We demonstrate that an equivalence of categories using ε-interleavings as a fundamental component exists between the model of persistence modules as graded modules over a polynomial ring and the model of persistence modules as modules over the total order of the real numbers.

In this paper, we study local graded Weyl modules and Demazure for twisted hypercurrent algebras. We prove that a algebra are isomorphic to the corresponding level 1 modules, moreover, they restrictions of untwisted algebra.