Finite Topological Closure of the Riemann Domain via the Poincaré Principle

We give a finite topological closure of the analytic Riemann domain by an explicit
homeomorphism $\Phi:(0,\infty)\times\mathbb{R}\times(0,\infty)\cong B^3(0,1)$ and, by
doubling along the boundary (“ear” sphere), obtain a compact simply connected model
homeomorphic to $S^3$. On this compact stage the windowed Poisson operator is
self–adjoint, strictly positive, and has a bounded inverse; the Archimedean part is
absorbed as a bounded boundary functional. With a rim-stabilized window and a
mean–zero renormalization of the Archimedean term, we certify Uniform window-positivity on the finite domain with explicit constants, and formulate a restricted Weil–type framework; we make no claim toward proving RH in this paper. The topology–analysis dictionary explains
why “making infinity finite” closes the analytic certificate without leaving the
zeta/Poisson side.

This preprint presents a finite compactification of the analytic Riemann domain using the Poincaré principle, establishing a finite-volume closure consistent with the Poisson–Laplace representation.

This work was conducted at the GhostDrift Mathematical Institute (https://www.ghostdriftresearch.com).

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