{"id":"W2951961788","doi":"10.48550/arxiv.1006.4104","title":"Abelian Primitive Words","year":2010,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"semigroups and automata theory","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Winnipeg; University of Manitoba","funders":"","keywords":"Abelian group; Combinatorics on words; Word (group theory); Rank of an abelian group; Mathematics; Context (archaeology); Arithmetic of abelian varieties; Set (abstract data type); Elementary abelian group; Enumeration; Pure mathematics; Discrete mathematics; Computer science; Biology; Geometry","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005372682,0.0005072735,0.0005342026,0.001247689,0.001568988,0.001756915,0.0009916547,0.0008265628,0.007937025],"category_scores_gemma":[0.003985452,0.0002850161,0.0005269467,0.00113652,0.003366282,0.00479167,0.001846854,0.001250892,0.001695781],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006034108,"about_ca_system_score_gemma":0.0004511876,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003268774,"about_ca_topic_score_gemma":0.0003616659,"domain_scores_codex":[0.998857,0.0002549221,0.00008649383,0.0002818269,0.0003297326,0.000190116],"domain_scores_gemma":[0.9961809,0.002033439,0.0005075129,0.0004564475,0.0006011862,0.0002205512],"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":[0.00006243684,0.00003088908,0.0009332924,0.000142582,0.00001109326,0.0004339785,0.0004219415,0.001335679,0.004777805,0.9728017,0.00199037,0.01705836],"study_design_scores_gemma":[0.00001027809,0.00005116676,0.0002832538,0.00003607389,0.00001513473,0.0005660043,0.0002420294,0.004290377,0.004796493,0.9672261,0.02246351,0.00001955683],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5118485,0.004076242,0.3170574,0.002197856,0.001056691,0.0002660516,0.0008934971,0.0007861935,0.1618176],"genre_scores_gemma":[0.9107273,0.0009115974,0.06366577,0.0005025819,0.0005194274,0.0001596156,0.0005967898,0.0001637514,0.02275332],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007937025,"threshold_uncertainty_score":0.02655196,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04436992039874969,"score_gpt":0.1752911875584094,"score_spread":0.1309212671596597,"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."}}