The higher units conjecture for complex K-theory

Let $KU$ be complex topological $K$-theory, and for each $n\geq 0$ let $\mathbb{G}_m^n(KU)$ denote the $n$th group of higher units, with $\mathbb{G}_m^0(KU)=\operatorname{GL}_1(KU)$ and $\Omega\mathbb{G}_m^n(KU)\simeq\mathbb{G}_m^{n-1}(KU)$. Let $I_{\mathbb{Z}}$ be the Anderson dual of the sphere spectrum, and let $\mathbb{S}$ be the sphere spectrum.

Higher units conjecture. For all $n\geq 0$ there are equivalences

$$\mathbb{G}_m^n(KU)[0,n+2]\simeq{}_{n+2}I_{\mathbb{Z}}.$$

Equivalently, there are equivalences

$$I_{\mathbb{Z}}(\mathbb{G}_m^n(KU)[0,n+2])\simeq\mathbb{S}[0,n+1].$$

This extends the proposed Brauer-spectrum identification to all higher units. It is motivated by the successive delooping pattern from units to Picard and Brauer spectra, but the general equivalence remains conjectural.