Basis-form conjecture for blockers of Master-Hits

Let $(a,b,m,n)\in\mathcal{M}$ be a Master-Hit, and call a prime divisor of $f_1$ that satisfies the relevant coprimality condition with $\mathcal{P}(a,b,m,n)$ a blocker. Basis-form conjecture. Every Master-Hit has at least one blocker. This is stated as a consequence of the universal exponent-one blocker conjecture, so it is not an independent strengthening. Its status therefore remains contingent on the unresolved central conjecture.