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Castellano, Ruiz, and Valenzuela recently observed a remarkable "pattern" ininfinite-distance limits of moduli spaces in quantum gravity, which relates thefield space variation of the mass of the lightest tower of particles to thefield space variation of the species scale. In this work, we show how a versionof this pattern can be proven to hold for BPS particles and strings throughoutthe vector multiplet moduli space of a 5d supergravity theory, even in regionswhere the particle masses and string tensions are substantially modifiedrelative to their asymptotic behavior in the infinite-distance limits. Thissuggests that a suitably defined version of the pattern may hold not merely inthe asymptotic limits of moduli space, but in the interior as well.

Persistence of the Pattern in the Interior of 5d Moduli Spaces