{"id":"W4387461903","doi":"10.1007/s00208-023-02698-4","title":"Rigorous analysis of the unified transform method and long-range instabilities for the inhomogeneous time-dependent Schrödinger equation on the quarter-plane","year":2023,"lang":"en","type":"article","venue":"Mathematische Annalen","topic":"Advanced Mathematical Physics Problems","field":"Mathematics","cited_by":37,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"National Natural Science Foundation of China","keywords":"Mathematics; Range (aeronautics); Quarter (Canadian coin); Plane (geometry); Mathematical analysis; Instability; Geometry; Mechanics; Physics","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":false,"about_ca":true,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002483246,0.0003107183,0.0006251818,0.0001614627,0.0003901679,0.00006976991,0.0005821352,0.000109669,0.0001170573],"category_scores_gemma":[0.0008727657,0.0001499634,0.0003629608,0.0009429082,0.0002077933,0.0001279668,0.0001156225,0.0002506293,0.00004004016],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003656056,"about_ca_system_score_gemma":0.00003182302,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001372664,"about_ca_topic_score_gemma":0.00006230431,"domain_scores_codex":[0.9977393,0.0002254682,0.0006816161,0.0003432113,0.0006340492,0.0003763616],"domain_scores_gemma":[0.9886057,0.009798104,0.0003884597,0.0009979054,0.000158278,0.00005156853],"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":[0.0001699818,0.0005886476,0.0000829394,0.00199287,0.003860979,0.000003935122,0.02489991,0.004979953,0.003452853,0.9476007,0.003106248,0.009260958],"study_design_scores_gemma":[0.0004099784,0.0001460727,0.0001691732,0.0001505006,0.001532858,0.000007441246,0.001191927,0.06034522,0.005505197,0.930117,0.0001654697,0.0002591436],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3203745,0.0003127621,0.6568912,0.009516188,0.0001443184,0.00618937,0.0004925454,0.0003811598,0.005697966],"genre_scores_gemma":[0.9871886,0.00006293822,0.008414878,0.000205515,0.00007512894,0.000838952,0.00002655509,0.0001056757,0.003081795],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.666814,"threshold_uncertainty_score":0.6115331,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07699052357513005,"score_gpt":0.3290519489281606,"score_spread":0.2520614253530306,"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."}}