The papers of Riemann from 1860 on shockwave propagation singularities along with his formulation of branch point topological functions points toward a potential proof of his prime number conjecture. This is because the linear zero line of 1/2 on the complex plane must be transformed into a point (analogous to the astronomical black hole.)
Both above functions physically provide a functional rationale for an evolution of complex manifold N + 1... dimensions spiral waveform (extended Zeta function) via a singularity. A proof that a infinite line transforms via a shockwave point of singularity not only in one dimension in a infinite series of possible media through which the rates of infinite variety of propagation potentials produce via analytic continuation singular branch points is sufficient and necessary condition for said proof. The abstraction to an algebraic representation of this analysis situs potential energy problem will be the productive path forward.
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