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Abstract In the anisotropic random geometric graph model, vertices correspond to points drawn from a high‐dimensional Gaussian distribution and two vertices are connected if their distance is smaller than a specified threshold. We study when it is possible to hypothesis test between such a graph and an Erdős‐Rényi graph with the same edge probability. If is the number of vertices and is the vector of eigenvalues, Eldan and Mikulincer, Geo. Aspects Func. Analysis: Israel seminar, 2017 shows that detection is possible when and impossible when . We show detection is impossible when , closing this gap and affirmatively resolving the conjecture of Eldan and Mikulincer, Geo. Aspects Func. Analysis: Israel seminar, 2017. 

Abstract Earth’s inner core exhibits strong seismic anisotropy, often attributed to the alignment of hexagonal close‐packed iron (hcp‐Fe) alloy crystallites with the Earth’s poles. How this alignment developed depends on material properties of the alloy and is important to our understanding of the core’s crystallization history and active geodynamical forcing. Previous studies suggested that hcp‐Fe is weak under deep Earth conditions but did not investigate the effects of the lighter elements known to be part of the inner core alloy. Here, we present results from radial X‐ray diffraction experiments in a diamond anvil cell that constrain the strength and deformation properties of iron‐nickel‐silicon (Fe–Ni–Si) alloys up to 60 GPa. We also show the results of laser heating to 1650 K to evaluate the effect of temperature. Observed alloy textures suggest different relative activities of the various hcp deformation mechanisms compared to pure Fe, but these textures could still account for the theorized polar alignment. Fe–Ni–Si alloys are mechanically stronger than Fe and Fe–Ni; extrapolated to inner core conditions, Si‐bearing alloys may be more than an order of magnitude stronger. This enhanced strength proportionally reduces the effectivity of dislocation creep as a deformation mechanism, which may suggest that texture developed during crystallization rather than as the result of postsolidification plastic flow.