{"id":"W4407477361","doi":"10.1090/proc/17239","title":"Borel complexity of the isomorphism relation of Archimedean orders in finitely generated groups","year":2025,"lang":"en","type":"preprint","venue":"Proceedings of the American Mathematical Society","topic":"Computability, Logic, AI Algorithms","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"National Research Council Canada","keywords":"Isomorphism (crystallography); Mathematics; Finitely-generated abelian group; Relation (database); Pure mathematics; Combinatorics; 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001670932,0.0006164814,0.001105368,0.002370274,0.002469299,0.005695315,0.00100497,0.00135253,0.007115743],"category_scores_gemma":[0.008236296,0.0006201326,0.001551931,0.001749788,0.005681043,0.01246072,0.003784402,0.004003454,0.0006850704],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.003945041,"about_ca_system_score_gemma":0.001072886,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.003479699,"about_ca_topic_score_gemma":0.00221258,"domain_scores_codex":[0.9968876,0.000787835,0.0001744806,0.0007188009,0.0008856258,0.000545658],"domain_scores_gemma":[0.9917037,0.005490461,0.0005626212,0.0007445275,0.0007658845,0.000732804],"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":[0.00007547266,0.00003444714,0.001462667,0.00004026556,0.00001688846,0.00006804473,0.0007147347,0.0009855792,0.0005063348,0.9912763,0.000792594,0.004026592],"study_design_scores_gemma":[0.00001632589,0.00002032749,0.0009426796,0.00001059801,0.00001055105,0.0000515078,0.0001791077,0.002776293,0.0005354556,0.9931003,0.002341248,0.00001557188],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8242615,0.002753931,0.08239721,0.008907577,0.0002174074,0.00006268085,0.0007480579,0.0004260968,0.08022545],"genre_scores_gemma":[0.9828684,0.0005370551,0.006500019,0.0003667906,0.0002877932,0.00005328353,0.0006014872,0.00008977256,0.008695473],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007115743,"threshold_uncertainty_score":0.0286234,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03629321683115332,"score_gpt":0.2685594236310841,"score_spread":0.2322662067999308,"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."}}