Smoothed zeta zero-count bound (${\sum }_{\rho }(1+|t-\Im \rho {|}^2{)}^{-1}\ll \log (|t|+3)$)

Evaluate the real logarithmic derivative of Riemann xi at real part two, where every summand is positive and comparable to this kernel. The gamma logarithmic derivative and the bounded zeta logarithmic derivative give the logarithmic bound. It implies the local unit-interval count, and conversely such local counts imply this smoothed bound by summing the decaying tails.