{"id":"W4415277997","doi":"","title":"Algebraic independence of solutions to multiple Lotka-Volterra systems","year":2025,"lang":"en","type":"article","venue":"ArXiv.org","topic":"Numerical methods for differential equations","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Invariant (physics); Algebraic number; Real algebraic geometry; Pairwise comparison; Algebra over a field; Tuple; Geometric invariant theory","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":[0.0004203791,0.0001590159,0.0003577509,0.0002007903,0.0001422689,0.00002008445,0.0003496906,0.0001146861,0.000065058],"category_scores_gemma":[0.00320532,0.0001498273,0.0001160618,0.0006484418,0.00007049747,0.00009578778,0.0002144438,0.0001982407,0.0001354364],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007805435,"about_ca_system_score_gemma":0.00008067639,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002878233,"about_ca_topic_score_gemma":0.00008706527,"domain_scores_codex":[0.9984176,0.000181781,0.0005231609,0.0002851936,0.0002720724,0.0003201676],"domain_scores_gemma":[0.9979606,0.001001743,0.0001485652,0.0005911255,0.0001889811,0.0001089538],"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":[0.0001037331,0.001409929,0.2226321,0.001086558,0.0005162239,0.000007935918,0.001647482,0.0003875594,0.1539905,0.6034653,0.003638753,0.01111396],"study_design_scores_gemma":[0.003709192,0.0007928298,0.4861715,0.002402512,0.001005325,0.00001723229,0.002607349,0.02501418,0.06982854,0.398555,0.007907255,0.001989054],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4483142,0.00005358904,0.5496927,0.0002841296,0.0005124272,0.0003719121,0.00001588386,0.00008712176,0.0006680581],"genre_scores_gemma":[0.9777686,0.000003441935,0.02041902,0.00008907814,0.00004745858,0.0001051204,0.000003915635,0.00002114202,0.001542247],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.5294544,"threshold_uncertainty_score":0.6109781,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.149686681060352,"score_gpt":0.3775243277805184,"score_spread":0.2278376467201665,"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."}}