I just spent posting after posting explaining you my stand point, I posted images and curves to prove it - apparently all in vain. I'm done here.
Rudeofus, there is no debate about what is pushing two stops, we all know what it is in theory and in practice.
Sure we agree that one thing is Pushing and another one is Increasing Film Speed.
Darkroom Cookbook:
"Increasing film speed is not the same as pushing ... is a process by which the film's ability to respond to low levels of light and record detail in shadow areas is increased ... such as the Hydrogen Peroxide Pushing Method or Acetic Acid Latensification, to create a true increase in film speed. Unfortunately, modern emulsions, whether they are conventional or flat-grained, rely on color dye sensitization to achieve their sensitivity as much as upon silver sensitivity. Color dyes do not respond to these speed increasing techniques. Hydrogen peroxide will do little or nothing and acetic acid latensification may ruin your film. I no longer recommend either."
It's clear what we do when pushing... we may optically print better the toe, but this is not increasing film speed by two stops.