The cancellation conjecture for Ramanujan-sum correlations

Let $f$ be an approximation function, let $\theta$ be an inhomogeneous shift, and let $\phi$ and $d$ denote Euler's totient and divisor-counting functions, respectively. Let $W(f,\theta)$ be the corresponding inhomogeneous well-approximable set. The cancellation conjecture.

$$\limsup_{N\to\infty}\frac{\sum_{n=1}^N\phi(n)f(n)/n}{\sqrt{\sum_{n=1}^N f(n)d(n)}}=\infty\implies W(f,\theta)\text{ has full Lebesgue measure.}$$

The proposed conclusion would follow from the conjectured cancellation estimate discussed immediately before it, and would improve one theorem while remaining weaker than a question posed earlier in the paper. The source gives no resolution.