Distributional traces and central moment tests for Vámos quartics

Abstract

For the stable quartics hλ = 4e₁e₃ + λa²b², we establish moving-graph traces of the joint corner expansion of hλ^(−1/2) and finite moving-plane jets at the endpoint λ = 64/27. Exact inverse equations provide uniform conormal ellipticity; a Bessel annihilator makes the facet symbol identically 4/3 on its moving plane. The leading facet trace is an explicit positive ellipse measure of mass √3/2. We also construct canonical signed central-band moment functionals and prove quantitative convergence to the moments of 2 Beta(1/4,1/4). Every fixed finite Hankel and associated localizer block is then strictly positive in sufficiently narrow bands. An all-order conditional beta law and exact exclusions of independent positive shifts and coordinate-monotone positive transports complete the structural picture.