Value-distribution conjecture for cyclotomic polynomial coefficients

Let $a_n(k)$ denote the coefficient of $x^k$ in the cyclotomic polynomial of order $n$, let $\delta(a_n(k)=v)$ denote the density of integers $n$ for which this coefficient equals $v$, and let $B(k)$ be the relevant coefficient bound. Value-distribution conjecture. For every $k\ge1$,

$$\delta(a_n(k)=1)\ge\delta(a_n(k)=-1).$$

If $k$ is odd, $B(k)\ge2$, and both $\delta(a_n(k)=B(k))$ and $\delta(a_n(k)=-B(k))$ are non-zero, then

$$\delta(a_n(k)=B(k))=2\delta(a_n(k)=-B(k)).$$

These assertions are based on the paper's numerical results; the source presents them as a conjecture and does not give a proof or resolution.