E zero and e one page conventions are universal across sources

Let $C_1=C_0=\mathrm{Z}$ with d=1, all other groups zero, and $F_{p}C=0$ for p<0, $F_{p}C=C$ for p≥0. Its associated graded is this nonzero two-term complex in column zero. By [F1], $E^0$ is nonzero, whereas ker(1)=0 and coker(1)=0 give $E^1=0$ by [F2] and [F4]. All subsequent pages are zero by [F3].

Every filtered piece and every graded quotient in this example has zero homology. Thus the triangle of homology groups of the filtration is the zero triangle. Here an exact couple means maps D→D→Q→D with image equal to the next kernel at every vertex; for the zero triangle every image and kernel is zero. Its differential Q→D→Q is zero, and deriving it replaces zero by im(0)=0 and H(0)=0, so every derived triangle is again zero. No general existence theorem for exact couples is used.

Vitolo, Appendix B p.33, the iteration immediately before the proposition on generic iteration, labels the input differential object of the generic exact couple $E_0$ and its first homology $E_1$. Applied to the zero triangle of step 2.1, its generic initial page $T_0$ is therefore zero. Weibel’s filtration exact-couple example and construction theorem, pp.155–156, instead label the initial homology couple term $E^1=H(\mathrm{gr}C)$. Thus the dictionary is $T_j=E^{j+1}$ on the common zero tail, while the library $E^0$ in step 1.1 is nonzero. These are actual different page-zero objects under two specified construction labels.

Vitolo's separately normalized filtered construction, the theorem on filtered differential objects pp.34–35, also inserts the associated graded at $E_0$ and agrees with the library on that point. The comparison in step 3.1 concerns its generic couple iteration only. For a nonzero homological differential, replacing r by j+1 while retaining coordinates changes its bidegree to $(-(j+1),j)$, not $(-j,j-1)$; the definition [F3] therefore requires the convention and grading translation to be stated together. In the displayed zero tail no degree conflict arises.