{"id":"W2917969845","doi":"10.5539/jmr.v11n2p30","title":"The Quadratic Diophantine Equations x^2− P(t)y^2− 2P′(t)x + 4P(t)y + (P′(t))^2− 4P(t) − 1 = 0","year":2019,"lang":"en","type":"article","venue":"Journal of Mathematics Research","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Diophantine equation; Integer (computer science); Prime (order theory); Combinatorics; Quadratic equation; Square (algebra); Discrete mathematics; Geometry","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaresearch","insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.02672046,0.0003206723,0.0008506012,0.0007236122,0.0007414949,0.0005108527,0.002291898,0.0001890484,0.001165217],"category_scores_gemma":[0.01843443,0.0001960206,0.0004506472,0.001337739,0.000573282,0.0003871038,0.0005302525,0.002107233,0.001626385],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003491568,"about_ca_system_score_gemma":0.000884881,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000109639,"about_ca_topic_score_gemma":0.00002374127,"domain_scores_codex":[0.9905759,0.001227405,0.001949985,0.0003089583,0.00470219,0.001235562],"domain_scores_gemma":[0.9706792,0.02371367,0.0008969464,0.001482248,0.002790934,0.0004370137],"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":[0.0001656028,0.001282422,0.0003944026,0.0008979297,0.0006153655,0.0001110825,0.003328983,0.00003143142,0.006694292,0.9613814,0.02360846,0.001488589],"study_design_scores_gemma":[0.001403621,0.0006287766,0.00004114904,0.0005885654,0.00009344267,0.0003130416,0.009085078,0.01066887,0.002250462,0.9687234,0.00590369,0.000299963],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8646719,0.001588526,0.03134235,0.01094438,0.001324068,0.003092286,0.00001867889,0.0001144421,0.08690333],"genre_scores_gemma":[0.9375181,0.0003588165,0.01604786,0.0000419298,0.0006211005,0.00003683068,0.000001757799,0.0001565195,0.04521711],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.07284614,"threshold_uncertainty_score":0.9997479,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2032112873571311,"score_gpt":0.4737314947923773,"score_spread":0.2705202074352462,"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."}}