{"id":"W4380791465","doi":"10.1090/stml/104/10","title":"The circle method and the Goldbach conjectures","year":2023,"lang":"en","type":"book-chapter","venue":"Student mathematical library","topic":"Graph theory and applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"Queen's University","funders":"","keywords":"Goldbach's conjecture; Mathematics; Art; Pure mathematics; Number theory","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":[],"consensus_categories":[],"category_scores_codex":[0.001175538,0.0003562475,0.0006132072,0.00005593145,0.0004736113,0.0003152942,0.0008799235,0.0002323385,0.0002996455],"category_scores_gemma":[0.0002247371,0.0001907654,0.0003187947,0.00006964679,0.0008257533,0.0000836348,0.0007421274,0.0006234078,0.0004265581],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000070858,"about_ca_system_score_gemma":0.00003263854,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":2.529949e-7,"about_ca_topic_score_gemma":8.370853e-7,"domain_scores_codex":[0.9980387,0.0001733064,0.0006234347,0.0003862937,0.0004815247,0.000296714],"domain_scores_gemma":[0.9859358,0.01269742,0.000259974,0.0009790614,0.00002374701,0.000103979],"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":[0.00002518127,0.00002872277,7.06978e-7,0.0001534398,0.00027721,0.0000050545,0.0005665527,1.633875e-7,0.000001017076,0.9816021,0.01539431,0.001945483],"study_design_scores_gemma":[0.0003813362,0.00001740136,0.00001567209,0.0001524091,0.0002622886,0.00002052242,0.0001637067,0.00002729433,0.00001101783,0.9566123,0.04211339,0.0002226963],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"other","genre_scores_codex":[0.00008663553,0.0007688379,0.002232315,0.006693456,0.0001318194,0.001751548,0.00006752575,0.0004870508,0.9877808],"genre_scores_gemma":[0.00196813,0.0007291373,0.005328781,0.0006413725,0.0003289705,0.000445656,0.00002121407,0.0002650295,0.9902717],"genre_candidate":"other","genre_consensus":"other","teacher_disagreement_score":0.02671908,"threshold_uncertainty_score":0.7779187,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02981831651331912,"score_gpt":0.3206129164962124,"score_spread":0.2907945999828933,"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."}}