{"id":"W2401899815","doi":"","title":"A characterization of the arithmetical hierarchy by language equations.","year":2004,"lang":"en","type":"article","venue":"DCFS","topic":"semigroups and automata theory","field":"Computer Science","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"Queen's University","funders":"","keywords":"Peano axioms; Arithmetic function; Mathematics; Concatenation (mathematics); Hierarchy; Expressive power; Class (philosophy); Axiom; Second-order arithmetic; Property (philosophy); Characterization (materials science); Analytical hierarchy; Discrete mathematics; Algebra over a field; Arithmetic; Pure mathematics; Computer science; Theoretical computer science; Analytic hierarchy process; Mathematical economics","routes":{"ca_aff":true,"ca_fund":false,"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":[0.0001031332,0.00003927527,0.00004949475,0.00002098261,0.00004063281,0.00002889743,0.0003635491,0.00002150405,0.00001187159],"category_scores_gemma":[0.0000374025,0.00002687727,0.00002804543,0.0002012192,0.00003815643,0.0001273654,0.00008857084,0.00004476789,0.00001648019],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001264934,"about_ca_system_score_gemma":0.0000244302,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001424873,"about_ca_topic_score_gemma":8.702508e-7,"domain_scores_codex":[0.9995837,0.000027858,0.00008953142,0.00009439079,0.0001253467,0.00007921449],"domain_scores_gemma":[0.9996243,0.00003054348,0.00003919308,0.0002710591,0.00001559658,0.00001936559],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"bench_or_experimental","study_design_scores_codex":[9.173527e-7,0.0000483869,0.00004269754,0.000004980072,0.000004250093,0.000001152227,0.001556932,0.000008295728,0.474588,0.5013263,0.00004039484,0.02237765],"study_design_scores_gemma":[0.0009454874,0.00008537687,0.01505022,0.00008116632,0.00001199204,0.00001559933,0.00009956722,0.02332537,0.8989403,0.05620525,0.004949539,0.0002901597],"study_design_candidate":"bench_or_experimental","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4265438,0.00002837707,0.5707166,0.002145841,0.0001003948,0.00006036351,0.000008310876,0.00004475095,0.0003516664],"genre_scores_gemma":[0.997246,0.000001786043,0.002175027,0.0004233898,0.00002646281,0.000004240432,0.000007583421,0.000002868848,0.0001126684],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.5707022,"threshold_uncertainty_score":0.1096023,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.00519566250757594,"score_gpt":0.2101366202119873,"score_spread":0.2049409577044113,"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."}}