  We are aimed at giving a differential geometric, and accordingly physical,
explanation of the 576-periodicity of TMF. In this paper, we settle the problem
of giving the lower bound 576. We formulate the problem as follows: we assume a
spectrum $\mathrm{SQFT}$ with some conditions, suggest from physical
considerations about the classifying spectrum for two-dimensional
$\mathcal{N}=(0,1)$-supersymmetric quantum field theories, and show that the
periodicity of $\mathrm{SQFT}$ is no less than 576. The main tool for the proof
is the analogue of the Anderson duality pairing introduced by the second-named
author and Tachikawa. We do not rely on the Segal-Stolz-Teichner conjecture, so
in particular we do not use any comparison map with TMF.
