In this paper, the author shows unconditionally that at least one of the following statements holds:

i) the distance between two consecutive Goldbach numbers is finite, i.e. there exists an absolute positive constant $C$ such that $g_{n+1}-g_{n}<C$, for all large enough $n$, where $g_{n}$ is the $n$-th Goldbach number,

ii) $\vert\mathcal{D}^{c}\cap[0,N]\vert\le N^{\kappa}$ for some $\kappa<1$ and $N$ a fixed large enough integer, where $\mathcal{D}$ is the set of de Polignac numbers, that is, numbers $m$ such that there exists infinitely many $i$ such that $p_{i+1}-p_{i}=m$, where $p_{i}$ denotes the $i$-th prime number.

Assuming i) holds, is it possible to make $C$ explicit with current technology?

Thanks in advance.