Description: This paper analyzes the Gram matrix of zero packets that arise in the smoothed high‑frequency remainder of the regularized logarithmic derivative of the Riemann zeta function. After Perron smoothing, each zero contributes a localized packet, and the mean‑square of the remainder becomes a Gram problem over these packets. The main result is a conditional Gram bound for the critical‑line packet model. Assuming a mean‑spacing pair‑counting condition on the ordinates of critical‑line zeros, and an envelope estimate for packet localization, the Gram form is shown to be bounded with only logarithmic losses. In particular, for localization scales larger than log T, the bound is proportional to T log T, and for fixed scales it is proportional to T (log T)². Both are subcritical in the high‑frequency loss accounting, since they involve no positive power of the parameter a⁻¹. The paper also isolates the obstruction caused by off‑critical zeros. Packets attached to zeros off the critical line carry an amplification factor that grows with the cutoff parameter, producing power‑amplified contributions. Thus, while critical‑line packets are conditionally controlled by pair counting, off‑line packets remain the genuine RH‑level obstruction. The contribution is structural: it clarifies that critical‑line pair counting controls packet interactions, while off‑line zeros must be excluded or separately handled. Together with earlier work on smoothed Perron remainders and sharp cutoff transfer, this paper identifies the precise analytic barrier in the high‑frequency route to the Riemann Hypothesis.