The Riemann Hypothesis as a Unique Coherence Fixed Point in Bounded-Capacity Variational Fields

Abstract We formulate the Riemann Hypothesis as a coherence fixed-point problem within a bounded-capacity variational field framework. The approach introduces an explicit axiomatic system, termed the Multi-dimensional Relational Optimization System (MROS), in which nontrivial zeros of the Riemann zeta function are mapped to geometric field coordinates measuring curvature deviation, reciprocity load, and equilibrium energy. Within this framework, we define an admissible arithmetic field as one satisfying area-preserving smoothing, finite compensatory capacity, and bounded equilibrium energy. We prove that, under these axioms, the configuration in which all nontrivial zeros lie on the critical line Re(s)=1/2 is the unique global coherence fixed point. Any alternative configuration leads to divergence of the equilibrium functional and violation of the bounded reciprocity constraint, rendering the field inadmissible. This result does not constitute a proof of the Riemann Hypothesis within classical ZFC number theory. Rather, it establishes that the hypothesis follows necessarily from coherence and bounded-capacity principles when arithmetic structures are treated as variational fields. The framework is mathematically explicit, computationally testable, and applicable to a broader class of L-functions.