Abstract

We retain the sharp zero-Cauchy harmonic dressing and its exact off-shell classical functional, and examine a boundary enlargement of the free polynomial Wick domain. The outcome is a specified continuity obstruction, not an algebra construction. For the fixed Minkowski de Donder two-point matrix, the full tensor calculation gives $H_{ww}=0$, while $H_{wh}$ contains a Cauchy-reflected frequency branch. Linear products, the insertion self-product, and a mixed quadratic test admit compact distributional polynomial representatives. Nevertheless, the mandatory ordered word $B_f\star W_g\star B_{f^{\prime }}$, with $W_g=\int g{h_{00}}^2$, has a fully contracted coefficient whose regular-kernel approximations grow logarithmically. We compute the nonzero coefficient explicitly as a product of reflected light-ray transforms. The approximating insertion kernels converge in a specified normal topology, so this divergence rules out a sequentially continuous extension of that coefficient. Consequently, it rules out a hypocontinuous Wick algebra extension satisfying the stated admission and coefficient-continuity requirements. The logarithmic coefficient can be nonzero for three pairwise disjoint observation supports. No free equation is imposed on configurations, no additional coordinate field is introduced, and no retarded product is constructed.