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   We study the black hole information problem within a semiclassicallygravitating AdS _d d black hole coupled to and in equilibrium with a d d -dimensionalthermal conformal bath. We deform the bath state by a relevant scalardeformation, triggering a holographic RG flow whose "trans-IR"region deforms from a Schwarzschild geometry to a Kasner universe. Thesetup manifests two independent scales which control both the extent ofcoarse-graining and the entanglement dynamics when counting Hawkingdegrees of freedom in the bath. In tuning either, we find nontrivialchanges to the Page time and Page curve. We consequently view the Pagecurve as a probe of the holographic RG flow, with a higher Page timemanifesting as a result of increased coarse-graining of the bath degreesof freedom. 

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   We describe a correspondence between the infinitesimal deformations of a periodic bar-and-joint framework and periodic arrangements of quadrics. This intrinsic correlation provides useful geometric characteristics. A direct consequence is a method for detecting auxetic deformations, identified by a pattern consisting of homothetic ellipsoids. Examples include frameworks with higher crystallographic symmetry. 

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