Donaldson–Scaduto conjecture on associative pairs of pants

Let $(X^4,\omega_1,\omega_2,\omega_3)$ be a hyperkähler $K3$ surface, and let $\alpha_1,\alpha_2,\alpha_3$ be irreducible $(-2)$-classes in $H^2(X^4;\mathbb{Z})$ satisfying $\alpha_1+\alpha_2+\alpha_3=0$. For each $i$, let $v_i=(\omega_1\cdot\alpha_i,\omega_2\cdot\alpha_i,\omega_3\cdot\alpha_i)\in\mathbb{R}^3$, let $J_i$ be the corresponding complex structure, let $\Sigma_i$ be the unique smooth embedded $J_i$-holomorphic sphere representing $\alpha_i$, and set $P_i:=\Sigma_i\times(\mathbb{R}^+\cdot v_i)\subset X^4\times\mathbb{R}^3$. Donaldson–Scaduto conjecture. There is a unique associative submanifold $P$ in $X^4\times\mathbb{R}^3$ with three ends asymptotic to cylinders $P_1$, $P_2$, and $P_3$. The existence of such an associative pair of pants was previously proved, and this paper proves uniqueness, so the conjecture is solved.