The Linear Independence Conjecture for zeta zeros

Assume that the Riemann zeta-function $\zeta(s)$ satisfies the Riemann Hypothesis. Let the positive ordinates of the non-trivial zeros of $\zeta(s)$ be counted with their distinct values. The Linear Independence Conjecture. The positive ordinates of distinct zeros are linearly independent over $\mathbb{Q}$.

If true, this conjecture implies that the weak Mertens bound $M(x)\ll x^{1/2}$ is false. The paper presents it as an unproved conjecture.