  We argue that if ultrahigh-energy (E > 10^10 GeV) cosmic rays are heavy
nuclei (as indicated by existing data), then the pointing of cosmic rays to
their nearest extragalactic sources is expected for 10^10.6 < E/GeV < 10^11.
This is because for a nucleus of charge Ze and baryon number A, the bending of
the cosmic ray decreases as Z/E with rising energy, so that pointing to nearby
sources becomes possible at highest energies. In addition, the maximum energy
of acceleration capability of the sources grows linearly in Z, while the energy
loss per distance traveled decreases with increasing A. Each of these two
points tend to favor heavy nuclei at the highest energies. The traditional
bi-dimensional analyses, which simultaneously reproduce Auger data on the
spectrum and nuclear composition, may not be capable of incorporating the
relative importance of these phenomena. In this paper we propose a
multi-dimensional reconstruction of the individual emission spectra (in E,
direction, and cross-correlation with nearby putative sources) to study the
hypothesis that primaries are heavy nuclei subject to GZK photo-disintegration,
and to determine the nature of the extragalactic sources. More specifically, we
propose to combine information on nuclear composition and arrival direction to
associate a potential clustering of events with a 3-dimensional position in the
sky. Actually, both the source distance and maximum emission energy can be
obtained through a multi-parameter likelihood analysis to accommodate the
observed nuclear composition of each individual event in the cluster. We show
that nucleus-emitting-sources exhibit a cepa stratis structure on Earth which
could be pealed off by future space-missions, such as POEMMA. We also show that
metal-rich starburst galaxies are highly-plausible candidate sources, and we
use them as an explicit example of our proposed multi-dimensional analysis.
