{"id":"W2183990329","doi":"10.1007/0-387-22602-8_2","title":"Problems Leading to Pell’s Equation and Preliminary Investigations","year":2003,"lang":"en","type":"book-chapter","venue":"Problem books in mathematics","topic":"History and Theory of Mathematics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Popularity; Quadratic equation; Constant (computer programming); Mathematics; Sample (material); Variable (mathematics); Mathematical analysis; Computer science; Physics; Law; Political science; Thermodynamics","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.002040897,0.0008242692,0.001193588,0.0006514098,0.0002468798,0.0001074347,0.0004249787,0.0006100027,0.0002571496],"category_scores_gemma":[0.0008093318,0.0008576767,0.000169551,0.00009989657,0.0002863137,0.0001874962,0.000216193,0.0008349893,0.0003418049],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003456565,"about_ca_system_score_gemma":0.0001333792,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001724714,"about_ca_topic_score_gemma":0.00003475161,"domain_scores_codex":[0.9963501,0.00008755442,0.001668437,0.0007123576,0.0006429572,0.0005386063],"domain_scores_gemma":[0.9965214,0.001249515,0.000859896,0.0009080996,0.0001595923,0.0003015314],"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":[0.000008065687,0.0001355428,0.000003443554,0.004908755,0.00006973114,0.00001518317,0.0114312,0.00006873629,0.00006108551,0.9772243,0.005447495,0.0006264278],"study_design_scores_gemma":[0.0003318662,0.0002010137,2.358208e-7,0.004621358,0.000212385,0.00007678736,0.0001590705,0.0005770461,0.00007809392,0.9519746,0.04093387,0.000833635],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"other","genre_scores_codex":[0.0004908573,0.0005596412,0.02380167,0.0003676466,0.0001711008,0.003762539,0.00003351985,0.0002784209,0.9705346],"genre_scores_gemma":[0.0003933693,0.00008395423,0.3682998,0.000232335,0.00007893611,0.0002811861,0.0000192748,0.0003245935,0.6302866],"genre_candidate":"other","genre_consensus":"other","teacher_disagreement_score":0.3444981,"threshold_uncertainty_score":0.9993874,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.09521781767095552,"score_gpt":0.2813256622744191,"score_spread":0.1861078446034636,"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."}}