{"id":"W2072229649","doi":"10.1007/s11511-011-0065-z","title":"Markoff–Lagrange spectrum and extremal numbers","year":2011,"lang":"en","type":"article","venue":"Acta Mathematica","topic":"semigroups and automata theory","field":"Computer Science","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Ottawa","funders":"","keywords":"Mathematics; Combinatorics; Irrational number; Bijection; Zero (linguistics); Integer (computer science); Real number; Geometry","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0001972768,0.0001297477,0.0001679562,0.00003852311,0.00006324781,0.00008494289,0.0005691897,0.00004092266,0.0002812478],"category_scores_gemma":[0.00003661745,0.0001051019,0.0000435389,0.0001298524,0.00005965225,0.0004140674,0.0002467918,0.00007725319,0.0001881651],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000007557061,"about_ca_system_score_gemma":0.00001147552,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000009553105,"about_ca_topic_score_gemma":0.000002114541,"domain_scores_codex":[0.9991619,0.00003052279,0.0001641338,0.0002663706,0.000143516,0.0002335835],"domain_scores_gemma":[0.999238,0.00009625304,0.00006700237,0.0004678026,0.000008725148,0.000122183],"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":[0.000009474896,0.0001314948,0.0002500923,0.0001064937,0.00003757399,0.00006193182,0.009389058,1.106272e-8,0.001281184,0.9771615,0.003757588,0.00781363],"study_design_scores_gemma":[0.0006701046,0.00019089,0.008276336,0.0001262633,0.0000422313,0.0004025229,0.0004831424,0.0213066,0.00647747,0.9566898,0.004592155,0.0007424394],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.3990412,0.0003138151,0.2512492,0.006217671,0.0004602318,0.0005985262,0.000006635413,0.001294536,0.3408182],"genre_scores_gemma":[0.9271697,0.00001379365,0.07217668,0.0003578855,0.00003272676,0.000007506042,3.823526e-7,0.00001198327,0.000229337],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.5281286,"threshold_uncertainty_score":0.4285931,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02479678303898649,"score_gpt":0.2057798386222955,"score_spread":0.180983055583309,"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."}}