{"id":"W4301954029","doi":"10.48550/arxiv.1411.7109","title":"Uniform positive existential interpretation of the integers in rings of\\n entire functions of positive characteristic","year":2014,"lang":"","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Differential Equations and Dynamical Systems","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Queen's University; American Institute of Mathematics; National Science Foundation","keywords":"Transcendental number; Mathematics; Interpretation (philosophy); Entire function; Class (philosophy); Pure mathematics; Ring (chemistry); Variable (mathematics); A priori and a posteriori; Transcendental function; Rationality; Existentialism; Discrete mathematics; Mathematical analysis; Computer science","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0003410851,0.0004380254,0.001105459,0.0004424686,0.0001229615,0.0000176863,0.0006825363,0.0004015566,0.00008754508],"category_scores_gemma":[0.0003404261,0.0004125047,0.0007227274,0.000793142,0.0006945715,0.0002321768,0.0007177635,0.0006275321,0.000008227723],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0004273406,"about_ca_system_score_gemma":0.0001685737,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007764635,"about_ca_topic_score_gemma":0.0002709901,"domain_scores_codex":[0.9970547,0.0004742035,0.001291224,0.0006626896,0.0002120399,0.0003051424],"domain_scores_gemma":[0.9950186,0.0007112875,0.002681302,0.0008369355,0.0006533968,0.00009845669],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.002986744,0.002842264,0.01669158,0.004734835,0.001706007,0.00002132852,0.01051815,0.2038345,0.007151668,0.7470677,0.000006575688,0.00243867],"study_design_scores_gemma":[0.001732799,0.0004010766,0.03063321,0.006127763,0.001255648,0.000004743291,0.003041227,0.8935648,0.001790981,0.0608728,0.000004164397,0.0005707568],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.593424,0.000007137178,0.4037053,0.00001315192,0.0004787047,0.000698414,0.0003048764,0.00001226482,0.001356153],"genre_scores_gemma":[0.9986025,0.00003232465,0.0002107998,0.000004792443,0.0000315078,0.000002979408,0.0001054308,0.00003234782,0.000977295],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.6897303,"threshold_uncertainty_score":0.9998327,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03375934817602544,"score_gpt":0.2039363724633544,"score_spread":0.1701770242873289,"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."}}