Abstract

Starting from the signed quadratic operator supplied by Landmark XI-A, we construct a free Einstein–scalar gauge-fixed multiplet on a finite Minkowski slab. One gauge fermion reproduces exactly the frozen de Donder term, fixes the ghost kinetic normalization, and introduces an independent Nakanishi–Lautrup field. The auxiliary field is retained for off-shell nilpotence.

We derive retarded and advanced Green operators for the graviton, scalar, ghost, and auxiliary blocks. The graviton inverse is minus trace reversal times the zero-data wave inverse; its coefficient is fixed by the handed-off action, with the Newtonian sign providing an independent check. A state-independent graded polynomial field algebra is constructed from the resulting causal kernels. The free differential is shown to preserve its equations and commutation relations.

The plateau algebra has trivial intersection with residual de Donder gauge. For classical de Donder fields, the ramp coordinate coefficient is the retarded response to a layer source, not a field supported only inside the layer. We give an explicit nonzero example and retain the fixed regulator width. The empty fixed-input Einstein jet of XI-A is not repaired: its gauge-fixed retarded response exists, but has nonzero divergence. No Hadamard state, interacting differential, tree, mixed loop, or relational BRST class is constructed.