  We prove a conjecture of Freed and Hopkins, which relates deformation classes
of reflection positive, invertible, $d$-dimensional extended field theories
with fixed symmetry type to a certain generalized cohomology of a Thom
spectrum. Along the way, we establish several results, including the
construction of a smooth variant of the Brown--Comenetz dual of the sphere
spectrum and a calculation of the "deformation type" of the extended geometric
bordism category.
