We study the second logarithmic derivative of the Riemann zeta function on the critical line, mollified on the mesoscopic scale L=log T, and develop a variance-equilibrium framework connecting the distribution of zeta zeros to prime number statistics through energy constraints. On the arithmetic side, we consider the mollified curvature field H_{L,T}(t) = ((log zeta)'' * v_{L,T} * K_{L,T})(t), where v_{L,T} is a modulated time-mollifier tuned to the prime frequency scale xi_T approx (log T)/(2 pi), and K_{L,T} is a bandpass spectral cap centered at +/- xi_T. Its windowed L^2-energy is defined as V_arith(T) := integral from T to 2T of |H_{L,T}(t)|^2 w_L(t) dt, where w_L is a baseband Fejer window. Using only the Dirichlet series for (log zeta)'' on Re s>1 and Montgomery--Vaughan type mean-value theorems for Dirichlet polynomials, we show that V_arith(T) is unconditionally locked to the scale V_arith(T) = (log T)^4 + O((log T)^3), with error O((log T)^3), with no hypothesis on the location of the nontrivial zeros of zeta(s). On the spectral side, we use the Hadamard product and the functional equation to express hat{H_{L,T}}(xi) = W_{L,T}(xi) Z(xi) + hat{R}(xi), where W_{L,T} is a smooth kernel supported on the bands |xi -/+ xi_T| = A/log T) from the critical line. We establish a conditional resolution of the Riemann Hypothesis: if the off-diagonal interference term cannot compensate for diagonal losses from off-line zeros, formalized as a "Global Compensation Bound" requiring that the diagonal deficit exceed the off-diagonal shift by an amount >= c (log T)^{4-delta_*} that dominates the variance identity's error term, then RH follows. We characterize precisely the "conspiracy" that would be required for off-line zeros to exist: the zero heights would need to produce structured negative correlations that nearly cancel the diagonal energy deficit in every mesoscopic window. We explain that such a mechanism would be incompatible with GUE statistics for zeta zeros, establishing that within the variance-equilibrium framework, the Riemann Hypothesis is equivalent to GUE-compatible zero correlations.