This is an intuitive proof that directly refutes Turing's intuition underlying his arguments for undecidability, by rectifying the decision paradox found in the diagonal computation for computable numbers. Once this paradox is rectified we find the resulting computation sufficient to compute a direct diagonal, but not sufficient to compute an inverse diagonal that could be used to "diagonalize" the computable numbers as Cantor did with the reals.

This is an application of novel intuition that I do not know how to formalize into more traditional forms of expression for computability. But Turing's rational also did not utilize those more formal expressions, which is why I'm applying the novel intuition directly against his paper and not elsewhere.