Maybe I can simplify this from strictly an engineering perspective.
The IAT at the air box determines the mass floww of air. The temperature after the intercooler determines the volume flow of air into the cylinders. The lower the temperature the lower the volumetric flow rate. Since the blower is positive displacement and the cylinder volume is fixed, the intercooler outlet temperature sets the blower discharge pressure.
All things being equal, lowering air charge temperature to the cylinders will produce the same horsepower with less boost pressure.
