Derived-equivalence conjecture for arbitrary weighted projective lines

Let $cX$ be a weighted projective line. For a Hom-finite $k$-linear triangulated category $cD$ with a Serre functor and a bounded t-structure $(cD^{cleq 0},cD^{cgeq 0})$ with heart $cB$, say that Assertion~ holds when the inclusion of $cB$ into $cD$ extends to an exact equivalence

$$\mathcal{D}^b(\mathcal{B})\simeq\mathcal{D}.$$

For $cD=\mathcal{D}^b(\mathbb{X})$, Assertion~ holds if and only if the Serre functor is right t-exact.

Derived-equivalence conjecture. Given an arbitrary weighted projective line $cX$, Assertion~ holds for $cD=\mathcal{D}^b(cX)$.

The domestic and tubular cases are proved in the paper; the conjecture concerns the remaining arbitrary-type case and is motivated by the corresponding result for finite-dimensional hereditary algebras.