Dyadic denominator bounds and a transfer principle for the phase constants of Jacobi zeros

A formal large-degree phase expansion associated with the zeros of the Jacobi polynomial $P_n^{(α,β)}$ contains a sequence of constants $κ_1,κ_2,\dots$, each of which is a polynomial in $α^2$ and $β^2$ with rational coefficients; for instance $κ_1=(α^2-β^2)/4$. This paper asks a simple arithmetic qu