Lekili–Ueda's tilting-object conjecture for maximally graded matrix factorizations

Let $f\in S^n$ be an invertible polynomial, and let $L_f$ be its maximal grading. Let $\operatorname{HMF}^{L_f}_{S^n}(f)$ be the homotopy category of maximally graded matrix factorizations. Lekili–Ueda's tilting-object conjecture. The category $\operatorname{HMF}^{L_f}_{S^n}(f)$ has a tilting object. The conjecture is motivated by the study of Cohen–Macaulay representations of graded Gorenstein rings and is implied by the conjecture on a full strong exceptional collection. The source does not establish it in general.