The square-free sieve conjecture

Let $P(x)\in\mathbb{Z}[x]$ be square-free. The square-free sieve conjecture. The set of integers $n$ for which $P(n)$ is divisible by the square of a prime larger than $\sqrt n$ has density $0$. This conjecture controls large squared prime divisors in polynomial values and is used together with Chowla's conjecture in the paper's conditional classification results. The source gives no resolution status.