I believe this to be false.
Using these smaller molecules in gasoline mixture results in multiple combustions in the engine's cylinder
Once ANY part of the fuel is ignited, it starts a chain reaction. It is not like the part of the fuel that burns the easiest starts burning then as temperatures get high enough the rest catches on fire. As soon as one molecule is broken down, all the energy holding it together is released and effects all the molecules next to it, lighting them off. The amount of heat given off in any one molecule combustion reaction of acetone or gasoline is enough to set off all the molecules around it. All the fuel burns as one. Since it is a homogenous mixture, it burns at an even rate.
rather than a single explosion when using just gasoline.
I'd really like to point this out. Gasoline does not explode, it burns in an even controlled rate inside the cylinder if the gasoline ever does explode, engine damage results.
Multiple combustions, or knocking, results in more unspent fuel. The more octane used in the gasoline blend, the less knocking;
Knocking is the spontaneous combustion of the remaining fuel, us normal folk not talking about cars call this an explosion. Octane is used to resist combustion from temperature and pressure. That is why you use it in a high compression engine; there is more pressure and heat.
I wonder if the increased mpg obtained by some acetone users that labored to find the beneficial ratio of acetone to gasoline for their vehicle, couldn't be acheived mechanically by finding the proper timing and fuel injection rate for their particular vehicle?
It easily can be done with a dyno and some good computer software. I'm very skeptical about what you just posted (I believe you quoted it from another source). It is full of falsities and just plain made up words like "negative catalysts". I think the guys playing around with acetone are just throwing stuff together without knowing what they are doing first.