{"id":"W4400722596","doi":"10.1016/j.jnt.2024.06.005","title":"On non-Zariski density of (D,S)-integral points in forward orbits and the Subspace Theorem","year":2024,"lang":"en","type":"article","venue":"Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"Acadia University; Université du Québec à Montréal; Carleton University; University of Waterloo","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Surjective function; Algebraic number field; Subspace topology; Divisor (algebraic geometry); Weierstrass factorization theorem; Pure mathematics; Projective variety; Field (mathematics); Base (topology); Discrete mathematics; Mathematical analysis; Factorization","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":[0.006781668,0.0002227207,0.0006154221,0.0002282418,0.00006026756,0.00004789405,0.0003188863,0.000135956,0.0008568882],"category_scores_gemma":[0.002120486,0.0001255097,0.0003062299,0.0004013845,0.0004388899,0.000190353,0.00009479213,0.0008348054,0.00004462033],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005745161,"about_ca_system_score_gemma":0.00008141353,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000007754094,"about_ca_topic_score_gemma":0.000009381753,"domain_scores_codex":[0.997773,0.0007078534,0.0006840085,0.0001722488,0.0004134535,0.0002494217],"domain_scores_gemma":[0.9912028,0.007907059,0.0003647337,0.0002985875,0.0001340111,0.00009280987],"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":[0.002078664,0.0001405994,0.0009135073,0.0001640631,0.0002343612,0.000143318,0.004823179,0.000002369638,0.00005370447,0.985023,0.00439216,0.002031113],"study_design_scores_gemma":[0.00140639,0.0001060556,0.001052079,0.0007934064,0.0001335634,0.0006567567,0.00190244,0.00008017242,0.001630729,0.9919029,0.0002036931,0.0001318384],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9833515,0.0003397004,0.003036106,0.0007593886,0.0004480375,0.0001769626,0.00001275405,0.000016086,0.01185945],"genre_scores_gemma":[0.9976745,0.00007735454,0.0007797406,0.0001811072,0.0001471736,0.000002860307,6.60008e-7,0.0000333078,0.001103329],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01432295,"threshold_uncertainty_score":0.9382325,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01222092855674242,"score_gpt":0.2861244061313192,"score_spread":0.2739034775745768,"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."}}