The twin-prime distribution conjecture in arithmetic progressions

Let $a,q$ be positive integers such that $(a(a+2),q)=1$. Let $\Pi_2$ denote the twin-prime constant, let $\varphi_2(q)$ denote the corresponding arithmetic-progression factor, and let $o_q(1)$ tend to zero as $x$ tends to infinity with $q$ fixed. Twin-prime distribution conjecture. The number of twin primes $p\leq x$ satisfying $p\equiv a\pmod q$ should satisfy

$$\#\{\text{twin primes }p:p\equiv a\pmod q\}=(2\Pi_2+o_q(1))\frac{x}{\varphi_2(q)\log^2x}.$$

This is motivated by the Cramér random model and asks whether twin primes are equidistributed among arithmetic progressions in the expected way. It remains open, as does the underlying twin prime conjecture.