Sum to Infinity of Reciprocal of n^4 by 2n Choose n/Historical Note

Historical Note on Sum to Infinity of Reciprocal of $\dfrac 1 {n^4 \dbinom {2 n} n}$
On the cited MathWorld page, this result is stated as a truth.

However, according to and  in their  of $1983$, this was merely a conjecture.