{"id":"W2090691106","doi":"10.1093/imrn/rns106","title":"Improved Bounds on Sárközy’s Theorem for Quadratic Polynomials","year":2012,"lang":"en","type":"preprint","venue":"International Mathematics Research Notices","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal","funders":"","keywords":"Mathematics; Quadratic equation; Combinatorics; Pure mathematics; Discrete mathematics; Algebra over a field; 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":["metaresearch","metaepi_narrow","scholarly_communication","research_integrity","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.01531317,0.00076277,0.00118121,0.001243548,0.0004663458,0.00122889,0.003906419,0.0007233146,0.001667521],"category_scores_gemma":[0.01887992,0.0006428196,0.0006732382,0.0002885995,0.0007557072,0.0003025102,0.002480635,0.002523816,0.0005865857],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001077873,"about_ca_system_score_gemma":0.0007337538,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00008241728,"about_ca_topic_score_gemma":0.00007497018,"domain_scores_codex":[0.9911751,0.0007927874,0.001597079,0.001091647,0.003685449,0.001657994],"domain_scores_gemma":[0.9738123,0.02058983,0.0008668617,0.001991383,0.002250001,0.0004895499],"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":[0.0004539603,0.002125536,0.00004317949,0.003470777,0.001483577,0.00001342143,0.003342922,0.00005899644,0.0009116596,0.9719608,0.01500318,0.001131953],"study_design_scores_gemma":[0.0008671096,0.0002017887,0.00001478079,0.001137035,0.0001507818,0.00000917306,0.001272956,0.04751939,0.002709032,0.9421424,0.00333505,0.0006404534],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.418539,0.001155192,0.1210701,0.02137163,0.0121302,0.02469709,0.00338097,0.001372346,0.3962835],"genre_scores_gemma":[0.8951027,0.00007647706,0.06884103,0.0001284551,0.003436621,0.002202565,0.0002107204,0.0004054847,0.02959595],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4765637,"threshold_uncertainty_score":0.999808,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2669965723119671,"score_gpt":0.4965281668862137,"score_spread":0.2295315945742465,"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."}}