{"id":"W1987032798","doi":"10.1016/j.jnt.2004.11.008","title":"The primitive solutions to <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si1.gif\" overflow=\"scroll\"><mml:msup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:mi>y</mml:mi></mml:mrow><mml:mrow><mml:mn>9</mml:mn></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mi>z</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math>","year":2005,"lang":"lv","type":"article","venue":"Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":19,"is_retracted":false,"has_abstract":false,"ca_institutions":"Simon Fraser University","funders":"University of Sydney","keywords":"Mathematics; Scroll; Algorithm; Computer science; Theology; Philosophy","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":["metaresearch","metaepi_narrow","metaepi_broad","sts","scholarly_communication","open_science","research_integrity","insufficient_payload"],"consensus_categories":["metaepi_narrow","sts","open_science","research_integrity","insufficient_payload"],"category_scores_codex":[0.01217199,0.004587446,0.001821214,0.003411568,0.008794825,0.00757859,0.01217631,0.0111805,0.9252655],"category_scores_gemma":[0.01374403,0.009163246,0.01084027,0.00654832,0.009585489,0.007797043,0.01026081,0.01035155,0.01388762],"about_ca_system_candidate":true,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001563517,"about_ca_system_score_gemma":0.009213669,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.004105565,"about_ca_topic_score_gemma":0.004789122,"domain_scores_codex":[0.9552933,0.004169824,0.00959231,0.007203556,0.01193588,0.01180515],"domain_scores_gemma":[0.9581569,0.01264762,0.01141256,0.009559244,0.001498964,0.006724719],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"not_applicable","study_design_gemma":"bench_or_experimental","study_design_scores_codex":[0.00766773,0.001544167,0.0000312249,0.002828258,0.008373977,0.006296683,0.005989383,0.003122978,0.002830942,0.3910175,0.5655437,0.004753415],"study_design_scores_gemma":[0.008731766,0.006507958,0.0002043963,0.005112873,0.009552071,0.01750498,0.01252694,0.01425027,0.8856733,0.001641716,0.03018438,0.008109379],"study_design_candidate":"bench_or_experimental","study_design_consensus":null,"genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.208997,0.005488145,0.002995352,0.003554287,0.01068112,0.0002145617,0.00245391,0.001000066,0.7646156],"genre_scores_gemma":[0.9476199,0.006584983,0.007994516,0.006743016,0.01249353,0.005446377,0.004801054,0.00504068,0.003275938],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.9113779,"threshold_uncertainty_score":0.9990659,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02027581866187407,"score_gpt":0.2530045165577434,"score_spread":0.2327286978958694,"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."}}