K-theoretic refinement conjecture for the dimensional reduction of a 1-2-3 theory

Let $F'$ be the dimensional reduction of a 1-2-3 theory $F$, and let $K$ denote $K$-theory, viewed as an $E^{\infty}$ ring spectrum. K-theoretic refinement conjecture. The dimensional reduction $F'$ is defined over $K$. Thus the integral refinement should be enhanced from abelian groups to a theory with values in $K$-modules. This is presented as a refinement of the conjecture that $F'$ is defined over $\mathbb{Z}$, motivated by the role of stable homotopy theory and $K$-theory; the source does not report a proof.