{"id":"W2021664701","doi":"10.4153/cjm-2009-057-2","title":"Close Lattice Points on Circles","year":2009,"lang":"en","type":"article","venue":"Canadian Journal of Mathematics","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal","funders":"","keywords":"Mathematics; Combinatorics; Lattice (music); RADIUS; Arc (geometry); Geometry; Arc length; Physics","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":[0.00175381,0.0001791723,0.0004326621,0.0004168806,0.0001299902,0.00008996089,0.0005701026,0.0001035532,0.0004947957],"category_scores_gemma":[0.002989349,0.0001525256,0.0001856542,0.0002439428,0.0001017135,0.0001287536,0.000009685665,0.0004549453,0.0002140962],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002292921,"about_ca_system_score_gemma":0.0007089578,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00004324717,"about_ca_topic_score_gemma":0.0007263989,"domain_scores_codex":[0.9981371,0.0001028959,0.0006643326,0.0001199898,0.0005082444,0.0004673933],"domain_scores_gemma":[0.9971927,0.0008177013,0.0003786667,0.0004489636,0.0003265678,0.000835348],"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":[0.00001913629,0.0002626912,0.0002039295,0.0001267848,0.0001314003,0.0007835533,0.002544221,0.00000477698,0.00008780109,0.9602454,0.03154124,0.004049103],"study_design_scores_gemma":[0.0004446088,0.0002951717,0.0002833544,0.0003657039,0.00007952447,0.0004997872,0.0009289664,0.0001292796,0.0004591177,0.9941602,0.002175868,0.0001783575],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9354697,0.000181866,0.003407203,0.005827712,0.0002674696,0.0002907743,0.00001831425,0.00002888773,0.0545081],"genre_scores_gemma":[0.964142,0.00001030242,0.03335465,0.0006568242,0.0002661868,7.587053e-7,6.053456e-7,0.00004217395,0.001526453],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.05298164,"threshold_uncertainty_score":0.6219813,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06370573642228397,"score_gpt":0.335746398798368,"score_spread":0.272040662376084,"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."}}