{"id":"W2951423746","doi":"10.48550/arxiv.math/0502007","title":"On sums of three squares","year":2005,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Simon Fraser University","funders":"","keywords":"Mathematical proof; Integer (computer science); Conjecture; Mathematics; Combinatorics; Value (mathematics); Square (algebra); Residual sum of squares; Multiple; Explained sum of squares; Discrete mathematics; Statistics; Arithmetic; Non-linear least squares; Computer science","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":[0.001275624,0.0005556452,0.0008345561,0.001721861,0.001323777,0.002377322,0.0009791693,0.001275471,0.007029174],"category_scores_gemma":[0.01033079,0.0003796349,0.000608277,0.001150497,0.003754609,0.003968334,0.002793083,0.002048939,0.0009771051],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008676842,"about_ca_system_score_gemma":0.0003475684,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004817388,"about_ca_topic_score_gemma":0.0003800537,"domain_scores_codex":[0.998765,0.0004425431,0.00004581391,0.0002267612,0.0003257313,0.0001940941],"domain_scores_gemma":[0.9965279,0.002161279,0.0003337977,0.0004041229,0.0002661856,0.0003067674],"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":[0.00006528221,0.00001277067,0.0005712569,0.000049911,0.000007222345,0.00009398469,0.0002051085,0.002346037,0.001574201,0.9820082,0.001821414,0.01124458],"study_design_scores_gemma":[0.000009593486,0.00001685515,0.0003908206,0.00002265437,0.000004282497,0.0002203554,0.00006259463,0.0151222,0.0006724648,0.9808286,0.002636128,0.00001337522],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7160053,0.003445087,0.1552623,0.003556761,0.0008583189,0.00004320463,0.0002639965,0.0003827684,0.1201823],"genre_scores_gemma":[0.967379,0.0007953568,0.01961753,0.0005286015,0.0005309772,0.00006808295,0.0001818231,0.0001486693,0.01074991],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007029174,"threshold_uncertainty_score":0.02351493,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1973224751777773,"score_gpt":0.264510641442004,"score_spread":0.06718816626422672,"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."}}