  Let p be a regular prime number, let Gp denote the Galois group of the
maximal unramified away from p extension of Q, and let H_et denote the
Heisenberg group over Qp with Gp-action given by H_et = Qp(1)^2 \oplus Qp(2).
Although Soul\'e vanishing guarantees that the map H^1(Gp, H_et) ---> H^1(Gp,
Qp(1)^2) is bijective, the problem of constructing an explicit lifting of an
arbitrary cocycle in H^1(Gp, Qp(1)^2) proves to be a challenge. We explain how
we believe this problem should be analyzed, following an unpublished note by
Romyar Sharifi, hereby making the original appendix to Explicit Chabauty-Kim
theory available online in an arXiv-only note.
