Gravitational-Wave Memory from G-Equivariance: A Ward Derivation with a Geometric Algebra Interpretation

This preprint develops the framework of Observer-Equivariance (OE) in the context of gravitational-wave memory. Starting from the Bondi–Sachs formalism, the memory effect is derived in a way that emphasizes observer equivalence rather than background structures. The derivation clarifies the relation between the Christodoulou (nonlinear) and linear memory contributions, and shows how the OE-principle constrains asymptotic symmetries. The work also provides an interpretation in geometric algebra, where the net memory can be understood as a residual rotor. Beyond offering a novel derivation, the paper illustrates how OE unifies physical law through equivalence across perspectives. Keywords: gravitational-wave memory, BMS symmetries, observer-equivariance, asymptotic flatness, geometric algebra