I can see that you have been given a great scientific answer to your question about gum and I do not doubt its validity.
Having said that, I am on day 14 of 21 and I chew gum. The fast has worked perfectly from day one and I have enjoyed all the benefits from it in spite of the gum.
I have also done the P&B shakes and that too worked just as described.
This is only a dissenting opinion because I think that a few sticks of gum in the grand scheme of things is not a big deal. If for years we have polluted our bodies with bad food, alcohol, nicotine, drugs, etc., I personally don't believe that gum during the cleansing process is going to matter.
For me, it doesn't make me hungry, but rather acts as a diversion. It just gives my mouth something to do and helps with the bad breath many experience.
Again, I am not disrecting the Science - I don't know if it is true or not - but I really don't believe that gum is going to alter its effectiveness in the least.