***I am not deriveing a valid algorithm! What I am saying is that no valid algorithm can fail to obey my equation. Those are very different statements.***

You will have to elaborate on this for me to get it.

But otherwise, you seem to agree that your sampling comes from invalid data where P=0, rather than where F=0.

If this is true, it is most mysterious to me. But mathematicians often prove things by proving that the negative or inverse cannot be true. This somehow sounds like the same thing. By finding constraints on all possible invalid algorithms, you automaticlly find constraints on the valid ones, assuming that there are no algorithms that are neither valid nor invalid.

It is unfortunate that you have such a low opinion of me as I suspect that no other has paid so much attention to you. I wish I could get the same attention for my work.