{"id":"W4206897161","doi":"10.1090/mbk/139/21","title":"The multiplicative structure of integers","year":2021,"lang":"en","type":"book-chapter","venue":"American Mathematical Society eBooks","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université Laval","funders":"","keywords":"Multiplicative function; Mathematics; Mathematical analysis","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":["metaepi_narrow","sts"],"consensus_categories":[],"category_scores_codex":[0.0005803516,0.0005599163,0.001324579,0.000031327,0.0002609378,0.00006304072,0.000931078,0.0003060505,0.0008589883],"category_scores_gemma":[0.0007859617,0.0003679755,0.001187862,0.00006442832,0.004646473,0.00001990497,0.0005378827,0.001264058,0.00005930859],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002063976,"about_ca_system_score_gemma":0.0002752771,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000009767306,"about_ca_topic_score_gemma":0.00001237254,"domain_scores_codex":[0.9967877,0.0001107753,0.0009443739,0.0005491721,0.001067695,0.0005403343],"domain_scores_gemma":[0.9909444,0.005931898,0.0009725592,0.001475564,0.0004615136,0.00021401],"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":[0.00001678218,0.0000261214,0.000001045386,0.0003184566,0.001075947,0.000004965584,0.00159035,1.543898e-7,0.0003864122,0.9854566,0.004581703,0.006541391],"study_design_scores_gemma":[0.0001704257,0.00007216321,6.198406e-7,0.0003512034,0.0002753325,0.00001905861,0.003050076,0.0001888212,0.001013557,0.9823168,0.01216773,0.000374193],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"other","genre_scores_codex":[0.0006343092,0.0001481782,0.009566624,0.0004289986,0.00004742035,0.001009839,0.0001439992,0.0001192299,0.9879014],"genre_scores_gemma":[0.02069359,0.00009362158,0.03609974,0.0002328434,0.0001973531,0.00003836619,0.00001704359,0.0002893178,0.9423381],"genre_candidate":"other","genre_consensus":"other","teacher_disagreement_score":0.04556328,"threshold_uncertainty_score":0.9998772,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03487546126465951,"score_gpt":0.3251930031614893,"score_spread":0.2903175418968298,"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."}}