{"id":"W2076329950","doi":"10.1016/j.difgeo.2012.06.002","title":"Integrability and conservation laws for two systems of hydrodynamic type derived from the Toda and Volterra systems","year":2012,"lang":"en","type":"article","venue":"Differential Geometry and its Applications","topic":"Nonlinear Waves and Solitons","field":"Physics and Astronomy","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"McGill University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Conservation law; Integrable system; Mathematics; Eigenvalues and eigenvectors; Decoupling (probability); Type (biology); Partial differential equation; Lax pair; Mathematical analysis; Pure mathematics; Physics","routes":{"ca_aff":true,"ca_fund":true,"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":[0.00009405016,0.00009461489,0.0001690652,0.00002065287,0.0001601962,0.00005106823,0.00005669629,0.00003180529,0.00001556442],"category_scores_gemma":[0.000008167172,0.0000669694,0.00002630805,0.00008475769,0.00006592165,0.00007231817,0.00004281208,0.00006363203,0.000001354695],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00000460207,"about_ca_system_score_gemma":0.000009245149,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008513441,"about_ca_topic_score_gemma":0.000008998344,"domain_scores_codex":[0.9994621,0.00003522204,0.0001875945,0.0001438302,0.00004989011,0.0001214184],"domain_scores_gemma":[0.9993722,0.0002508228,0.00009460913,0.0001507905,0.00006848847,0.0000630346],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"observational","study_design_scores_codex":[0.00009440156,0.0006210713,0.3176587,0.0004467431,0.0005249046,2.355955e-8,0.001400156,0.00002052654,0.1013442,0.5682014,0.0002794294,0.009408415],"study_design_scores_gemma":[0.004354315,0.0002532401,0.5952851,0.0002763502,0.001155939,0.000005350866,0.007746236,0.3490005,0.005611781,0.007747457,0.02731548,0.001248185],"study_design_candidate":"observational","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.974466,0.001083384,0.02292105,0.00007171234,0.0001253575,0.0006617278,0.000586135,0.00000789258,0.00007671976],"genre_scores_gemma":[0.9990932,0.00001973842,0.00005011207,0.000007793853,0.0003369966,0.0001205707,0.0002796105,0.000007541787,0.0000844087],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.560454,"threshold_uncertainty_score":0.2730933,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01857122304429676,"score_gpt":0.2717487494190342,"score_spread":0.2531775263747374,"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."}}