
Description: This paper investigates the shifted‑contour remainder in the smoothed Perron decomposition of the high‑frequency remainder for the regularized logarithmic derivative of the Riemann zeta function. After smoothing, the remainder splits into four parts: nontrivial zero packets, trivial zeros, the main‑pole correction, and the shifted‑contour term. While the trivial and pole terms are directly harmless, the shifted‑contour contribution requires separate analysis. The paper shows that the shifted‑contour remainder can be expressed as a vertical convolution of the logarithmic derivative of the zeta function along a shifted line. Three regimes are distinguished: Right‑side regime (0 < A < a): the contour lies to the right of the critical line and is controlled by translated vertical mean‑square estimates. Singular regime (A = a): the contour passes through the critical line, encountering poles at zeros of the zeta function, and is therefore singular unless regularized. Left‑side regime (A > a): the contour lies to the left of the critical line. By the functional equation and reflection symmetry, this reduces to right‑side estimates plus explicit gamma and trigonometric terms, which contribute only harmless logarithmic factors. The main conclusion is structural: the shifted‑contour remainder is not an independent obstruction. It reduces to the same type of vertical mean‑square problems already present in the high‑frequency barrier, together with manageable gamma‑factor contributions. The paper does not prove the Riemann Hypothesis and does not establish the required right‑side mean‑square bounds. Its contribution is to clarify that shifted‑contour regularity is essentially another form of the vertical mean‑square barrier, not a new analytic difficulty.
