{"id":"W1967784590","doi":"10.4153/cmb-2011-143-x","title":"An Asymptotic Bound on the Composition Number of Integer Sums of Squares Formulas","year":2011,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Integer (computer science); Identity (music); Combinatorics; Composition (language); Asymptotic formula; Discrete mathematics","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.0007696809,0.0002371436,0.0005197178,0.000106316,0.0000958336,0.00002932715,0.0004614243,0.0001589349,0.02844417],"category_scores_gemma":[0.0006895601,0.0001584827,0.0001789105,0.0001416712,0.0003170552,0.00004104153,0.00003199256,0.0002223467,0.001253078],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007082774,"about_ca_system_score_gemma":0.00008382664,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000593569,"about_ca_topic_score_gemma":0.0003215843,"domain_scores_codex":[0.9981595,0.0001261177,0.0007524452,0.0002167609,0.0003519168,0.0003932266],"domain_scores_gemma":[0.9972306,0.001238251,0.0002551904,0.0007484474,0.0001645318,0.0003630063],"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":[0.00001990297,0.000323555,0.00006811193,0.0003611284,0.00004778824,0.000007491369,0.001112378,5.311749e-7,0.0002344341,0.9959629,0.001754524,0.0001072177],"study_design_scores_gemma":[0.0001989092,0.0001773866,0.0001555218,0.0004124196,0.00007362938,0.00002493327,0.0004174021,0.00232992,0.002901664,0.9927867,0.000300286,0.0002212282],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8499163,0.000006291659,0.008462697,0.0007878364,0.00004975616,0.0006028837,0.00007112068,0.00003327323,0.1400698],"genre_scores_gemma":[0.9921334,0.000001518357,0.007186506,0.0002562406,0.00002413976,0.00003159622,0.000007450156,0.00004521196,0.0003139711],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.142217,"threshold_uncertainty_score":0.9995245,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04892748061165162,"score_gpt":0.2866152045131127,"score_spread":0.2376877239014611,"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."}}