{"id":"W3178335194","doi":"10.1016/j.jmaa.2022.126580","title":"Sums of triangular numbers and sums of squares","year":2022,"lang":"en","type":"article","venue":"Journal of Mathematical Analysis and Applications","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"Northwestern Polytechnic; University of Lethbridge","funders":"Natural Sciences and Engineering Research Council of Canada; Pacific Institute for the Mathematical Sciences; University of Lethbridge; University of Calgary","keywords":"Mathematics; Combinatorics","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0009295364,0.0001251928,0.000886562,0.0003233211,0.0001146609,0.00001823516,0.0002109337,0.00003690376,0.0004389183],"category_scores_gemma":[0.0003870254,0.00009813873,0.0003265204,0.0006867443,0.000227691,0.00009523125,0.0001419466,0.00017325,8.618201e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002223711,"about_ca_system_score_gemma":0.00002537465,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00000572508,"about_ca_topic_score_gemma":0.000004711295,"domain_scores_codex":[0.9979613,0.00008198704,0.001180076,0.0001300359,0.0005206543,0.0001259103],"domain_scores_gemma":[0.9971265,0.001262915,0.001022759,0.0002820471,0.0001981301,0.0001076424],"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":[0.00003209111,0.000600813,0.0006194201,0.0009073228,0.001364557,0.000003442555,0.0009904613,0.0000730381,0.004273325,0.9899854,0.000295543,0.0008546077],"study_design_scores_gemma":[0.0003558002,0.00009162543,0.0001536526,0.00004045253,0.002122824,0.00004482912,0.002810284,0.0006585282,0.002594972,0.9907111,0.0003125272,0.0001033906],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6215732,0.0008274415,0.3746993,0.0004459878,0.00001438075,0.0004185046,0.00006561107,0.00001548689,0.001940139],"genre_scores_gemma":[0.9501336,0.0001189992,0.04913175,0.00001240792,0.00003249396,0.00004975296,0.000002392643,0.00001723819,0.0005013527],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3285605,"threshold_uncertainty_score":0.4805848,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02344416176531177,"score_gpt":0.3193830571540809,"score_spread":0.2959388953887691,"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."}}