{"id":"W4399830286","doi":"10.4204/eptcs.403.26","title":"A Symmetry Property of Christoffel Words","year":2024,"lang":"en","type":"article","venue":"Electronic Proceedings in Theoretical Computer Science","topic":"semigroups and automata theory","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Christoffel symbols; Symmetry (geometry); Cardinality (data modeling); Property (philosophy); Mathematics; Bivariate analysis; Pure mathematics; Algebra over a field; Computer science; Geometry; Philosophy; Statistics; Epistemology","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0009556951,0.0003084739,0.000538199,0.0008832297,0.001369096,0.001903405,0.0006579179,0.00052672,0.004847907],"category_scores_gemma":[0.005243573,0.000247091,0.0006576587,0.000978991,0.002375134,0.00338728,0.001177939,0.001143435,0.0009985898],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009234683,"about_ca_system_score_gemma":0.000928257,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001022789,"about_ca_topic_score_gemma":0.0005411808,"domain_scores_codex":[0.9986635,0.0001937923,0.0001116659,0.0003399136,0.0004046018,0.0002864261],"domain_scores_gemma":[0.9972173,0.0008685776,0.000412079,0.000539924,0.0006391645,0.0003229982],"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":[0.00005761228,0.00001980462,0.0006997774,0.00002506532,0.000004959908,0.0001359304,0.0003010325,0.0008544914,0.005082056,0.9838783,0.0005590946,0.008381954],"study_design_scores_gemma":[0.00002236965,0.00009805267,0.000759907,0.00001958891,0.00001197398,0.0005634411,0.0002576688,0.009529661,0.007264338,0.9732648,0.008164478,0.00004381762],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5755056,0.00053387,0.3565961,0.0006278604,0.0003418451,0.0001419903,0.000717285,0.0004067587,0.06512868],"genre_scores_gemma":[0.9637823,0.000286145,0.02633145,0.0001669034,0.0002372655,0.00009495117,0.0003441663,0.000119115,0.008637825],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004847907,"threshold_uncertainty_score":0.01621789,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.004598778382710914,"score_gpt":0.2280578442376645,"score_spread":0.2234590658549536,"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."}}