Finite-Height Horizontal Monotonicity of the Riemann ξ-Function up to 3×10 12

We prove that Re[ξ′(σ + it) / ξ(σ + it)] > 0 for 1/2 < σ ≤ 1, |t| ≤ 3 × 10¹². Equivalently, for every fixed t in this range, |ξ(σ + it)| is strictly increasing as σ moves to the right of the critical line. The proof combines the rigorous verification of the Riemann hypothesis up to the Platt–Trudgian height H = 3,000,175,332,800 with an explicit unconditional bound on the total contribution of all unverified zeros above H. In particular, hypothetical off-critical zeros above the verified height are treated collectively and adversarially, yet their total contribution is shown to be insufficient to reverse horizontal monotonicity throughout the region 1/2 < σ ≤ 1, |t| ≤ 3 × 10¹².