Semiclassical corrections to an optimized positive-energy warp shell: A fixed background benchmark of scale dependence, magnitude and the vacuum exterior.

We evaluate an approximate renormalized vacuum stress tensor, for a massless, conformally coupled scalar field, on a fixed background, and compare it with the classical energy-condition margins of an optimized positive-energy warp shell. The approximation is the Anderson–Hiscock–Samuel (AHS) analytic approximation in its zero-temperature, Boulware-like state, and the background is the static, zero-shift member of the shell family. We prove symbolically, for every static spherical metric, that the scale-dependent part of the AHS tensor is proportional to the metric variation of the Weyl-squared action. A change of renormalization scale is therefore a running of that coupling, and the physical quantum source splits into a conserved design-and-state part plus local curvature terms weighted by renormalized couplings. In the Schwarzschild exterior, the AHS energy density and both null combinations are negative at every radius, in closed form. On the static member, a 160-bit ball-arithmetic certificate bounds the quantum correction relative to the classical stress tensor and shows that every energy-condition margin stays positive throughout a stated radial region, for all couplings in a broad illustrative box. The paper also reports the first-order backreaction and a flat-space quantum-inequality scale benchmark. All results hold within the AHS approximation, whose error relative to the exact renormalized stress tensor is not quantified. Code: https://doi.org/10.6084/m9.figshare.34914837