This contribution presents a unified theoretical framework that transfers the problem of the Riemann Hypothesis from the continuous domain of unbounded complex analysis to the deterministic simplicial geometry of integer partitions. Grounding the logical architecture in Presburger Arithmetic and Ehrhart-Macdonald reciprocity, partitions are explicitly mapped onto A₊-₁ root systems and Weyl chambers. The analytic engine of the proof is Bonelli's Kaleidoscopic Filter Theorem: by applying the coefficients of the Weyl reflections of dimension k to the infinite sequence of unrestricted partitions p (n), all lower-dimensional geometry is entirely canceled out. The result of this equation exactly quantifies the number of partitions of n formed exclusively by parts strictly greater than k. This elision of topological "noise" allows for the construction of a combinatorial Hamiltonian operator associated with the scattering of partitions. It is proven that this geometric operator is compact, strictly self-adjoint, and confined within the Schatten-von Neumann nuclear class S₁. By projecting the lattice into the spatial thermodynamic limit, the disintegration matrix analytically converges via a transition to the Fredholm determinant, which maps isomorphically onto the Weierstrass product expansion of the Riemann entire function (s). Finally, since the polarization on the primitive cohomology of the operator is strictly positive definite (by virtue of the Hodge-Riemann bilinear relations and the Hard Lefschetz Theorem), the formation of asymmetric complex eigenvalues is structurally precluded, thereby deterministically and definitively locking all non-trivial zeros onto the critical line = 1/2.
Antonio Bonelli (Mon,) studied this question.