{"id":"W2330504708","doi":"10.14288/1.0066490","title":"Partitions into prime powers and related divisor functions","year":2008,"lang":"en","type":"article","venue":"Open Collections","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"","keywords":"Divisor (algebraic geometry); Mathematics; Prime (order theory); Arithmetic; Combinatorics; 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":"codex-gemma-dda1882f352a","candidate_categories":["sts","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.000126497,0.0001362488,0.0002327504,0.00008331615,0.004005253,0.0003136059,0.0001693414,0.00007172914,0.001827096],"category_scores_gemma":[0.0007084182,0.0001348808,0.00006170972,0.0007809641,0.0002465346,0.000475719,0.0002231673,0.000174717,0.0001096387],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00009282707,"about_ca_system_score_gemma":0.0000886127,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004503365,"about_ca_topic_score_gemma":0.0006186818,"domain_scores_codex":[0.9990314,0.00005398033,0.0003197809,0.0002441425,0.0001452771,0.0002054164],"domain_scores_gemma":[0.9989432,0.0004227567,0.00008857825,0.0003189222,0.0001041985,0.0001223321],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"not_applicable","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00002123538,0.0006834351,0.00008429078,0.00004779354,0.0002115064,0.0000238148,0.00250644,0.00002910202,0.0002198074,0.06233489,0.9337454,0.00009232909],"study_design_scores_gemma":[0.0005175708,0.00008020942,0.0001103041,0.00003922276,0.00007993334,0.0002306806,0.0009443194,0.0001304404,0.0001804741,0.9796348,0.0178436,0.0002083964],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"other","genre_gemma":"other","genre_scores_codex":[0.01001592,0.00007665298,0.02005876,0.0007777756,0.0004384362,0.001241559,0.00003951523,0.0003653307,0.9669861],"genre_scores_gemma":[0.06355909,0.00006645842,0.02178461,0.00003197567,0.00002812224,0.0003808886,0.000008758234,0.0000387997,0.9141013],"genre_candidate":"other","genre_consensus":"other","teacher_disagreement_score":0.9173,"threshold_uncertainty_score":0.9990854,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04822134473132196,"score_gpt":0.3142709996488703,"score_spread":0.2660496549175483,"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."}}