The infinitely categorified absolute Galois group conjecture for the real numbers

The field $bb R$ has an absolute Galois group whose categorification is related to the extension of real vector spaces by complex super vector spaces. The paper proposes an infinitely categorified absolute Galois group conjecture. There is an infinitely-categorified version of commutative algebra, and in it the “infinitely categorified absolute Galois group” of $bb R$ is $\mathrm O(\infty)$. This extends the paper's categorification of the absolute Galois group of $bb R$ from $pi_{\leq 1}\mathrm O(\infty)$ to the full orthogonal group. The claim is presented as a conjectural direction rather than a result.