Scaling-limit conjecture for affine preferential attachment looptrees

Fix $\delta>-1$, let $S$ be a finite tree, and let $({T}^{(S),\delta}_n)_{n\geq |S|}$ be the affine preferential attachment tree sequence started from $S$. Write $\mathsf{Loop}(T)$ for the looptree associated with a tree $T$.

Scaling-limit conjecture. There exists a random compact metric space $\mathcal{L}^{(S)}_{\delta}$ such that

$$n^{-\frac{1}{2+\delta}}\cdot\mathsf{Loop}(T^{(S),\delta}_n)\mathop{\longrightarrow}^{a.s.}_{n\to\infty}\mathcal{L}^{(S)}_{\delta}$$

holds almost surely for Gromov–Hausdorff convergence. Moreover, almost surely, the Hausdorff dimension of $\mathcal{L}^{(S)}_{\delta}$ is $2+\delta$.

This predicts the scaling limit and dimension of the looptree associated with the affine preferential attachment tree. The statement is presented as a conjecture, and no proof or resolution is supplied in the source.