Collapse with a nonsplit extension problem

Substituting the zero stalk differential into the formulas of [F3] gives every $r$-cycle numerator as $F_p$ and every denominator as $F_{p-1}$. Thus every page has ℤ/2 at (0,0) and (1,-1), zero elsewhere; [F4] makes all page differentials zero. The underlying stalk itself has homology ℤ/4 in degree zero and zero elsewhere, with the original filtration. This realizes the collapse phenomenon of [F1].

The extension is $0\to \mathbb{Z}\mathrm{/}2\stackrel{[a]\mapsto [2a]}{\to }\mathbb{Z}\mathrm{/}4\stackrel{[b{]}_4\mapsto [b{]}_2}{\to }\mathbb{Z}\mathrm{/}2\to 0$. The first map has image {0,2}, exactly the kernel of the second, and the second is onto. A section would lift 1 to 1 or 3; both double to 2≠0, contradicting the relation 1+1=0 in its source. Hence the extension is nonsplit despite collapse.