{"id":"W2059159864","doi":"10.1007/s00526-014-0802-1","title":"Sign-changing solutions to elliptic second order equations: glueing a peak to a degenerate critical manifold","year":2014,"lang":"en","type":"article","venue":"Calculus of Variations and Partial Differential Equations","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":14,"is_retracted":false,"has_abstract":false,"ca_institutions":"Pacific Institute for the Mathematical Sciences","funders":"","keywords":"Degenerate energy levels; Sign (mathematics); Manifold (fluid mechanics); Nonlinear system; Order (exchange); Mathematics; Mathematical analysis; Bubble; Function (biology); Pure mathematics; Mathematical physics; Physics; Quantum mechanics; Mechanics","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":["metaresearch","metaepi_narrow","sts"],"consensus_categories":[],"category_scores_codex":[0.0007572424,0.000404888,0.0005633857,0.0006937867,0.001627717,0.0003509156,0.0003017597,0.0001946624,0.0006192274],"category_scores_gemma":[0.01009843,0.0004295397,0.0001961194,0.001251372,0.0001123804,0.0002865339,0.00031666,0.0002290922,0.0001821065],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00009449683,"about_ca_system_score_gemma":0.0001758278,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00007842325,"about_ca_topic_score_gemma":0.0008580461,"domain_scores_codex":[0.9962252,0.0004078946,0.001217734,0.0006402042,0.0005661419,0.0009428377],"domain_scores_gemma":[0.9941692,0.003408769,0.0002222041,0.0006522245,0.0008465513,0.0007010694],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00003225505,0.0003374624,0.000005789193,0.0000561146,0.00008370735,6.314617e-7,0.001036007,0.0006925969,0.03338474,0.9617327,0.0002284434,0.002409575],"study_design_scores_gemma":[0.001114018,0.0005360873,0.0003817879,0.0001713823,0.0006043437,0.000004407363,0.0002406737,0.9607571,0.005981002,0.02721621,0.002092361,0.0009006406],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.02308702,0.00006254625,0.9726943,0.001692617,0.0006902747,0.0009005796,0.0002558683,0.0001563836,0.0004604218],"genre_scores_gemma":[0.9824086,0.000006055303,0.01545798,0.0001585491,0.0005726019,0.0004286351,0.0001167134,0.00007342635,0.0007774277],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.9600645,"threshold_uncertainty_score":0.9998156,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05961807854179869,"score_gpt":0.3244283988112239,"score_spread":0.2648103202694252,"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."}}