The asymptotic probability of being a 2-Sophie Germain prime

Let $p$ range over the prime numbers, and call $p$ a 2-Sophie Germain prime (or $2$-SGP) when it satisfies the paper's definition of an $a$-Sophie Germain prime with $a=2$. The probability refers to the limiting proportion of such primes among primes as $p$ tends to infinity.

The 2-Sophie Germain prime probability conjecture. The probability that a given prime $p$ is $2$-SGP converges to $0.76$ as $p\to\infty$.

The conjecture is motivated by numerical tables and computed estimates showing convergence toward $0.76$; no proof or resolution is supplied in the source.