{"id":"W1810220960","doi":"10.1090/tran/6829","title":"Quadratic equations in hyperbolic groups are NP-complete","year":2015,"lang":"en","type":"preprint","venue":"Transactions of the American Mathematical Society","topic":"Geometric and Algebraic Topology","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"McGill University","funders":"Engineering and Physical Sciences Research Council; National Science Foundation","keywords":"Mathematics; Quadratic equation; Bounded function; Constant (computer programming); Torsion (gastropod); Upper and lower bounds; Variable (mathematics); Mathematical analysis; Combinatorics; 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001161329,0.0010723,0.001154154,0.0007348579,0.001874694,0.003453228,0.001751561,0.001299684,0.02383151],"category_scores_gemma":[0.006664454,0.0007871767,0.001821718,0.001442472,0.002418739,0.007493724,0.003425342,0.006038059,0.004092522],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002474127,"about_ca_system_score_gemma":0.001753299,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.004955342,"about_ca_topic_score_gemma":0.006771249,"domain_scores_codex":[0.9980518,0.0003147929,0.0001342736,0.0005059394,0.0005904511,0.0004027518],"domain_scores_gemma":[0.9916041,0.00632105,0.0004569113,0.0004463054,0.0008991661,0.0002724092],"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":[0.000614024,0.0004012162,0.003593951,0.001679799,0.0002348939,0.001292275,0.002329914,0.02410517,0.007048644,0.8597271,0.04767471,0.05129826],"study_design_scores_gemma":[0.0002405843,0.00006253242,0.001061349,0.00006199534,0.00009376609,0.0003578203,0.0004611857,0.03537229,0.00356755,0.9381226,0.02055389,0.00004438672],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4624291,0.002476225,0.2791188,0.02391497,0.0009927399,0.0005541276,0.01298466,0.003787405,0.213742],"genre_scores_gemma":[0.8622375,0.001160824,0.05618654,0.002820318,0.0009193645,0.0003527774,0.0105751,0.0007353703,0.06501228],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.02383151,"threshold_uncertainty_score":0.07972437,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08095551249230226,"score_gpt":0.3236176047566527,"score_spread":0.2426620922643504,"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."}}