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 Δrₕ ~ 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/τc) • 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".