A Conditional Set-Theoretic Reduction of the Riemann Hypothesis and the Generalized Riemann Hypothesis in ZFC

This paper formulates a conditional reduction of the Riemann Hypothesis and the Generalized Riemann Hypothesis within ZFC set theory. Starting from the reflection symmetry of completed L-functions, it associates to any hypothetical off-critical zero configuration a bilateral system together with finite power-set encodings, yielding a strictly descending chain of subsets compatible with analytic refinement. The paper shows that if the resulting tail admits membership realization in the set-theoretic sense, then the assumed off-critical configuration is incompatible with the axiom of regularity. In this way, RH and GRH are reduced to a final set-theoretic realization statement rather than claimed unconditionally. A parallel Lean 4 formal companion is provided for the abstract steps used in the main text.