{"id":"W4320853708","doi":"10.48550/arxiv.2302.05857","title":"Sums, series, and products in Diophantine approximation","year":2023,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"University of Toronto; Université de Lille","keywords":"Series (stratigraphy); Diophantine approximation; Mathematics; Diophantine equation; Analytic continuation; Combinatorics; Pure mathematics; Arithmetic; Discrete mathematics; Algebra over a field; Mathematical analysis","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":[0.0004698634,0.0002563762,0.0004434925,0.0002281763,0.00005118794,0.0000512779,0.000259701,0.0002546568,0.00002203263],"category_scores_gemma":[0.0004956988,0.0002741786,0.0000615107,0.0003552909,0.00008777043,0.000149966,0.0006959558,0.0004080506,0.00003011928],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007602268,"about_ca_system_score_gemma":0.00005725911,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00006275141,"about_ca_topic_score_gemma":0.0001062793,"domain_scores_codex":[0.9986364,0.00007270691,0.0002888204,0.0006638553,0.00007913986,0.0002591271],"domain_scores_gemma":[0.9988477,0.0001848621,0.0002235702,0.0005743214,0.00009112217,0.00007842392],"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":[0.00004838705,0.0001749419,0.001099758,0.002552482,0.00005527031,0.0001985501,0.0002533231,0.0008911549,0.00007576498,0.9942502,0.00029577,0.0001043736],"study_design_scores_gemma":[0.0003002284,0.00002425684,0.0007725811,0.0002925175,0.00006115136,0.000004481402,0.00009343091,0.1195058,0.00006153448,0.8784894,0.0000897959,0.0003049161],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9743817,0.00003640114,0.0220212,0.0003089711,0.0002215138,0.0008008059,0.00005013531,0.000229322,0.00194999],"genre_scores_gemma":[0.9885541,0.0002963228,0.003518874,0.000009776737,0.00005583276,0.000003286761,0.0000542549,0.00004757726,0.007460021],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1186146,"threshold_uncertainty_score":0.999971,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1604425752661819,"score_gpt":0.2216613637132662,"score_spread":0.06121878844708431,"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."}}