It is possible that this second recursion doesn’t hold at N=3 (because there is enough of the density covered by the fraction of real polynomials), but then onl

It is possible that this second recursion doesn’t hold at N=3 (because there is enough of the density covered by the fraction of real polynomials), but then only starts at higher degrees (it will eventually be easier because the N-2 degree will have a higher chance to have a root higher than the new complex b). So this makes is certainly more complicated to prove but still seems intuitively correct to me.