Talagrand's orthogonal structures conjecture for mixed p-spin glasses

Let $G_N$ be the Gibbs measures of a mixed $p$-spin glass model on the hypercube with zero external field. The model admits an Orthogonal Structure if there is a sequence $(a_k)_{k\geq 0}$ with $a_k>0$ such that, for every $k_0\in\mathbb{N}$ and every positive $\epsilon$, there is an $N_0$ such that for $N\geq N_0$, with probability at least $3/4$, there is a random collection of sets $\{A_{k,N}\}_{k\leq k_0}\subset\Sigma_N$ satisfying

$$G_N(A_{k,N})\geq a_k$$

and, for every distinct $k,l\leq k_0$,

$$\left\langle\lvert R_{12}\rvert\mathbb{1}_{\sigma^1\in A_{k,N},\sigma^2\in A_{l,N}}\right\rangle<\epsilon.$$

Talagrand conjectured that, at zero external field, mixed $p$-spin glass models admit such orthogonal structures. This conjecture is proved in the source by the stated low-temperature theorem.