Okay, well I've reviewed the article as well as your work and also trying to understand your code. I understand how you say the logical chain was broken because of a false assumption. However, I still do not understand why if you modded the code to incorporate the factor of 1/2 that you would have to start the whole thing over. I can imagine that it makes a difference using the factor of 1/2, but I do know know to what extent.
Please let me know if you can help on this.