{"id":"W3011769116","doi":"10.1016/j.apal.2023.103316","title":"Companionability characterization for the expansion of an o-minimal theory by a dense subgroup","year":2023,"lang":"en","type":"article","venue":"Annals of Pure and Applied Logic","topic":"Advanced Topology and Set Theory","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":false,"ca_institutions":"McMaster University","funders":"National Science Foundation","keywords":"Mathematics; Multiplicative function; Unary operation; Abelian group; Predicate (mathematical logic); Characterization (materials science); Morphism; Discrete mathematics; Base (topology); Pure mathematics; Combinatorics; Computer science; Mathematical analysis","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":[0.0008952327,0.00008924018,0.0002109387,0.00002779172,0.0001014535,0.000003471836,0.0001032833,0.00008803583,0.00002184153],"category_scores_gemma":[0.0001199715,0.00005841159,0.00004515193,0.00009082658,0.0002114109,0.00004641544,0.0000350039,0.00006126279,0.000001303299],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000001313674,"about_ca_system_score_gemma":0.0000086106,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":4.156564e-7,"about_ca_topic_score_gemma":0.000001177106,"domain_scores_codex":[0.9993544,0.00007210371,0.0002178472,0.0001483269,0.00007342479,0.0001338516],"domain_scores_gemma":[0.9985708,0.001005868,0.0001482899,0.0001920256,0.00005671068,0.00002629561],"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":[0.0004895973,0.0001300847,0.00002925898,0.0001211189,0.00002892856,3.056675e-7,0.000892136,0.000005948992,0.1003949,0.8888866,0.0004179424,0.008603168],"study_design_scores_gemma":[0.0002099872,0.0001459647,0.001676304,0.000007187782,0.00002296315,0.000001196988,0.001111272,0.0001435657,0.04784367,0.9485233,0.0002448361,0.00006973084],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9846038,0.00007460519,0.0142669,0.0004164005,0.00002813456,0.0003776847,0.00008852771,0.0000368329,0.0001071815],"genre_scores_gemma":[0.9989951,0.00008156239,0.0003949854,0.0002570494,0.00003041883,0.00005082679,0.0001006595,0.000009277908,0.00008008101],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.0596367,"threshold_uncertainty_score":0.2381956,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08079708343801577,"score_gpt":0.3528783710157186,"score_spread":0.2720812875777028,"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."}}