The K-theoretic no-poles conjecture for generalized invariants

Let $\mathcal A$ be the category under consideration, let $\alpha$ be a class and let $\mu$ be a stability condition, with $\varepsilon_\alpha^\mu$ the associated generalized $K$-theoretic invariant and $\mathbb K^\mathrm{reg}(\mathcal A)$ the regular Lie subalgebra. No-poles conjecture. We have $\varepsilon_\alpha^\mu\in \mathbb K^\mathrm{reg}(\mathcal A)$. In particular, $\varepsilon_\alpha^\mu$ satisfies the finiteness condition given by equation (finiteness). The conjecture is presented as the $K$-theoretic analogue of the no-pole theorem; the supplied text does not establish its status.