{"id":"W1974601014","doi":"10.4064/aa166-1-5","title":"A generalization of a theorem of Erdős–Rényi to m-fold sums and differences","year":2014,"lang":"en","type":"article","venue":"Acta Arithmetica","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Omega; Combinatorics; Generalization; Integer (computer science); Discrete mathematics; Mathematical analysis","routes":{"ca_aff":true,"ca_fund":true,"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":[0.001980374,0.0008209856,0.0009577313,0.001818152,0.00133763,0.001829169,0.001277844,0.0009349025,0.005449678],"category_scores_gemma":[0.005124478,0.0003552476,0.001240941,0.00137447,0.003791521,0.007885035,0.004109073,0.003224724,0.001107671],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001291426,"about_ca_system_score_gemma":0.0005351793,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004888924,"about_ca_topic_score_gemma":0.0002988518,"domain_scores_codex":[0.9988073,0.0002363754,0.00008113401,0.0004016048,0.0003428719,0.0001306642],"domain_scores_gemma":[0.9982772,0.0008385953,0.0001744152,0.000348975,0.0002244558,0.0001363936],"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":[0.00001420595,0.000006737201,0.0001237022,0.00003592356,0.000004987676,0.00003406567,0.000149691,0.0005172542,0.0007957999,0.9897206,0.0007652326,0.007831756],"study_design_scores_gemma":[0.000008155495,0.00002241373,0.0002058042,0.0000140402,0.000006284553,0.0001786509,0.00004201208,0.001895089,0.0008866141,0.9882529,0.008474913,0.00001313484],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1593151,0.003258204,0.6536931,0.003753737,0.001419189,0.000114935,0.000448528,0.0004073262,0.1775898],"genre_scores_gemma":[0.8088751,0.002614939,0.1318488,0.002348479,0.00183989,0.0003148093,0.0002766847,0.0002694396,0.05161193],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005449678,"threshold_uncertainty_score":0.01823097,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0205513266444521,"score_gpt":0.2712826928504924,"score_spread":0.2507313662060404,"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."}}