Universal exponent-one blocker conjecture for Master-Hits

Let $(a,b,m,n)\in\mathcal{M}$ be a Master-Hit, and let $f_1$ and $\mathcal{P}(a,b,m,n)$ denote the associated integer and set of primes. For a prime $\ell$, write $v_\ell(f_1)$ for its exponent in $f_1$. Universal exponent-one blocker conjecture. For every Master-Hit $(a,b,m,n)\in\mathcal{M}$ there exists a prime $\ell\mid f_1$ such that

$$v_\ell(f_1)=1$$

and

$$\gcd(\ell,N)=1$$

for every $N\in\mathcal{P}(a,b,m,n)$. This predicts an exponent-one prime divisor of $f_1$ that is coprime to every member of the associated set $\mathcal{P}(a,b,m,n)$. The paper presents this as the central empirical conjecture and explicitly does not claim a proof; its computational verification supports it only over the tested dataset.