Lets start with this old article from 2006: https://bikesportbicycles.com/wp-content/uploads/docs/TireDrop-OptimizingTirePressure.pdf
It got this handy graph from Frank Berto about optimum tire pressure for a certain tire load. Thats the point you shouldn’t forget: My optimum tire pressure (for my weight) is different from your optimum tire pressure (for your weight)!
The guys from Silca did run some tests, regarding the difference between tire rolling resistance on drum roll tests and real world road surfaces: https://blog.silca.cc/part-4b-rolling-resistance-and-impedance
Thats the rolling resistance graph you get from drum roll rolling resistance tests, like you find at https://www.bicyclerollingresistance.com
The higher the tire pressure, the lower the rolling resistance (= the faster the tire)
While these tests are a valid tool to compare the rolling resistance of different tires, they don’t paint the whole picture.
On real world street surfaces, the tires behave a bit differently. Above a certain tire pressure (for a given rider weight), the rolling resistance actually increases.
Rider and bike total weight was 190 lbs, we used water inside water bottles to maintain equivalent total mass over the duration of the testing.
To wrap it up, just watch this very interesting interview with Josh Poertner the boss of Silca about optimum tire pressure