The Riemann Hypothesis as a Global Structural Constraint in Object Mathematics H2

his paper studies global structural stability constraints in categorical semantics within the formalism of Object Mathematics H² (o-math/H²). A constraint inspired by the Riemann Hypothesis is introduced and formulated purely structurally as a modal condition on an internal validity predicate, using a Lawvere–Tierney topology in the internal logic of a topos. The results establish necessity, closure properties under the H² constructors, and minimality of the constraint, together with explicit counterexamples showing non-triviality. All statements are internal to a fixed axiomatic framework and are independent of analytic, arithmetic, or number-theoretic formulations of the classical Riemann Hypothesis.