{"id":"W2962907371","doi":"10.48550/arxiv.1907.08247","title":"The abelian complexity of infinite words and the Frobenius problem","year":2019,"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","funders":"","keywords":"Abelian group; Mathematics; Algebra over a field; Pure 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001550447,0.0004155504,0.0007239142,0.001378838,0.001363269,0.002205003,0.0007766644,0.001137756,0.002959619],"category_scores_gemma":[0.008663085,0.0003648369,0.0006382412,0.0008122068,0.005089109,0.007707454,0.001765031,0.001735162,0.0003478223],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001573844,"about_ca_system_score_gemma":0.0007932766,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001007713,"about_ca_topic_score_gemma":0.0006232017,"domain_scores_codex":[0.9987692,0.0004259511,0.00006081515,0.0002318463,0.0002891443,0.0002228892],"domain_scores_gemma":[0.988379,0.009741896,0.0006565867,0.0003576605,0.0004067787,0.0004580493],"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":[0.00008832393,0.00003709397,0.001112919,0.00006757997,0.00001681817,0.0001441195,0.0004939311,0.007690376,0.001580859,0.982805,0.0007228949,0.005240034],"study_design_scores_gemma":[0.00001834214,0.00002200492,0.0004849886,0.00001050365,0.000006213168,0.00009023521,0.0001570111,0.01505584,0.0008394492,0.9821104,0.001188424,0.0000165472],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8490534,0.00117651,0.1149924,0.003273673,0.00009404241,0.00003573865,0.0001657563,0.0001031771,0.03110534],"genre_scores_gemma":[0.983012,0.0003911014,0.01061059,0.0001506007,0.0003173476,0.00004841422,0.0001256179,0.00003984569,0.005304405],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002959619,"threshold_uncertainty_score":0.01141912,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05682712978585749,"score_gpt":0.1779442085952423,"score_spread":0.1211170788093849,"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."}}