{"id":"W4410694889","doi":"10.1016/j.aim.2025.110358","title":"Vojta's abc conjecture for algebraic tori and applications over function fields","year":2025,"lang":"en","type":"article","venue":"Advances in Mathematics","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Calgary","funders":"Natural Science Foundation of Hunan Province; Natural Sciences and Engineering Research Council of Canada; National Natural Science Foundation of China; National Science and Technology Council","keywords":"Mathematics; Conjecture; Function field; Algebraic number; Torus; Function (biology); abc conjecture; Pure mathematics; Combinatorics; Field (mathematics); Algebra over a field; Collatz conjecture; Mathematical analysis; 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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003479609,0.0001630514,0.000277651,0.0001202094,0.0001161467,0.0000250789,0.000143855,0.0001435147,0.00007343227],"category_scores_gemma":[0.0003472637,0.000146778,0.0000572878,0.0003030253,0.00007724048,0.0001825507,0.00005278159,0.0001531329,0.000004972143],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003134233,"about_ca_system_score_gemma":0.00002269365,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":9.591598e-7,"about_ca_topic_score_gemma":0.00002074528,"domain_scores_codex":[0.9990951,0.0000223828,0.0003469617,0.0002307438,0.0001048364,0.0001999076],"domain_scores_gemma":[0.997847,0.001630223,0.0001214046,0.000326155,0.00004229939,0.00003289395],"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":[0.00001995973,0.0001116315,0.0002460861,0.001027405,0.00002743019,3.750212e-7,0.0002957112,0.00001325159,0.00002017832,0.9850257,0.0005303738,0.01268187],"study_design_scores_gemma":[0.000497412,0.00003630505,0.0001053193,0.0001135459,0.00005993335,0.000003115266,0.0004361105,0.0003051117,0.000217395,0.9623919,0.03569402,0.0001398492],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.02912698,0.003157667,0.9477596,0.0002674198,0.000368126,0.001286209,0.00001636074,0.0001221379,0.01789556],"genre_scores_gemma":[0.8779798,0.0008600338,0.1083682,0.0009405004,0.0004103348,0.001538087,0.00002783553,0.00007116327,0.009804027],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.8488528,"threshold_uncertainty_score":0.5985435,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.009993467772148018,"score_gpt":0.3103236003469907,"score_spread":0.3003301325748428,"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."}}