{"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":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001755947,0.0001618557,0.0006476379,0.0001265997,0.00002872624,0.00001398171,0.0002504644,0.0001341619,0.007836576],"category_scores_gemma":[0.001260042,0.0001168487,0.0002062396,0.0001416588,0.0002886621,0.0002221261,0.00007380774,0.0002466328,0.0000282256],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001516514,"about_ca_system_score_gemma":0.00006008921,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000006318036,"about_ca_topic_score_gemma":3.088804e-7,"domain_scores_codex":[0.9982542,0.0003519147,0.0008325357,0.00009866113,0.000288937,0.0001737324],"domain_scores_gemma":[0.9959184,0.00230528,0.001121692,0.00025142,0.0002920015,0.0001112392],"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":[0.001582581,0.001468391,0.01550287,0.001524172,0.002468203,0.00006530235,0.01595013,0.000005503917,0.03543938,0.7979671,0.1141752,0.01385115],"study_design_scores_gemma":[0.0007457577,0.0001887783,0.002203136,0.000236553,0.000139696,0.0004671045,0.00183321,0.00000190699,0.01601443,0.9775726,0.0004729937,0.0001238404],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9891537,0.0004889733,0.0006280008,0.0001629993,0.0001902388,0.0001271478,0.00002249364,0.000007501756,0.009218941],"genre_scores_gemma":[0.994959,0.00003848241,0.003309301,0.00008325111,0.0001498628,0.000001007275,6.194219e-7,0.0000228504,0.001435633],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1796055,"threshold_uncertainty_score":0.9930704,"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."}}