{"id":"W2102041446","doi":"10.1090/s0002-9939-08-09737-2","title":"Transcendence of power series for some number theoretic functions","year":2008,"lang":"en","type":"article","venue":"Proceedings of the American Mathematical Society","topic":"semigroups and automata theory","field":"Computer Science","cited_by":21,"is_retracted":false,"has_abstract":true,"ca_institutions":"Simon Fraser University","funders":"Natural Sciences and Engineering Research Council of Canada; Mitacs","keywords":"Transcendence (philosophy); Series (stratigraphy); Power (physics); Power series; Mathematics; Philosophy; Mathematical analysis; Epistemology; Physics; Geology","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":[0.0003212089,0.0001324895,0.000336458,0.00001152236,0.0001640864,0.000019695,0.0009167298,0.00002801627,0.00002585515],"category_scores_gemma":[0.0001236881,0.00008580271,0.0004354662,0.0003982527,0.001335894,0.0003810625,0.0001510129,0.00009914243,0.000006677906],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000018196,"about_ca_system_score_gemma":0.00003339153,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002272595,"about_ca_topic_score_gemma":1.719929e-8,"domain_scores_codex":[0.9989288,0.000006653391,0.0003044816,0.000215761,0.0003102492,0.0002340529],"domain_scores_gemma":[0.9990367,0.0002075203,0.0003271262,0.0002175716,0.0001582994,0.00005283224],"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":[0.0000144147,0.0001540984,0.0005095059,0.0002108444,0.00005314884,7.063781e-8,0.004557405,0.000001303393,0.0119053,0.9799938,0.002278499,0.0003216394],"study_design_scores_gemma":[0.0003015831,0.0002370026,0.002181167,0.0001244648,0.00005059797,0.0001133197,0.003066233,0.004285827,0.04553943,0.9435998,0.0002411377,0.0002594352],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.910397,0.00003140502,0.08406566,0.002140937,0.00007335289,0.0003546531,0.00001312813,0.0001232866,0.002800608],"genre_scores_gemma":[0.9345819,0.0000276372,0.06477506,0.0002615498,0.00002145087,0.00003503119,1.357979e-7,0.00001228336,0.0002849844],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.03639397,"threshold_uncertainty_score":0.4922156,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0108907296399684,"score_gpt":0.2324695318110135,"score_spread":0.2215788021710451,"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."}}