  Magnetic quivers have been an instrumental technique for advancing our
understanding of Higgs branches of supersymmetric theories with 8 supercharges.
In this work, we present the decay and fission algorithm for unitary magnetic
quivers. It enables the derivation of the complete phase (Hasse) diagram and is
characterised by the following key attributes: First and foremost, the
algorithm is inherently simple; just relying on convex linear algebra. Second,
any magnetic quiver can only undergo decay or fission processes; these reflect
the possible Higgs branch RG-flows (Higgsings), and the quivers thereby
generated are the magnetic quivers of the new RG fixed points. Third, the
geometry of the decay or fission transition (i.e. the transverse slice) is
simply read off. As a consequence, the algorithm does not rely on a complete
list of minimal transitions, but rather outputs the transverse slice geometry
automatically. As a proof of concept, its efficacy is showcased across various
scenarios, encompassing SCFTs from dimensions 3 to 6, instanton moduli spaces,
and little string theories.
