{"id":"W4293543740","doi":"10.4236/ojapps.2022.128101","title":"A Method to Reduce the Lehmer Measure in a Multi-Term Machin-Like Formula for π","year":2022,"lang":"en","type":"article","venue":"Open Journal of Applied Sciences","topic":"Mathematical and Theoretical Analysis","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Thoth Technology (Canada); York University","funders":"National Research Council Canada; York University","keywords":"Measure (data warehouse); Term (time); Quotient; Integer (computer science); Mathematics; Algebra over a field; Applied mathematics; Pure mathematics; Computer science; Data mining; Physics; Programming language","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":[0.01037593,0.0001150041,0.0004060187,0.0001368775,0.0005184788,0.0001746018,0.001834298,0.00002047731,0.0004626409],"category_scores_gemma":[0.0002536138,0.00006061143,0.000150052,0.0007164361,0.0001264571,0.0001034438,0.0004805532,0.0002507937,0.000004075696],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004243984,"about_ca_system_score_gemma":0.0001064752,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000007559294,"about_ca_topic_score_gemma":0.00001751297,"domain_scores_codex":[0.9981703,0.0001604479,0.000559936,0.0001993168,0.000647,0.0002630035],"domain_scores_gemma":[0.9984077,0.0009466117,0.0002893682,0.0001722537,0.00007003564,0.00011404],"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":[0.0002934553,0.000362059,0.00001310342,0.00002901894,0.00005580534,0.000005192554,0.004038163,0.0005063424,0.002592266,0.9790051,0.001019038,0.01208048],"study_design_scores_gemma":[0.0009386329,0.0002536518,0.00001837027,0.00003886043,0.00009159389,0.00004920053,0.004502431,0.006595821,0.002061101,0.982506,0.002790973,0.0001533161],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1496263,0.0001177847,0.7779256,0.01319663,0.0002595256,0.003509658,0.00002846139,0.00001706953,0.05531898],"genre_scores_gemma":[0.5746406,7.915218e-7,0.4243236,0.0005123139,0.00002812898,0.0001310636,1.761861e-7,0.000008584542,0.0003546969],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.4250144,"threshold_uncertainty_score":0.5065594,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.148685192239081,"score_gpt":0.4283609929879202,"score_spread":0.2796758007488392,"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."}}