List decodability of Reed-Solomon codes up to capacity

Let $\mathbb{F}_q$ be a finite field and let $D\subseteq\mathbb{F}_q$ be an evaluation set. For rate $\rho>0$, write $\mathsf{RS}[\mathbb{F}_q,D,\rho]$ for the corresponding Reed-Solomon code, and let ${\mathcal L}(\mathbb{F}_q,D,d,\delta)$ denote the maximum, over received words, of the number of codewords within relative Hamming distance $\delta$, where $d=\rho|D|$.

List decodability of Reed-Solomon codes up to capacity. For every $\rho>0$, there is a constant $C_\rho$ such that every Reed-Solomon code of length $n$ and rate $\rho$ is list-decodable from a $1-\rho-\varepsilon$ fraction of errors with list size at most $\left(\frac{n}{\varepsilon}\right)^{C_\rho}$. Equivalently,

$${\mathcal L}(\mathbb{F}_q,D,d=\rho|D|,1-\rho-\varepsilon)\leq\left(\frac{|D|}{\varepsilon}\right)^{C_\rho}.$$

This conjecture proposes list decodability up to the information-theoretic capacity threshold, with polynomial list size in the block length and inverse gap parameter. The surrounding discussion notes that it is consistent with known limitations and contrasts it with the weaker Johnson-bound guarantee; its resolution status is not specified in the source.