  We give a new proof of a recent resolution by Michelen and Sahasrabudhe of a
conjecture of Shepp and Vanderbei that the moduli of roots of Gaussian Kac
polynomials of degree $n$, centered at $1$ and rescaled by $n^2$, should form a
Poisson point process. We use this new approach to verify a conjecture of
Michelen and Sahasrabudhe that the Poisson statistics are in fact universal.
