Scaling-limit conjecture for uniformly random graphic sequences

Let $D_1\ge\dotsb\ge D_n$ be a uniformly random graphic sequence of length $n$. The scaling-limit conjecture. There exists a random continuous function $D:[0,1]\to\mathbb{R}$ such that

$$\left(n^{-1/2}\big(D_{\lfloor tn\rfloor}-(1-t)n\big),0\le t\le 1\right)\overset{d}{\to}\left(D_t,0\le t\le 1\right)$$

in the uniform topology.

This conjecture proposes a functional scaling limit for fluctuations of a uniformly random graphic sequence around the deterministic profile $(1-t)n$. The source presents it as a direction for future work and does not identify the limiting process or establish the convergence.