Erdős–Pólya–Turán conjecture for linear forms in consecutive prime gaps

Let $d_n=p_n-p_{n-1}$ be the gap between consecutive primes, let $\ell$ be a positive integer, and let $\alpha_1,\dots,\alpha_\ell$ be real numbers. Consider the expression

$$\sum_{i=1}^{\ell}\alpha_i d_{n+i}.$$

Erdős–Pólya–Turán conjecture. The expression $\sum_{i=1}^{\ell}\alpha_i d_{n+i}$ changes sign infinitely often as $n$ runs through all integers if and only if the nonzero elements among $\alpha_1,\dots,\alpha_\ell$ do not all have the same sign.

This is presented as an equivalent formulation of the conjecture about linear forms in consecutive primes. The paper says that the original conjecture is proved there using recent ideas on bounded gaps between primes, but the supplied status is unknown.