Tensor Propagation, Causal Structure, and Gravitational-Wave Consistency in the Latency–Erasure Field Theory Linearized Dynamical Modes, Retarded Response, Screened Generation, and Horizon-Adjacent Signatures in a Finite-Capacity Gravity Program

We develop the dynamical wave sector of the latency–erasure field theory and derive its causal propagation structure, tensor/scalar mode decomposition, and gravitational-wave phenomenology. Earlier branches of the finite-capacity program established weak-field gravity, screened solar-system viability, cosmological erasure, nonequilibrium latency memory, stochastic timing fluctuations, and unified source closure. The present work turns that static and sectoral framework into a dynamical propagation theory. Starting from the covariant latency action with unified source hierarchy, we linearize the theory around admissible backgrounds and separate transverse-traceless tensor perturbations from scalar latency perturbations. We show that the far-zone tensor sector propagates on the standard metric null cone in the admissible weak-background regime, thereby preserving the observationally required gravitational-wave speed, while the latency scalar sector remains source-driven, screened, and regime-dependent. A retarded Green-function formulation is introduced to enforce causal sourcing and replace static-kernel intuition by explicitly delayed response. We derive the scalar dispersion relation, identify propagating, overdamped, and screened regimes, and formulate conditions under which the theory avoids wrong-sign kinetic structure, gradient instability, and tachyonic growth. We then study source generation and show that scalar-latency wave activity is generically suppressed in ordinary far-zone inspiral regimes but can become nontrivial near strong-field, overwrite-active, or saturation-adjacent configurations. This leads to concrete horizon-proximate signatures including ringdown shifts, echo-like delayed structure, and phase anomalies, while preserving far-zone timing consistency. The resulting theory upgrades the finite-capacity gravity program from a static screened phenomenology to a causally explicit dynamical field theory with gravitational-wave predictions.