(I have already asked this on Math.SE, but it didn't draw much attention there, so I am reposting it here.)
Example 1.1.4 of Jacob Lurie's DAGX says that the stabilization $\operatorname{Stab}((\mathrm{CAlg}_k)_{/k})$ of the $\infty$-category of augmented $\mathbb{E}_\infty$ algebras over $k$ can be identified with the $\infty$-category of $k$-module spectra $\mathrm{Mod}_k$.
The reference mentioned there is Theorem 7.3.5.14 of Lurie's Higher Algebra. However, there is no Theorem 7.3.5.14 in (the current version of) Higher Algebra, and Lemma 7.3.5.14 is just a characterization of idempotent morphisms, so I don't think that the above identification would follow from it.
I suspect that the relevant theorem got renumbered since the writing of DAGX. Could someone point to a reference for this fact (or sketch the proof)?
