Kerr cavity mean-field equation: da/dt = [−κ/2 + i(Δ + χ|a|²)]a + F. The steady-state |a|² vs F curve is S-shaped (bistable) when |Δ| > κ√3/2. Sweeping F up/down traces different branches, producing hysteresis — a driven-dissipative first-order phase transition.