Goldbach's conjecture for prime-like distributions

Let $Q$ be a subset of the natural numbers, and let $\pi_Q(n)$ denote the number of elements of $Q$ less than or equal to $n$. Let $\pi(n)$ denote the number of primes less than or equal to $n$. The distribution of $Q$ is similar to the distribution of primes if there exists $c\ta\in\mathbb{N}$ such that

$$|\pi_Q(n)-\pi(n)|<c$$

for every integer $n$.

Generalization of Goldbach's conjecture. Let $Q$ be a subset of natural numbers whose distribution is similar to primes. There exists $N_Q\in\mathbb{N}$ such that, for any even integer $2n>N_Q$, there exist $q_1,q_2\in Q$ satisfying

$$q_1+q_2=2n.$$

This proposes that the Goldbach representation property depends on having a prime-like counting distribution rather than on primality itself. The source gives computational evidence for particular shifted-prime constructions, but does not establish the assertion for every subset with the stated distribution property.