A Hilbert-Pólya Approach to the Riemann Hypothesis via Cartan Torsion and the Weil Positivity Criterion

This repository contains the official preprint and LaTeX source code for the paper: "A Hilbert-Pólya Approach to the Riemann Hypothesis via Cartan Torsion and the Weil Positivity Criterion". Abstract:We construct a self-adjoint operator HT,disc on the multiplicative Hilbert space L^2(R_+, dx/x) whose spectrum, via the Weil explicit formula, is constrained to be real if and only if the Riemann Hypothesis holds. The operator arises naturally from a Cartan torsion field T(x) = 1/α + C/x as the unique self-adjoint extension of the Berry-Keating Hamiltonian compatible with the Haar measure structure of (R_+, ·). The singular perturbation by prime-indexed delta potentials is shown to be form-bounded via the Rellich-Kato theorem, with Sobolev constant C_S(y_p) = ln p · I_1(ln p) · K_1(ln p) → 1/2 as p → ∞. The positivity criterion of Weil (1952), formulated with a symmetric test function Φ(τ) = g(τ - γ_0) + g(τ + γ_0) to avoid Cauchy principal value artefacts, is shown to be violated by any zero off the critical line. Density of the prime delta measures in M^+(R_+) follows from the Müntz-Szász theorem combined with the Widder-Bernstein uniqueness theorem for Laplace transforms of σ-finite measures. Contents:- Martini2026_RH_Cartan_Torsion.pdf: Compiled manuscript (6 sections, including Introduction, Operational Pillars, and Technical Outlook).- Martini2026_RH_Cartan_Torsion.tex: Full LaTeX source code for verification and transparency. All commercial and intellectual rights are reserved under the authorship of Ariel Fernando Martini. Independent researcher, Buenos Aires, Argentina (ORCID: 0009-0005-1037-9741).