An EMA-based coherence statistic for structured sequences: benchmarks on zeta-zero spacings, sampled trajectories, and a simulated response assay

We introduce a fixed exponential-moving-average (EMA) coherence statistic for detecting local ordering structure in sequential data after transformation into a phase-native coordinate. The method maps a sequence to a cumulative addressability variable ϕ\phiϕ, normalizes local gaps δ\deltaδ, and applies an EMA with fixed α=0.01\alpha = 0.01α=0.01 to cos⁡(2πδ)\cos(2\pi\delta)cos(2πδ), yielding a bounded local coherence measure CCC and an associated lock metric dij=−log⁡(C+10−12)d_{ij} = -\log(C + 10^{-12})dij=−log(C+10−12). We evaluate the probe across four roles: a positive benchmark on unfolded Riemann zeta zero spacings, a negative control on sampled Collatz trajectories, an exploratory EEG motor-task case study, and a response-level simulation assay derived from a reduced ribosome cusp-fold model. On Odlyzko’s first 2×1062\times10^62×106 zeta zeros, the probe produces a reproducible decay pattern and clear separation from shuffled controls, indicating sensitivity to non-random local ordering under a fixed construction. Sampled Collatz trajectories do not reproduce this behavior, providing an explicit failure-mode control. In EEG, the final retained comparison does not support a reliable classical contralateral motor-imagery lateralization effect; instead, the pattern is more consistent with a bilateral or global task-state shift. In a ribosome response-level assay, the probe strongly separates simulated R(ϕ)R(\phi)R(ϕ)-derived increments from shuffled surrogates, consistent with sensitivity to structured branch-separated transitions, while remaining a methods-aligned simulation check rather than a standalone biological confirmation. Taken together, these results support the EMA coherence statistic as a descriptive probe of local ordering structure whose scope can be tested directly through benchmarks, controls, and transparent artifact analysis.