Metric Spectral Geometry of $\mathbb{Z}^d$-Crossed Products beyond Equicontinuity

We construct linearly twisted spectral triples on $C^\ast$-crossed products $\mathfrak{A}\rtimes_α\mathbb{Z}^d$, starting from a spectral triple $(\mathfrak{A},\mathcal{H},D)$ and an action $α$ admitting an adapted weight. The weight compensates for the growth of the base Dirac operator under the dy