  Parisi's hypercube model describes a charged particle hopping on a
$d$-dimensional hypercube with disordered background fluxes in the large $d$
limit. It was noted previously [Jia and Verbaarschot, J. High Energy Phys. 11
(2020) 154] that the hypercube model at leading order in $1/d$ has the same
spectral density as the double-scaled Sachdev-Ye-Kitaev (DS-SYK) model. In this
work we identify the set of observables that have the same correlation
functions as the DS-SYK model, demonstrating that the hypercube model is an
equally good microscopic model for near-AdS$_2$/near-CFT$_1$ holography. Unlike
the SYK model, the hypercube model is not $p$-local. Rather, we note that the
shared feature between the two models is that they both have a large amount of
disordered but uniform fluxes on their Fock-space graphs, and we propose this
is a broader characterization of near-CFT$_1$ microscopics. Moreover, we
suggest that the hypercube model can be viewed as the operator growth model of
the DS-SYK model. We explain some universality in subleading corrections and
relate them to bulk vertices. Finally, we revise a claim made the
aforementioned reference about the existence of a spectral gap.
