  The holographic principle suggests that regions of space contain fewer
physical degrees of freedom than would be implied by conventional quantum field
theory. Meanwhile, in Hilbert spaces of large dimension $2^n$, it is possible
to define $N \gg n$ Pauli algebras that are nearly anti-commuting (but not
quite) and which can be thought of as "overlapping degrees of freedom". We
propose to model the phenomenology of holographic theories by allowing
field-theory modes to be overlapping, and derive potential observational
consequences. In particular, we build a Fermionic quantum field whose effective
degrees of freedom approximately obey area scaling and satisfy a cosmic
Bekenstein bound, and compare predictions of that model to cosmic neutrino
observations. Our implementation of holography implies a finite lifetime of
plane waves, which depends on the overall UV cutoff of the theory. To allow for
neutrino flux from blazar TXS 0506+056 to be observable, our model needs to
have a cutoff $k_{\mathrm{UV}} \lesssim 500\, k_{\mathrm{LHC}}\,$. This is
broadly consistent with current bounds on the energy spectrum of cosmic
neutrinos from IceCube, but high energy neutrinos are a potential challenge for
our model of holography. We motivate our construction via quantum mereology,
i.e. using the idea that EFT degrees of freedom should emerge from an abstract
theory of quantum gravity by finding quasi-classical Hilbert space
decompositions. We also discuss how to extend the framework to Bosons. Finally,
using results from random matrix theory we derive an analytical understanding
of the energy spectrum of our theory. The numerical tools used in this work are
publicly available within the GPUniverse package,
https://github.com/OliverFHD/GPUniverse .
