{"id":"W4396827217","doi":"10.1111/sapm.12702","title":"Pitchfork bifurcation along a slow parameter ramp: Coherent structures in the critical scaling","year":2024,"lang":"en","type":"article","venue":"Studies in Applied Mathematics","topic":"Nonlinear Dynamics and Pattern Formation","field":"Computer Science","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Banff International Research Station for Mathematical Innovation and Discovery; National Science Foundation","keywords":"Pitchfork bifurcation; Parameter space; Instability; Bifurcation; Mathematics; Scaling; Mathematical analysis; Saddle-node bifurcation; Bifurcation theory; Generalization; Statistical physics; Nonlinear system; Physics; Geometry; Mechanics; Quantum mechanics","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.000668672,0.0001311118,0.0001761162,0.0001194975,0.0000707537,0.0002090749,0.0003942983,0.00004700745,0.000002205838],"category_scores_gemma":[0.0001043005,0.00008557185,0.00003638342,0.0003867426,0.00007530669,0.000107915,0.0001621931,0.0002155285,0.0000196749],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006426328,"about_ca_system_score_gemma":0.00001771227,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004101172,"about_ca_topic_score_gemma":0.00002900228,"domain_scores_codex":[0.9989309,0.00002580867,0.0003735933,0.0002010241,0.0002615017,0.0002071548],"domain_scores_gemma":[0.9987311,0.0008857538,0.00003926031,0.0003048332,0.00002307108,0.00001595416],"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":[0.000001679012,0.00006705699,0.00005426475,0.0006920688,0.00002384079,0.00001233275,0.04185829,0.0003788157,0.00005240329,0.9274661,0.0001534451,0.02923973],"study_design_scores_gemma":[0.0001119457,0.00001442349,0.0001737805,0.0002292732,0.000009935792,0.00001399098,0.002566769,0.4909343,0.00009153678,0.5054587,0.0002567672,0.000138616],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1716138,0.001040384,0.8219641,0.001664089,0.0008264902,0.0007072084,0.000005454906,0.000131205,0.002047204],"genre_scores_gemma":[0.8804825,0.00005764484,0.1191229,0.0001756613,0.00005703831,0.0000881775,0.000003347507,0.000008246525,0.000004510441],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.7088686,"threshold_uncertainty_score":0.3489519,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05446879977069417,"score_gpt":0.352530135123048,"score_spread":0.2980613353523539,"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."}}