PASS: exact S_4 polynomial and positive sum-of-squares decomposition.
PASS: exact normalization of the stated Y density and Gaussian-polynomial U density.
PASS: 1/[(1+2t^2)(1+t^4)] partial fractions, all coefficients exact.
PASS: explicit-pair variance from the second-order transform coefficient is 8.
Scope: finite exact identities do not certify global parameter regions, external KPS inputs, or novelty.