The continuous flow dynamics can be discretized into a Markov chain over five states: OFF, LAMINAR, TRANSITION, VORTEX, and CHAOS. The generator matrix L encodes transition rates between states.
Under correct operator order, the generator L_correct has a positive spectral gap — the smallest nonzero eigenvalue of −L is bounded away from zero. The system returns exponentially fast to the VORTEX state after any perturbation. VORTEX is a stable non-absorbing attractor.
Under wrong operator order, L_wrong drives the system to CHAOS, which functions as an absorbing barrier: once reached, P(CHAOS → VORTEX) = 0. No spontaneous recovery occurs. The only escape is a physical reset — draining the basin and recommissioning.
The spectral gap also determines the recovery timescale after a storm surge temporarily disrupts the vortex. A larger gap means faster recovery. The contact geometry of the correct-order system maximizes this gap.
| State space | S = {OFF, LAMINAR, TRANSITION, VORTEX, CHAOS} |
| Correct generator | L_correct: TRANSITION → VORTEX (non-absorbing) |
| Wrong generator | L_wrong: TRANSITION → CHAOS (absorbing) |
| Spectral gap | gap(L_correct) > 0 → exponential return |
| Absorbing barrier | P(CHAOS → VORTEX) = 0 without reset |