I think you need to read the book Jenijeni. I know it seems like a dauting task but it will help you understand the terms better. Ketosis is the fat burning state achieved through a low carb diet. Atkins is one of the few low carb diets, from my understanding, where ketosis is achieved due to the very low carb count required during the induction phase. As you get into OWL and increase carbs, your level of ketosis starts to go down as well. However, this does not mean that you are no longer losing lbs, or inches.

I try to stay at very low inductuion level carbs as I have a lot to lose and it should come off quicker according to Atkins by doing it this way. I increase my carbs on day that I am exercising. However, I have noticed that sugar alcohols without a combined fiber intake throw me out of ketosis as well...even if my carb count is down.

However, I have found sugar free granola that has sugar alcohol in it, but due to the fiber count (4 grams), it doesn't impact me.