Do I have proof??? Only my personal experience and knowledge of chemistry. Higher octane gas burns faster, and produces more power. Less Octane produces less pickup, performance, but burns slower so better gas mileage, does that makes sense? I have used 85 octane in mountainous areas (high altitude) and have very impressive mpg's in my LS430. Most people think the opposite, but there are dead wrong. think about racing fuel 100-104 octane or alcohol . burns VERY fast . Lots of power and acceleration but terrrible mpg.
Also, we have ethanol where i live. Octane rating is 89 with 10% ethanol. It is about 5-8 cents CHEAPER a gallon than 87 (pure). I use it alot instead of regular but I think i get best mileage with regular. So it depends on the price for what I use. Sometimes I do one tank of one and another tank of the other.
I havent used premium for year, including several mercedes, bmw's, 1 porche, and 4 lexus. The only time i use premium in all these years, is when I was doing some autocross racing.
I have had no problem running 87 or even less octane. Try 3 tankfuls yourself and you decide.
Cary in SD.