Weave-realizability for D–type

We study exact Lagrangian fillings of Legendrian links $D_n$-type in the standard contact 3-sphere. The main result is existence a filling, represented by weave, such that any algebraic quiver mutation associated intersection can be realized as geometric weave mutation. method proof via calculus and construction appropriate 1-cycles whose intersections realize required numbers. In particular, we show $D$-type, each cluster chart moduli microlocal rank-1 sheaves induced at least one embedded filling. Hence, have many Hamiltonian isotopy classes seeds algebra, their exchange graph for disk surgeries contains $D_n$-type.