So, in a single run emulsion, pAg will start low in the kettle and increase as the excess of halide is exhausted, and also rise slightly because of the slight solubility of the AgBr.

In a double run, then, you can regulate the excess of halide and therefore control pAg, or at least keep it somewhat constant. (barring the sensor)

Then that's why you pretty much have to use a double run with specific concentrations of salt and silver to get a specific grain?