Yes, the two resistors model the behavior of the pot as the wiper is moved. Note that if the parameter K changes, that causes one resistor to get bigger while the other automatically gets smaller.
By connecting the two fixed resistors at the ends of the pot, it desensitizes the pot so moving the wiper is not so touchy. This is the electrical version of a a
hundred-turn pot
Look at the internal schematic on the data sheet for the LM431 below. Note that the Ref pin connects to an non-inverting input of an opamp. Connecting the wiper to there tricks the LM431 to acting as a comparator; with the output being taken at the anode pin. Since the opamp is running open-loop, and it has a gain of ~40K, it does a pretty good job of acting as a comparator.
The positive feedback that comes through the high value resistor from the output to the Ref pin is what gives the circuit positive feedback (snap action) and the required hysteresis.