Global Geometric Structure in Earth Systems: Statistical Tests of High-Symmetry Spherical Grids Against Geophysical Data

We investigate whether large-scale geophysical features on Earth exhibit statistically significant alignment with fixed, high-symmetry spherical point sets. Using a unified computational framework, we test alignments between spherical grids derived from random projections of the ($E_8$) lattice and five independent global datasets: volcanoes, earthquake epicenters, tectonic plate boundaries, mid-ocean ridges, and mantle hotspot centers. For each dataset, we perform a two-stage global orientation search over three rotational degrees of freedom and quantify alignment using the root-mean-square great-circle distance to the nearest grid vertex. Statistical significance is assessed using matched null models that explicitly control for orientation-search optimization, including Haar-uniform ($\mathrm{SO}(3)$) rotation nulls, matched best-of-search nulls, and latitude-preserving longitude randomizations. Robustness is further evaluated through grid-resolution sensitivity tests, bootstrap resampling, domain-specific hotspot partitioning, and ridge-network perturbations. We find a clear hierarchy of alignment strength across datasets. Tectonic plate boundaries provide the strongest and most robust signal, remaining significant under all tested nulls. Mid-ocean ridges also show statistically significant and stable alignment, including under ridge-network perturbations. Earthquake epicenters exhibit weaker but repeatable alignment, while volcanoes do not remain significant once search bias is fully controlled. Mantle hotspots display domain-dependent behavior: pooled global analyses are weak, whereas Indo–Atlantic and Pacific subsets show significant alignment that disappears under cross-domain testing. These results indicate that certain Earth systems, particularly those governed by global-scale network geometry, exhibit non-random affinity with highly symmetric spherical grids. The framework provides a conservative and reproducible approach for testing large-scale geometric organization in Earth and planetary datasets.