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.