On the Uniqueness of Sarkar-Seed-Szabo Construction

In an attempt to consolidate Szabo's geometric chain complex and Bar\hyp Natan's chain complex, Sarkar-Seed-Szabo defined a total complex $CTot(L)$ over $\mathbb{F}_{2}$ by adding some extra terms $\{h_{i} \}_{i=2}^{\infty}$ in the differential. In this paper we prove the uniqueness of $\{h_{i} \}_{i=2}^{\infty}$ upto some properties. This in turn implies that the total complex $CTot(L)$ is unique.