Evaluating geometric interval midpoints across Base-3 boundaries $(3^{x-1}, 3^x]$ yields $y_{\text{mid}}(x) = \sqrt{3^x \cdot 3^{x-1}} = 3^{x - 1/2}$[span_18](start_span)[span_18](end_span). The exponent shift of exactly $-1/2$ provides a geometric analogy to the classical Riemann critical line $\sigma = 1/2$[span_19](start_span)[span_19](end_span).
To stabilize infinite series without exponential divergence, the system incorporates a bounded trinary phase clock $e^{i 2\pi x / 3}$[span_20](start_span)[span_20](end_span). Rotating smoothly around the complex unit circle, it embeds Base-3 geometry while inheriting functional reflection symmetry $\Xi(s, t) = -\Xi(1 - s, -t)$[span_21](start_span)[span_21](end_span).
This graph renders the magnitude envelope $|\Xi(\sigma + i\tau)|$ across real power states $\sigma \in [0.1, 0.9]$[span_22](start_span)[span_22](end_span). The continuous potential curve forms a symmetric global variance minimum locked precisely at $\sigma = 0.5$[span_23](start_span)[span_23](end_span).