Cauchy-Hyperboloidal Evolution

I present a Cauchy-Hyperboloidal Evolution (CHE) scheme that advances the vacuum Einstein equations to future null infinity on a scri-fixed, conformally compactified background using a Maurer-Cartan formulation devised by Andrea Nützi. The unknown, consisting of a frame, connection, and Weyl curvature, obeys a symmetric-hyperbolic system regular at future null infinity. Cauchy data from 3+1 numerical relativity simulations are injected on a timelike worldtube to and evolved to future null infinity with no outer boundary conditions; constraints propagate automatically. For small-data near Minkowski, the evolution enables unambiguous waveform and flux extraction. I outline the worldtube map, gauge choices, discretization on the Minkowski diamond, validation on small-amplitude tests, and comparisons linear hyperboloidal extraction.