Undecidability conjecture for three-block Presburger arithmetic with non-quadratic scalar multiplication

Let $\alpha$ be a non-quadratic scalar. Undecidability conjecture. $\alpha$-Presburger arithmetic sentences with three alternating blocks of quantifiers are undecidable. The paper contrasts this with the known complexity results for one and three alternating blocks in the quadratic case; the conjecture concerns the unresolved complexity and decidability landscape for non-quadratic scalar multiplication.