A Topological Phase-Portrait Mapping for the Asymptotic Space of the Riemann Zeta Function

This paper introduces a novel geometric visualization framework to study the extremevertical compression of non-trivial zeros in the Riemann Zeta function at high altitudes (y →∞). We present a localized conformal scaling mapping that regularizes the visual spacing ofthe roots inside a moving frame, balancing the apparent density variations. Furthermore, weproject the phase behavior onto a multi-sheeted Riemann surface mapping of its logarithm,creating an intuitive 3D topological phase-portrait that unrolls the phase velocity gradients.Rather than claiming an analytical proof of individual root locations, this framework servesas a geometric and computational visualization tool to analyze complex phase structuresand structural balance at trans-computational scales.