Collective Contraction in the de Bruijn--Newman Heat Flow: Off-Zero Logarithmic Derivatives and Certified Barrier Refinements

We study the de Bruijn--Newman family $H_τ(z)$, with heat-deformation parameter $τ$ and $H_0(z)=\tfrac18,ξ(\tfrac12+\tfrac{iz}{2})$. The moving zeros considered here are therefore zeros of $H_τ$, not directly of $ζ(s)$. Retaining the collective interaction term in the zero dynamics, we prove that fo