History-Dependent Gravity XVI: Emergent Causality from Temporal Memory Kernels

In standard general relativity, causality is strictly enforced by the local light-cone structure of hyperbolic field equations. However, theories incorporating temporal memory---such as History-Dependent Gravity (HDG) ---inevitably introduce temporal nonlocality through convolution kernels. A common concern is that such nonlocality may lead to violations of causality, instabilities, or ghost-like excitations. In this work, we demonstrate that HDG does not inherently violate causality; rather, it generalizes it. We introduce the concept of Soft Causality, defined as a continuous hierarchy of causal structures parameterized by the temporal asymmetry of the memory kernel. By analyzing the analytic and spectral properties of the kernel K (), we classify HDG models into strictly retarded, weakly nonlocal, and strongly symmetric regimes. We derive a quantitative causality parameter that measures the relative weight of advanced contributions and show that, in the soft regime, these contributions are perturbatively suppressed and act as effective global boundary conditions rather than sources of acausal signaling. The corresponding Green's function acquires a controlled advanced component that does not enable information transfer to the past. We prove that the spectral density remains positive up to corrections of order O (), ensuring the absence of negative-norm states. Finally, we discuss observational implications, including small phase shifts in gravitational wave propagation and modifications to the growth of large-scale structure. We show that the soft-causality parameter is testable through gravitational-wave phase shifts and large-scale structure observations, making HDG a falsifiable nonlocal theory. These results position HDG as a physically consistent nonlocal theory in which causality emerges as a limiting case of a broader temporally nonlocal dynamics.