Universal Circle and Global Stability

This component introduces the Universal Circle as the limiting geometric case of the TDD “zoom mode,” representing the scale at which local structure is fully absorbed into global averaging. As the probe radius approaches the full extent of the critical strip, individual zeros cease to dominate and only persistent structural bias within the potential field remains detectable. In this universal-scale regime, the Budget Lemma (Conjecture B) attains its strongest interpretation: not merely as an analytic bound, but as a global conservation law enforced by the functional equation symmetry. Harmonic fluctuations are suppressed, cancellation mechanisms vanish, and any non-neutral density imbalance survives averaging. The Universal Circle provides the geometric resolution linking the Footprint Lemma and the Global Budget constraint. Off-critical-line singularities generate rigidity contributions that grow linearly with height, while the admissible budget grows only at the rate permitted by critical-line zero density. Because the coercive rigidity floor prevents dilution or cancellation, this imbalance propagates upward through the strip and becomes unavoidable at universal scale. Viewed from this limit, the Riemann Hypothesis emerges as a global confinement condition: the critical line is the unique neutral manifold on which logarithmic singularities may exist without destabilizing the analytic universe. What survives universal averaging is not numerical fluctuation, but structural truth.