Higher central charges and Witt groups

In this paper, we introduce the definitions of signatures braided fusion categories, which are proved to be invariants their Witt equivalence classes. These signature assignments define group homomorphisms on group. The higher central charges pseudounitary modular categories can expressed in terms these signatures, applied prove that Ising have infinitely many square roots This result is further a conjecture Davydov-Nikshych-Ostrik super-Witt group: torsion subgroup generated by completely anisotropic s-simple has infinite rank.