A Proposed Operator-Theoretic Framework for the Riemann Hypothesis

We introduce an operator-theoretic framework on the adèle class space L^2(\mathbb{A}_\mathbb{Q}/\mathbb{Q}^\times) that interprets certain classical features of the Riemann zeta function in terms of truncated projections and Sonin-type spaces. Building on the Connes–Consani–Moscovici approach to the Weil explicit formula, Riemann’s bilinear relations for complex tori, Hardy’s theorem on zeros of the zeta function, and the Rodgers–Tao theorem on the de Bruijn–Newman constant, we propose that the Riemann Hypothesis may be viewed as a spectral self-consistency condition for a family of adèlic truncation operators. We analyze the possibility of a proof of the Riemann Hypothesis. We formulate a precise set of equivalences, one conjecture stated in falsifiable form, and open analytic problems whose resolution would imply the Hypothesis within this framework. An appendix records informal numerical experiments motivating the conjecture