AI 中文总结
本文证明了广义标准形式下Riemann层级标量tau对称哈密顿形变由其第一哈密顿密度中特定系数唯一确定，结合Buryak--Rossi构造，确立了非零色散下的Hodge普适性猜想。
AI 中文摘要
我们证明了广义标准形式下Riemann标量tau对称哈密顿形变由第一哈密顿密度中$u_x^2$的非零系数及$u_{xx}^g$（$g\ge2$）的系数唯一确定。这决定了原始层级在正常Miura变换下的等价类。结合Buryak--Rossi对Hodge类双分叉层级的构造，我们确立了非零色散下的Hodge普适性。
英文摘要
We prove that a scalar tau-symmetric Hamiltonian deformation of the Riemann hierarchy in generalized standard form is uniquely determined by the nonzero coefficient of $u_x^2$ and the coefficients of $u_{xx}^g$, $g\ge2$, in its first Hamiltonian density. This determines the original hierarchy up to normal Miura transformations. Combined with the construction of Hodge-class double ramification hierarchies by Buryak--Rossi, this establishes Hodge universality at nonzero dispersion.
Comments35 pages
