Is it a good idea to reopen this question? I really can not get a complete answer from some comments on (the final version) of the question.
It's generally a complete disaster when someone asks a question, has it answered via an trivial comment, and then changes the question to the question 'they really wanted to ask'.
To anyone coming along later, it's near impossible to understand what's going on. It's nearly always best, if your initial question turns out to be broken in some way, to say thanks, and post an entirely new question (hopefully with at least a comment below it explaining that this is the question you really meant to ask all along, with a link, and explanation, of the previous broken question).
(The automatically added notice on closed questions, encouraging you to edit if possible, is basically unhelpful and inappropriate on MathOverflow.)