{"id":"W2962852487","doi":"10.1515/integ.2009.027","title":"Christoffel Words and Markoff Triples","year":2009,"lang":"en","type":"article","venue":"Integers","topic":"semigroups and automata theory","field":"Computer Science","cited_by":36,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université du Québec à Montréal","funders":"","keywords":"Christoffel symbols; Mathematics; Algebra over a field; Arithmetic; 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":[0.0007990359,0.0004306053,0.0003429665,0.002089962,0.001995807,0.002295806,0.0006121499,0.0009309603,0.008276266],"category_scores_gemma":[0.002292989,0.0002817215,0.0004719059,0.001290455,0.002346663,0.004421969,0.002095062,0.001224571,0.001341923],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008444395,"about_ca_system_score_gemma":0.0004823354,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006213445,"about_ca_topic_score_gemma":0.0005712432,"domain_scores_codex":[0.998908,0.0002767661,0.00008059831,0.0002100213,0.0003312927,0.0001932915],"domain_scores_gemma":[0.9990515,0.0003690923,0.0001295128,0.0001023296,0.0002112726,0.000136308],"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":[0.00002423384,0.00001182095,0.0001120573,0.00002860089,0.000003001728,0.00008434429,0.0002938152,0.0002432991,0.0009802196,0.9908029,0.0008986057,0.0065171],"study_design_scores_gemma":[0.00001100265,0.00002707662,0.0001867414,0.00003335462,0.00000964828,0.0002960117,0.0003628679,0.002052051,0.002908191,0.9654592,0.02862667,0.00002720775],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3439883,0.003087398,0.4085988,0.002328219,0.001579333,0.0002106326,0.0006146527,0.001087862,0.2385048],"genre_scores_gemma":[0.9166656,0.0009194026,0.05980945,0.0005546934,0.0003884333,0.0001413203,0.0002884533,0.0001581807,0.0210743],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.008276266,"threshold_uncertainty_score":0.02768683,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.005713033424047182,"score_gpt":0.2143417746951708,"score_spread":0.2086287412711236,"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."}}