{"id":"W1830103037","doi":"10.1142/s1793042105000091","title":"THE CONVOLUTION SUM $\\sum\\limits_{m<n/9}\\sigma(m)\\sigma(n-9m)$","year":2005,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":35,"is_retracted":false,"has_abstract":true,"ca_institutions":"Carleton University","funders":"","keywords":"Mathematics; Sigma; Combinatorics; Convolution (computer science); Physics; Quantum mechanics","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":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.005205848,0.0002757685,0.0003789661,0.0001980602,0.0002660365,0.0002419386,0.001830206,0.0001442669,0.006085662],"category_scores_gemma":[0.003265181,0.0001906358,0.000438768,0.0001878771,0.0004435256,0.0005731612,0.0002540468,0.0007807606,0.0006290285],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005312663,"about_ca_system_score_gemma":0.0002815732,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000005392443,"about_ca_topic_score_gemma":0.00003193411,"domain_scores_codex":[0.9955584,0.0007228014,0.001149598,0.0002384064,0.001835938,0.0004948706],"domain_scores_gemma":[0.9919034,0.004990633,0.0008739901,0.0004584176,0.00154597,0.0002275497],"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":[0.0009807299,0.0003584116,0.0009209976,0.00001353425,0.001103093,0.0001241573,0.0006750321,0.00006416676,0.0003062082,0.863953,0.1003566,0.03114413],"study_design_scores_gemma":[0.001361202,0.00006396413,0.0003697941,0.0001758731,0.0001120253,0.001259305,0.0008279337,0.0006974844,0.0009385529,0.7396655,0.2542671,0.0002612972],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4076479,0.0030969,0.1553067,0.04143373,0.01090052,0.001407139,0.000406581,0.0003827244,0.3794178],"genre_scores_gemma":[0.9671689,0.0002900789,0.003236681,0.0005255037,0.003044702,0.00001266943,0.00001039903,0.00007536728,0.02563566],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.559521,"threshold_uncertainty_score":0.9948229,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0417070806920368,"score_gpt":0.3686513642876856,"score_spread":0.3269442835956488,"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."}}