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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 in \cite{Jia_2020} that the hypercube model at leadingorder in $1/d$ has the same spectral density as the double-scaledSachdev-Ye-Kitaev model. In this work we identify the set of observables thathave the same correlation functions as the double-scaled SYK (DS-SYK) model,demonstrating that the hypercube model is an equally good microscopic model fornear-AdS$_2$/near-CFT$_1$ holography. Unlike the SYK model, the hypercube modelis not $p$-local. Rather, we note that the shared feature between the twomodels is that they both have a large amount of disordered but uniform fluxeson their Fock-space graphs, and we propose this is a broader characterizationof near-CFT$_1$ microscopics. Moreover, we suggest that the hypercube model canbe viewed as the operator growth model of the DS-SYK. We explain someuniversality in subleading corrections and relate them to bulk vertices.Finally we revise a claim made in \cite{Jia_2020} about the existence of aspectral gap.

Parisi's hypercube, Fock-space fluxes, and the microscopics of near-AdS$_2$/near-CFT$_1$ duality