{"id":"W1967372194","doi":"10.1016/j.tcs.2007.01.020","title":"On critical exponents in fixed points of non-erasing morphisms","year":2007,"lang":"en","type":"article","venue":"Theoretical Computer Science","topic":"semigroups and automata theory","field":"Computer Science","cited_by":33,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Mathematics; Morphism; Alphabet; Exponent; Eigenvalues and eigenvectors; Fixed point; Finite field; Degree (music); Combinatorics; Algebraic number; Discrete mathematics; Field (mathematics); Matrix (chemical analysis); Critical exponent; Pure mathematics; Mathematical analysis; Geometry; Scaling","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":[0.003234369,0.001425696,0.002261813,0.006190132,0.003701903,0.005674456,0.00161617,0.002590448,0.006879713],"category_scores_gemma":[0.01922332,0.001127599,0.001386717,0.002239103,0.007674327,0.009977567,0.004565711,0.004561666,0.0005980215],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002835897,"about_ca_system_score_gemma":0.0008742015,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001168617,"about_ca_topic_score_gemma":0.001073632,"domain_scores_codex":[0.9988601,0.0003202616,0.00008180127,0.0001970077,0.0002402572,0.0003005568],"domain_scores_gemma":[0.9830517,0.01240228,0.001188714,0.0008306545,0.001086066,0.001440489],"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":[0.0001184884,0.00003131924,0.0007609543,0.00007198442,0.00001610386,0.0004017733,0.001077225,0.001884907,0.001461133,0.9910668,0.0004710763,0.002638245],"study_design_scores_gemma":[0.00006655852,0.00003321909,0.0004296257,0.00005036265,0.00001952453,0.0001538284,0.0003152476,0.007738985,0.0007472838,0.9893028,0.001118596,0.00002398738],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8271224,0.003788359,0.1205115,0.00231574,0.0004398034,0.0001432932,0.0002056983,0.0004333521,0.04503989],"genre_scores_gemma":[0.9799393,0.001046306,0.01013049,0.0001874008,0.0003272104,0.00009753333,0.0001248558,0.0001438244,0.008003078],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006879713,"threshold_uncertainty_score":0.02301496,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.00930701070768034,"score_gpt":0.2771171212431067,"score_spread":0.2678101105354263,"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."}}