{"paper":{"title":"Liouville integrable Lotka-Volterra systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Lotka-Volterra systems in 2m and 2m-1 dimensions form large Liouville integrable families.","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"David I. McLaren, G.R.W. Quispel, Peter H. van der Kamp","submitted_at":"2026-04-02T08:03:27Z","abstract_excerpt":"We present $\\frac{m^{2}}{4}+\\frac{m}{2}+\\frac{1-\\left(-1\\right)^{m}}{8}$ homogeneous $(3m-2)$-parameter families of Liouville integrable $(2m)$- and $(2m-1)$-dimensional Lotka-Volterra systems. We also study inhomogeneous versions of these systems."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We present m²/4 + m/2 + (1-(-1)^m)/8 homogeneous (3m-2)-parameter families of Liouville integrable (2m)- and (2m-1)-dimensional Lotka-Volterra systems.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the constructed systems actually possess a sufficient number of independent, commuting integrals of motion to satisfy the Liouville criterion (details of the Poisson structure and integrals are not visible in the abstract).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Explicit families of Liouville integrable Lotka-Volterra systems are constructed, with (3m-2) free parameters in (2m) and (2m-1) dimensions for each integer m.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Lotka-Volterra systems in 2m and 2m-1 dimensions form large Liouville integrable families.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"1553639486d137357f44a9df58727595124b68f7787c4079171182c8eddee788"},"source":{"id":"2604.01743","kind":"arxiv","version":3},"verdict":{"id":"d1fd2fd5-9fdc-450f-9937-a72c503aa669","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-13T21:07:42.784414Z","strongest_claim":"We present m²/4 + m/2 + (1-(-1)^m)/8 homogeneous (3m-2)-parameter families of Liouville integrable (2m)- and (2m-1)-dimensional Lotka-Volterra systems.","one_line_summary":"Explicit families of Liouville integrable Lotka-Volterra systems are constructed, with (3m-2) free parameters in (2m) and (2m-1) dimensions for each integer m.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the constructed systems actually possess a sufficient number of independent, commuting integrals of motion to satisfy the Liouville criterion (details of the Poisson structure and integrals are not visible in the abstract).","pith_extraction_headline":"Lotka-Volterra systems in 2m and 2m-1 dimensions form large Liouville integrable families."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.01743/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}