{"id":"W2964005405","doi":"10.1017/prm.2019.28","title":"Linear instability and nondegeneracy of ground state for combined power-type nonlinear scalar field equations with the Sobolev critical exponent and large frequency parameter","year":2019,"lang":"en","type":"article","venue":"Proceedings of the Royal Society of Edinburgh Section A Mathematics","topic":"Advanced Mathematical Physics Problems","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Victoria","funders":"","keywords":"Ground state; Exponent; Sobolev space; Instability; Nonlinear system; Scalar (mathematics); Scalar field; Physics; Mathematical analysis; Mathematics; Critical exponent; Critical frequency; Mathematical physics; Quantum mechanics; Phase transition; 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":[0.0009364157,0.0002404254,0.000566251,0.00002643378,0.0001687464,0.00002795781,0.0002393339,0.0001283335,0.00003757444],"category_scores_gemma":[0.001909627,0.0001468789,0.0001916043,0.0002634652,0.0004072108,0.0002049237,0.0001969003,0.0002843436,1.876721e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003390092,"about_ca_system_score_gemma":0.00004457187,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000009778847,"about_ca_topic_score_gemma":0.000001471142,"domain_scores_codex":[0.998304,0.00001102315,0.0006902177,0.0002699637,0.000457602,0.0002672052],"domain_scores_gemma":[0.9950795,0.002913257,0.0006390177,0.000265896,0.001035395,0.00006698778],"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":[0.001050362,0.009823489,0.008312237,0.04021267,0.001945024,1.991453e-7,0.08382975,0.000371067,0.1503149,0.6960256,0.007475419,0.0006392536],"study_design_scores_gemma":[0.001484585,0.001208594,0.00009808203,0.0005663353,0.0002953182,0.000003238823,0.004327166,0.08860464,0.03214341,0.8709213,0.00004907756,0.0002982336],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9179248,0.00004033815,0.07944413,0.0008916977,0.0001006371,0.001327619,0.00003213291,0.00002949278,0.0002091299],"genre_scores_gemma":[0.8188322,0.0000107079,0.1808147,0.0000619161,0.00003635858,0.00004421088,0.000001248648,0.00003145913,0.0001672871],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1748957,"threshold_uncertainty_score":0.5989546,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02170146738118002,"score_gpt":0.288463934622222,"score_spread":0.266762467241042,"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."}}