Sachs Equations and Plane Waves VI: Penrose Limits
This paper establishes that the Penrose limit of a Lorentzian metric along a null geodesic is an intrinsic geometric object defined on a weighted associated-graded model determined by the null filtration, where the standard dilation scaling reduces coordinate freedom to a residual weighted gauge group that canonically identifies the limit with a homogeneous plane-wave germ via a tautological soldering over the jet bundle of contact scales.