{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.006986731,0.00246862,0.002688282,0.004065409,0.002215243,0.004051639,0.004709637,0.001552313,0.01693483],"category_scores_gemma":[0.03256625,0.0008379535,0.002660789,0.003273676,0.004484485,0.01275554,0.007055653,0.009853447,0.00373779],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002957148,"about_ca_system_score_gemma":0.001268915,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009276178,"about_ca_topic_score_gemma":0.0009543293,"domain_scores_codex":[0.9954482,0.0009083741,0.0001527984,0.001011823,0.001602545,0.0008762127],"domain_scores_gemma":[0.9696196,0.02198511,0.000894793,0.003688249,0.002341942,0.001470324],"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":[0.0009438097,0.0002061025,0.00192867,0.0007134251,0.000112938,0.0002871129,0.0004290408,0.0265392,0.006536734,0.8697509,0.03320359,0.05934853],"study_design_scores_gemma":[0.00008197342,0.000167883,0.001312674,0.0001557874,0.00009789119,0.0003064787,0.0000967978,0.08268858,0.004216149,0.8915239,0.019269,0.00008287478],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1384261,0.01495309,0.6048,0.0150644,0.004090377,0.0002221264,0.002656374,0.001651805,0.2181358],"genre_scores_gemma":[0.8115842,0.006483737,0.1405598,0.003117501,0.006233714,0.00046551,0.002404012,0.001053964,0.02809752],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01693483,"threshold_uncertainty_score":0.05665267,"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."}}