Goodwillie–Whitehead conjecture: weak form

Let $E_r^{k,t}(S^1)$ denote the pages of the Goodwillie spectral sequence (GSS) for $S^1$. Goodwillie–Whitehead conjecture, weak form. The GSS for $S^1$ collapses at the $E_2$-page. This is stated as a consequence of the strong form and is the spectral-sequence formulation of the calculus version of the Whitehead conjecture. The source gives no resolution of this weak form.