The square-free values asymptotic conjecture for separable polynomials

Let $f(X)\in\mathbb{Z}[X]$ be a separable polynomial of degree $g\geq 1$, and suppose that $\gcd\{f(n):n\in\mathbb{Z}\}$ is square-free. For $N\geq 1$, define

$$\delta_f(N)=\left|\{a\pmod N:f(a)\equiv 0\pmod N\}\right|.$$

Square-free values asymptotic conjecture. There is a positive constant

$$C_f=\prod_p\left(1-\frac{\delta_f(p^2)}{p^2}\right)$$

such that

$$\left|\{1\leq n\leq X:f(n)\text{ is square-free}\}\right|\sim C_fX\quad\text{as }X\longrightarrow\infty.$$

In particular, infinitely many values of $f(n)$ are square-free, and a positive proportion are square-free. The conjecture is known for degrees at most $3$ and, conditionally, in broader settings under the abc conjecture; degree at least $4$ remains unresolved in general.