{"id":"W2050595654","doi":"10.1063/1.4900833","title":"All the Lagrangian relative equilibria of the curved 3-body problem have equal masses","year":2014,"lang":"en","type":"article","venue":"Journal of Mathematical Physics","topic":"Spacecraft Dynamics and Control","field":"Engineering","cited_by":15,"is_retracted":false,"has_abstract":true,"ca_institutions":"Pacific Institute for the Mathematical Sciences; University of Victoria","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Gaussian curvature; Lagrangian; Mathematics; Constant curvature; Constant (computer programming); Equilateral triangle; Mathematical analysis; Curvature; SPHERES; Three-body problem; Elliptic curve; Classical mechanics; Physics; Geometry","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005890824,0.0007336372,0.0004964811,0.001054001,0.001394522,0.001591749,0.0008940528,0.001605991,0.00835845],"category_scores_gemma":[0.003038427,0.0002881495,0.0005779564,0.0004103587,0.001951421,0.002753421,0.002046331,0.0009618665,0.0009119947],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008085326,"about_ca_system_score_gemma":0.0005673479,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001258921,"about_ca_topic_score_gemma":0.001093353,"domain_scores_codex":[0.99972,0.00006931477,0.00001569528,0.00005436222,0.00007109848,0.00006943221],"domain_scores_gemma":[0.9993666,0.0001857483,0.0001882542,0.00003428782,0.0001068041,0.0001182732],"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":[0.0000630767,0.00002500324,0.0007597863,0.00006323897,0.0000160534,0.0001925163,0.0001908423,0.01934164,0.001717323,0.9710549,0.0007538491,0.005821801],"study_design_scores_gemma":[0.00005305196,0.00009802735,0.0007468214,0.00004665951,0.00001463916,0.0002412182,0.0005054849,0.142102,0.002355636,0.8500439,0.003754645,0.00003799811],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6163149,0.000404633,0.3298258,0.001560092,0.0001268137,0.0001006674,0.0002321333,0.0001230586,0.05131194],"genre_scores_gemma":[0.9574328,0.0002608077,0.02879458,0.0001866745,0.00006419206,0.0001139526,0.0002589233,0.00007368174,0.01281436],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.00835845,"threshold_uncertainty_score":0.02796179,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01116066750651356,"score_gpt":0.2255082937376371,"score_spread":0.2143476262311235,"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."}}