[0.9757088,0.001149403,0.006860701,0.001386835,0.002051615,0.0000419828,0.0002329464,0.00009419557,0.01247347],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.00808954,"threshold_uncertainty_score":0.02706224,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01528911964267106,"score_gpt":0.2826402654114537,"score_spread":0.2673511457687826,"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."}}