{"id":"W3163894475","doi":"10.1007/s00208-021-02307-2","title":"Lemke Oliver and Soundararajan bias for consecutive sums of two squares","year":2021,"lang":"en","type":"article","venue":"Mathematische Annalen","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"Concordia University","funders":"Knut och Alice Wallenbergs Stiftelse; Fonds Québécois de la Recherche sur la Nature et les Technologies; Concordia University","keywords":"Conjecture; Mathematics; Heuristic; Constant (computer programming); Context (archaeology); Lack-of-fit sum of squares; Least-squares function approximation; Combinatorics; Arithmetic; Explained sum of squares; Algorithm; Statistics; Non-linear least squares; Computer science; Mathematical optimization","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":[0.004428473,0.0008898049,0.001633718,0.002869099,0.002377792,0.003337327,0.002217386,0.002162031,0.01663689],"category_scores_gemma":[0.06554856,0.0009791926,0.001297699,0.002885612,0.004534745,0.009222019,0.004229167,0.004197468,0.003220884],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002258046,"about_ca_system_score_gemma":0.001380386,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001364097,"about_ca_topic_score_gemma":0.001350146,"domain_scores_codex":[0.996618,0.001223529,0.0001912343,0.0007469136,0.0008515541,0.0003687247],"domain_scores_gemma":[0.9699914,0.02243963,0.001425859,0.002646604,0.002616731,0.0008797862],"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":[0.0001178584,0.000021789,0.0007506224,0.0001046598,0.00001903977,0.00008599278,0.0002140868,0.001790779,0.0007306808,0.9816969,0.003477736,0.01098987],"study_design_scores_gemma":[0.0000117888,0.000008608876,0.0001613412,0.00001881212,0.00001160908,0.0000978057,0.00002878767,0.00721401,0.0003429963,0.9897675,0.002315583,0.00002114773],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2296427,0.01070059,0.6303523,0.01572547,0.002386316,0.0001319913,0.0006465141,0.001086017,0.1093281],"genre_scores_gemma":[0.8286833,0.002541667,0.1048284,0.002994561,0.00172707,0.0002557121,0.0004453893,0.001428283,0.05709547],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01663689,"threshold_uncertainty_score":0.0556559,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1924881499805745,"score_gpt":0.4158536170533874,"score_spread":0.2233654670728129,"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."}}