{"id":"W2950350370","doi":"10.48550/arxiv.math/0602454","title":"On the rational subset problem for groups","year":2006,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"semigroups and automata theory","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Carleton University","funders":"","keywords":"Decidability; Mathematics; Free product; Monoid; Abelian group; Combinatorics; Discrete mathematics; Group (periodic table); Commutative property; Direct product; Free monoid; Product (mathematics)","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":[0.0007388248,0.0002584224,0.0002189061,0.00005153099,0.0002524435,0.0002185888,0.001655963,0.0001661743,0.00003403314],"category_scores_gemma":[0.00005886016,0.0001777525,0.0001919794,0.0001239732,0.00006101521,0.0001329942,0.0007662314,0.0003727496,0.000139647],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000545512,"about_ca_system_score_gemma":0.0001230489,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002347775,"about_ca_topic_score_gemma":0.00001333337,"domain_scores_codex":[0.9983448,0.0000961905,0.000302831,0.0006311964,0.0002822852,0.0003426518],"domain_scores_gemma":[0.9979961,0.0006101145,0.0002141131,0.00104672,0.00008827457,0.00004466385],"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":[0.0000103761,0.00009587598,0.004989313,0.00005701578,0.00004324913,0.000004924756,0.0001877933,0.001860344,0.0001359092,0.9219257,0.06920794,0.001481607],"study_design_scores_gemma":[0.0004170438,0.0001099912,0.06883007,0.0001901582,0.00002353824,0.000008108541,0.00001345832,0.03428629,0.001193576,0.8822309,0.0120807,0.0006161936],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6166747,0.0001822744,0.3673586,0.008257886,0.001364581,0.001279823,0.00008240085,0.0004066791,0.004393102],"genre_scores_gemma":[0.9804476,0.00000691144,0.01444396,0.002619167,0.0007188891,0.0005230727,0.0001762024,0.00003032172,0.001033839],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.363773,"threshold_uncertainty_score":0.7248535,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03801478463653996,"score_gpt":0.2499666468721628,"score_spread":0.2119518622356228,"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."}}