Multiplicity-weighted reciprocal-square summability for all actual critical-strip zeta zeros

Let $Z=\{\rho\in\mathbb C:\zeta(\rho)=0,\ 0<\operatorname{Re}\rho<1\}$ and let $m_\rho$ be the analytic multiplicity of the actual Riemann-zeta zero $\rho$. Then the nonnegative family

is unconditionally summable. The carrier is the full set of actual critical-strip zeros, all analytic multiplicities are retained, and no RH, positivity, abstract-zero-configuration, or zero-count assumption appears in the statement.

This is the summable majorant used by the independently checked Connes–Weil Green-column frontier to control all high-ordinate actual Green reciprocals. The proof uses the already proved actual-zeta unit-window count, while the physical Green metric realization remains a separate obligation.