{"id":"W2022390604","doi":"10.1007/s00220-005-1410-x","title":"Superpotentials and the Cohomogeneity One Einstein Equations","year":2005,"lang":"en","type":"article","venue":"Communications in Mathematical Physics","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":14,"is_retracted":false,"has_abstract":false,"ca_institutions":"McMaster University","funders":"","keywords":"Mathematics; Einstein; Complex system; Regular polygon; Pure mathematics; Mathematical physics; Hamiltonian system; Mathematical analysis; Hamiltonian (control theory); Geometry","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":[],"consensus_categories":[],"category_scores_codex":[0.001477425,0.0001469608,0.0004277212,0.00007520313,0.0002888805,0.00009225516,0.0008157341,0.00007575735,0.00009841425],"category_scores_gemma":[0.001849442,0.0001037704,0.000130649,0.000767728,0.0005496502,0.0001763901,0.0004410747,0.0003399685,0.00009346574],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004364878,"about_ca_system_score_gemma":0.00002575935,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000009966052,"about_ca_topic_score_gemma":0.00008251124,"domain_scores_codex":[0.9984342,0.0003398377,0.0005747492,0.0001676067,0.0002868833,0.0001966715],"domain_scores_gemma":[0.9938489,0.003910071,0.0001412849,0.001932203,0.0001121556,0.00005543447],"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":[0.000004093874,0.0005632142,0.00004894028,0.00002618625,0.00005618596,7.301526e-8,0.0007635406,0.00002516571,0.00003360463,0.9895703,0.0001500307,0.008758662],"study_design_scores_gemma":[0.0007430564,0.000006270956,0.0001432424,0.00004761121,0.000161461,0.000001433302,0.0002637283,0.06306774,0.00006183376,0.9345333,0.0008381117,0.0001321939],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.08956704,0.002833835,0.8284942,0.02568593,0.00004050661,0.001697014,0.00002117869,0.0001777969,0.05148252],"genre_scores_gemma":[0.9041025,0.0002381067,0.09503131,0.0001694217,0.0000657081,0.0001182375,0.00001102149,0.00001695528,0.0002467178],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.8145355,"threshold_uncertainty_score":0.4231634,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1159794069969939,"score_gpt":0.3480236370314894,"score_spread":0.2320442300344955,"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."}}