# Contractibility of the stability manifold for silting-discrete algebras

## TL;DR

This paper proves that the space of Bridgeland stability conditions for silting-discrete algebras is contractible, by showing all bounded t-structures have length hearts with finitely many simples.

## Contribution

It establishes the contractibility of the stability manifold for silting-discrete algebras and characterizes bounded t-structures as algebraic with finite-length hearts.

## Key findings

- All bounded t-structures are algebraic with finitely many simples.
- The stability manifold for silting-discrete algebras is contractible.
- Provides a structural understanding of the derived category for silting-discrete algebras.

## Abstract

We show that any bounded t-structure in the bounded derived category of a silting-discrete algebra is algebraic, i.e. has a length heart with finitely many simple objects. As a corollary, we obtain that the space of Bridgeland stability conditions for a silting-discrete algebra is contractible.