  The asynchronous computability theorem (ACT) uses concepts from combinatorial
topology to characterize which tasks have wait-free solutions in read-write
memory. A task can be expressed as a relation between two chromatic simplicial
complexes. The theorem states that a task has a protocol (algorithm) if and
only if there is a certain chromatic simplicial map compatible with that
relation.
  While the original proof of the ACT relied on an involved combinatorial
argument, Borowsky and Gafni later proposed an alternative proof that relied on
a algorithmic construction, termed the "convergence algorithm". The description
of this algorithm was incomplete, and presented without proof. In this paper,
we give the first complete description, along with a proof of correctness.
