{"id":"W2564585807","doi":"10.48550/arxiv.1612.02852","title":"Radial solutions of a fourth order Hamiltonian stationary equation","year":2016,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"","keywords":"Lagrangian; Hamiltonian (control theory); Mathematics; Graph; Mathematical analysis; First order; Mathematical physics; Applied mathematics; Combinatorics; Mathematical optimization","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003297174,0.0007922888,0.0004865853,0.0009607615,0.0005647364,0.001091447,0.0007564779,0.001125253,0.002561307],"category_scores_gemma":[0.001124339,0.0002747547,0.0003630965,0.000374502,0.001825115,0.001132128,0.001497097,0.0008730332,0.0003122774],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007334813,"about_ca_system_score_gemma":0.0005201852,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002361179,"about_ca_topic_score_gemma":0.001565311,"domain_scores_codex":[0.9998783,0.00003771455,0.000005443467,0.00001899614,0.00002599879,0.00003347623],"domain_scores_gemma":[0.9997068,0.00006652562,0.00007690394,0.00001832047,0.00005829402,0.00007319082],"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":[0.0001003363,0.0000668847,0.001191971,0.00007134848,0.00003430157,0.0008082021,0.0002658257,0.06785511,0.01302231,0.9110759,0.001165902,0.004341977],"study_design_scores_gemma":[0.00008364819,0.000107011,0.0007616782,0.00003135043,0.00001808352,0.0002885085,0.0004220933,0.5695832,0.00303853,0.4239445,0.001664277,0.00005706368],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8421105,0.0004554249,0.1269514,0.001452102,0.00009609812,0.00004264495,0.0001275748,0.0001536625,0.02861064],"genre_scores_gemma":[0.9738368,0.0002427021,0.01331669,0.0001376255,0.00005836835,0.0000309895,0.00009315715,0.00003770924,0.01224595],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002561307,"threshold_uncertainty_score":0.008568406,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1616068341200979,"score_gpt":0.2217791653229733,"score_spread":0.06017233120287543,"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."}}