Classification of tau-symmetric Hamiltonian deformations at zero dispersion

Determine whether every scalar tau-symmetric Hamiltonian deformation of the Riemann hierarchy with vanishing coefficient of the dispersive term is equivalent to the trivial hierarchy, thereby establishing the zero-dispersion case of the Hodge universality conjecture.

Background

The paper proves uniqueness and Hodge universality only on the nonzero-dispersion locus, where the coefficient a of u_x^2 satisfies a\ne0. The recalled conjecture has a separate assertion for a=0: all higher corrections H_{1,2g} should vanish in standard form.

The authors explicitly state that their argument does not address this case and defer it to another work. Thus the zero-dispersion classification remains unresolved within the paper.