{"id":"W4408444984","doi":"10.5070/c65165014","title":"On the number of squares in a finite word","year":2025,"lang":"en","type":"article","venue":"Combinatorial Theory","topic":"semigroups and automata theory","field":"Computer Science","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Université du Québec à Montréal","keywords":"Word (group theory); Computer science; Least-squares function approximation; Mathematics; Arithmetic; Statistics; Geometry","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001234466,0.0001041166,0.0001629797,0.0000909156,0.00006071496,0.0000469376,0.001067808,0.00006000195,0.00007566979],"category_scores_gemma":[0.0005659446,0.00007150875,0.00006699633,0.0005915158,0.00009823466,0.00009810513,0.0002662287,0.000169491,0.00004024139],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002711548,"about_ca_system_score_gemma":0.00005823757,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000007513333,"about_ca_topic_score_gemma":5.192813e-7,"domain_scores_codex":[0.9989207,0.0003568741,0.0001909274,0.0002047369,0.0001547796,0.0001719765],"domain_scores_gemma":[0.9960857,0.003135618,0.00006582413,0.0006586543,0.00003400234,0.00002016839],"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":[0.00004709073,0.00009678305,0.0002433183,0.000007392073,0.000009311818,0.000003545541,0.0002635699,0.0000112993,0.00006562835,0.9909616,0.0008879369,0.007402514],"study_design_scores_gemma":[0.0004819567,0.00002197591,0.0006522975,0.0001032501,0.000002383043,4.127437e-7,0.00005061946,0.0007727977,0.002441014,0.9942825,0.001117123,0.00007366386],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8530539,0.0003157507,0.03152445,0.002432679,0.009633587,0.000446402,0.000004192421,0.0002227792,0.1023663],"genre_scores_gemma":[0.998939,0.000005414966,0.00009893209,0.0005058247,0.00003758123,0.00001934112,3.927733e-7,0.000004648301,0.0003889068],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1458851,"threshold_uncertainty_score":0.2916042,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.008094390021761747,"score_gpt":0.2546233772361189,"score_spread":0.2465289872143572,"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."}}