{"paper":{"title":"Toda Equations and $\\sigma$-Functions of Genera One and Two","license":"","headline":"","cross_cats":["math.AG","math.MP"],"primary_cat":"math-ph","authors_text":"Shigeki Matsutani","submitted_at":"2003-05-04T12:03:07Z","abstract_excerpt":"We study the Toda equations in the continuous level, discrete level and ultradiscrete level in terms of elliptic and hyperelliptic $\\sigma$ and $\\psi$ functions of genera one and two. The ultradiscrete Toda equation appears as a discrete-valuation of recursion relations of $\\psi$ functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0305008","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}