{"id":"W2098995696","doi":"10.1142/s1793042106000383","title":"THIRTY-TWO GOLDBACH VARIATIONS","year":2006,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":35,"is_retracted":false,"has_abstract":true,"ca_institutions":"Dalhousie University","funders":"","keywords":"Mathematical proof; Variety (cybernetics); Goldbach's conjecture; Euler's formula; Identity (music); Harmonic number; Algebra over a field","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":[0.0007006951,0.000120023,0.0002124652,0.0001178896,0.00004445334,0.00008090123,0.0004967736,0.00004446886,0.005008312],"category_scores_gemma":[0.001145519,0.0001000545,0.0001824034,0.0000756871,0.00008262201,0.0004242792,0.00007480349,0.0002142167,0.0001909074],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001317861,"about_ca_system_score_gemma":0.00005760656,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000007613254,"about_ca_topic_score_gemma":0.000008322835,"domain_scores_codex":[0.9983636,0.0001053526,0.0006568513,0.00008875914,0.0006420619,0.00014338],"domain_scores_gemma":[0.9968984,0.001692479,0.0005468215,0.0001469925,0.000666036,0.00004929775],"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":[0.00003345126,0.0002678623,0.0001408007,0.000008484926,0.0001376195,0.00006657866,0.0001481538,0.00003903201,0.0001482162,0.9750224,0.02364081,0.0003466233],"study_design_scores_gemma":[0.0005475137,0.00001199956,0.0002164553,0.00009218734,0.00004707047,0.00054302,0.0001231305,0.00005391194,0.0003721432,0.9911835,0.006708513,0.000100625],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.05007354,0.0001218805,0.5284653,0.001482636,0.002816206,0.0001745915,0.0001400596,0.000115981,0.4166098],"genre_scores_gemma":[0.8553477,0.00001388656,0.110147,0.0001880637,0.002038466,0.000008262577,0.00001285153,0.00005156334,0.0321922],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.8052742,"threshold_uncertainty_score":0.9959012,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02219150538033221,"score_gpt":0.3536649628456861,"score_spread":0.3314734574653539,"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."}}