  In exploring supersymmetric theories with 8 supercharges, the Higgs branches
present an intriguing window into strong coupling dynamics. Magnetic quivers
serve as crucial tools for understanding these branches. Here, we introduce the
decay and fission algorithm for unitary magnetic quivers. It efficiently
derives complete phase diagrams (Hasse diagrams) through convex linear algebra.
It allows magnetic quivers to undergo decay or fission, reflecting Higgs branch
RG-flows in the theory. Importantly, the algorithm generates magnetic quivers
for the RG fixed points and simplifies the understanding of transverse slice
geometry with no need for a list of minimal transitions. In contrast, the
algorithm hints to the existence of a new minimal transition, whose geometry
and physics needs to be explored.
