Which kernel is it is unclear. There are zero details in the paper, not even which OS is this (Linux? Windows? Some BSD?). There are no mentions of ASLR, stack protectors or any other security mechanisms either.
In fact, there is nothing novel in the paper at all. I suspect author spent too much time with AI.
And you still haven't answered my question - that vulnerabile code that you plan to exploit, does it exist anywhere yet? Or is the whole thing something you made up?