The Fiber of $S{q}^n$

A colleague asked about the Adams filtrations of the homotopy classes in the homotopy of the fiber of a particular map between GEMs. The theorem proved in arXiv:2105.02601v3 [math.AT] proves to be effective in answering this (Theorem 4.4). We show that this and some related Adams spectral sequences all collapse at $E_3$ and we determine the value of $E_3=E_{\mathrm{\infty }}$. Notably, we do not need to determine the cohomology of the fiber or the $E_2$ term of the Adams spectral sequence to do this.