This bench runs a whole planet as one number: its global-mean temperature T. Each moment, absorbed sunlight warms it and outgoing heat cools it; the ball rolls downhill in the landscape those two flows carve out. Where they balance, the ball rests — a stable climate.
The twist is the ice. Bright ice reflects sunlight; dark ocean drinks it in. So a colder planet has more ice, reflects more, and stays cold — while a warmer one has less ice, absorbs more, and stays warm. That ice-albedo feedback is what splits the landscape into two valleys with a ridge between: over a band of sunlight, an icy world and an ice-free world are both stable at once.
Turn the sun up past the melt cliff (about 114% of today's) and the icy valley simply stops existing — the ball drops to ice-free. Now turn the sun back to where it started: nothing. The ice that used to reflect is gone, so the same sunlight now holds an ice-free planet. You must drop below the re-freeze cliff (about 90%) before ice returns. The gap between those two cliffs is hysteresis — the path back is not the path you came.
Honest caveat: this is the simplest system that is truly bistable, not a forecast of real Earth (which sits on a partially-iced branch, not this idealized snowball). The cliffs here are emergent properties of the equation, not scripted — the landscape you see and the temperature the ball obeys are computed from the very same constants.
Something in the simulation stopped unexpectedly — the lesson continues without it. You can move on; nothing you did was wrong.