{"id":"W2763393928","doi":"10.1007/s00220-008-0640-0","title":"Justification of the Lattice Equation for a Nonlinear Elliptic Problem with a Periodic Potential","year":2008,"lang":"en","type":"article","venue":"Communications in Mathematical Physics","topic":"Nonlinear Waves and Solitons","field":"Physics and Astronomy","cited_by":24,"is_retracted":false,"has_abstract":false,"ca_institutions":"McMaster University","funders":"Engineering and Physical Sciences Research Council","keywords":"Floquet theory; Elliptic function; Nonlinear system; Lattice (music); Jacobi elliptic functions; Elliptic operator; Elliptic curve; Toda lattice; Algebraic equation","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":[0.0001335865,0.0000926633,0.0001618887,0.00001893746,0.0002355232,0.00001447964,0.0004691737,0.00002543614,0.00001294077],"category_scores_gemma":[0.00001798762,0.00006553458,0.00008656254,0.0002443956,0.0003041811,0.00007973873,0.0001009811,0.000152097,0.0000102292],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001739996,"about_ca_system_score_gemma":0.00009584326,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001051007,"about_ca_topic_score_gemma":0.000001180741,"domain_scores_codex":[0.9992775,0.00006094137,0.0002962044,0.0001093221,0.0001299879,0.0001260802],"domain_scores_gemma":[0.9984832,0.0002201361,0.0001570908,0.0009815871,0.0001335588,0.00002435949],"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":[0.00002317287,0.001833183,0.002099369,0.0001598767,0.00005957658,9.298854e-8,0.003162751,0.002283726,0.0008363516,0.9866636,0.00005532166,0.002822912],"study_design_scores_gemma":[0.00102283,0.00007259945,0.001464252,0.0002241683,0.0001483018,0.000003163857,0.0008339248,0.5870881,0.001506997,0.4067076,0.0006770781,0.0002509311],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.257276,0.00005399849,0.7316252,0.001373871,0.00003379146,0.001632444,0.0001168711,0.00002814012,0.007859661],"genre_scores_gemma":[0.8352554,0.000004638396,0.1643342,0.00001203151,0.00006141028,0.0001166025,0.00006086569,0.00001398736,0.0001408711],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.5848044,"threshold_uncertainty_score":0.2672423,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.057663824361963,"score_gpt":0.3013763128800722,"score_spread":0.2437124885181092,"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."}}