Derived-stack universal vector bundle conjecture

Let $n=\infty$, let $\mathscr{C}$ be the opposite of animated commutative rings, and let $\mathrm{St}_{\mathscr{C}}$ be the category of derived stacks. For each $X$, set

$$\mathcal{V}_X:=\underline{\mathrm{Spec}}_X\mathrm{L}\mathrm{Sym}^*(-).$$

Derived-stack universal vector bundle conjecture. These choices satisfy the assumptions introduced for the moduli stack of vector bundles and its universal vector bundle.

This conjecture is stated as future work; the supplied text gives no resolution status. A warning immediately afterward notes that, in spectral algebraic geometry, the relative spectrum of the symmetric algebra of a locally free sheaf might fail to be flat.