Abstract

This paper presents a structural reinterpretation of the Riemann Hypothesis within the Paton System framework. Rather than approaching the hypothesis as a purely analytic statement about the distribution of zeros of the Riemann zeta function, it is reframed as a constraint on admissible alignment relative to a central datum. The critical line Re(s) = 1/2 is interpreted as a zero-tolerance symmetry condition. Deviation from this line represents structural inadmissibility within the system. The paper introduces admissibility and tolerance as governing principles, where admissibility determines continuation and tolerance defines allowable deviation from constraint. The framework positions the hypothesis as a condition on structural coherence rather than solely as a problem of zero distribution. It further introduces datum dependence as a prerequisite for coherent problem formulation, highlighting that misalignment of reference frames may contribute to perceived complexity. This work does not provide a proof of the Riemann Hypothesis and does not introduce new analytic techniques. Its contribution is interpretive and structural, offering a constraint-based perspective linking symmetry, admissibility, and system stability.