{"id":"W4416348003","doi":"10.1051/ita/2025016","title":"A symmetry property of Christoffel words","year":2025,"lang":"","type":"article","venue":"RAIRO. Theoretical informatics and applications","topic":"semigroups and automata theory","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université du Québec à Montréal","funders":"Natural Sciences and Engineering Research Council of Canada; Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada","keywords":"Christoffel symbols; Property (philosophy); Cardinality (data modeling); Symmetry (geometry); Bivariate analysis","routes":{"ca_aff":true,"ca_fund":true,"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":[0.0007903734,0.0002657778,0.000483166,0.0008029179,0.001205703,0.001734909,0.0005610489,0.0004658352,0.004104075],"category_scores_gemma":[0.004698419,0.0002246994,0.0006101761,0.0009389271,0.002202217,0.003085651,0.001043764,0.0009886684,0.0008201622],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008802161,"about_ca_system_score_gemma":0.0008144753,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009321918,"about_ca_topic_score_gemma":0.0005467284,"domain_scores_codex":[0.9989333,0.0001655292,0.00008981318,0.0002746027,0.0003236948,0.0002131002],"domain_scores_gemma":[0.997414,0.0009108484,0.0004116104,0.0004840705,0.0005150384,0.0002643318],"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":[0.00006617965,0.00002106548,0.0009737893,0.00003097454,0.000006582217,0.0001675819,0.0003467166,0.001133574,0.006650448,0.9788252,0.0006451659,0.01113276],"study_design_scores_gemma":[0.00002233366,0.0001038232,0.0009651711,0.00002026939,0.00001491295,0.0006478261,0.0002938142,0.01182721,0.009783866,0.9673123,0.008966047,0.00004238555],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6075659,0.000553457,0.3258083,0.0006556981,0.000287912,0.0001186968,0.0006781641,0.0003756354,0.06395615],"genre_scores_gemma":[0.9711274,0.0002465772,0.0210207,0.0001335896,0.0001870771,0.0000706279,0.0002841181,0.00008888647,0.006841093],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004104075,"threshold_uncertainty_score":0.01372951,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.005791708219538981,"score_gpt":0.240717505541032,"score_spread":0.234925797321493,"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."}}