History-Dependent Gravity XIX: Toward a Unified Memory-Based Theory of Gravity — Covariant Temporal Nonlocality and Observable Signatures Across All Scales

We construct a fully covariant formulation of History-Dependent Gravity (HDG) by promoting the temporal kernel K(t-t') to a causal spacetime bitensor K(x,x') defined via Synge's world function. The resulting theory admits a compact operator form (1+η𝒦)G_μν = 8πG T_μν with 𝒦 = □_ret⁻¹ exp(-ℓ²□). Key results:• Black hole horizons acquire finite thickness Δr_h ~ ℓ (horizon nonlocality)• Hawking evaporation can terminate, producing stable remnants• Gravitational waves receive a universal -1PN phase correction• Cosmological growth is modified via μ(a) = 1 + η exp(-t/τ_c)• Mild preference for η ≈ -0.04 from DESI data, addressing the S₈ tension Combining constraints from EHT, LIGO, LISA, DESI, and Planck, we show HDG is a fully testable extension of General Relativity. Core claim: Gravity is nonlocal in time — it possesses memory. Part 19 of the HDG series (Papers I-XIX). Community: "Temporal Nonlocality and Fundamental Physics".