Catastrophe instrument 062 · fixed-step memory study
Cusp Foundry
Turn a heavy stress wheel. A bead follows one valley even while another becomes deeper—until its old valley ceases to exist. The wheel is smooth; the snap is not. A weakly disordered rack shares the released load and may fall together.
Turn the wheel. Inside the cusp, the bead can remain in either well at the same stress; the route taken decides which one.
coral fold / snap
What the foundry is calculating
The bead descends the canonical potential V(x)=x⁴/4+a·x²/2−b·x with a fixed negative shape parameter. Stationary points solve x³+a·x−b=0. Two minima coexist inside the cusp; the bead does not teleport to the globally deeper one.
The rack contains thirty bistable cells with deterministic weak disorder. At each fixed field, only flips that lower the ferromagnetic rack energy are accepted. A neighbour's flip changes the next cell's stability, so one released load can cascade through the whole rack.
The guided patient and hurried loops use the same endpoints and fixed time step. Faster driving leaves less time for downhill relaxation, delaying the dynamic snap and widening the observed loop. This rate dependence is a model consequence, not a decorative speed setting.