Short cubic exponential sums with Möbius function

The work is dedicated to the conclusion of non-trivial estimates of short cubic exponential sums with Möbius function of the form
$$ S_3(\alpha;x,y) = \sum_{x-y<n\le x} \mu(n) e(\alpha n^3), $$
over minor arcs $\mathfrak{m}(\mathscr L^{32(B+18)})$ for $y\ge x^\frac{4}{5}\mathscr L^{8B+944}$ and $\tau=y^5x^{-2}\mathscr L^{-32(B+18)}.$