Unconditional Geometric-Spectral Resolution of the Riemann Hypothesis via the Hilbert-Pólya Method (v2, Corrected Edition, Supersedes Zenodo: 17488361)

This work presents the unconditional resolution of the Riemann Hypothesis (RH) within the framework of the Hilbert–Pólya Spectral Program. The central thesis establishes a bijective correspondence between the spectrum (eigenvalues) of the constructed Dirac-type operator $\Htebac$ on a 13-dimensional manifold and the non-trivial zeros of the Riemann $\xi$-function. The central novelty is the Topological Enforcement Theorem (TET). A specific Topological Selection Rule ($\mathbf{c_2 + p_1 = 0}$) is proven to be the necessary and sufficient invariant (via the Atiyah–Singer Index) that enforces the $\mathbf{C^\infty}$ regularity of the arithmetic potential $\Phi$. This regularity, via the Kato-Rellich theorem, ensures the operator's essential self-adjointness ($\Htebac^* = \Htebac$), which unconditionally concentrates the entire spectrum on the Critical Line ($\mathfrak{R}(s)=1/2$). The proof culminates by demonstrating the absolute spectral equivalence $\det_{\zeta}(s - \Htebac) \equiv \xi(s)$, which requires the Geometric-Arithmetic Balance (GAB) condition $\mathbf{A_1=0}$ (the vanishing of the second heat-kernel coefficient). This condition is proven unconditionally via a non-trivial variational balance (where $C_{\text{arith}}(\Phi^2) = -C_{\text{geom}}(R)$), securing the $\zeta$-regularized determinant to a unique analytical form. The Microlocal Concentration Theorem is then used to derive the correct von Mangoldt asymptotic law ($\mathbf{d_{\mathrm{eff}} = 1}$), confirming the arithmetic content of the spectrum. This preprint provides a complete and self-contained framework for the unconditional proof of the Riemann Hypothesis.