  We prove a recent conjecture by Harlow and Ooguri concerning a universal
formula for the charged density of states in QFT at high energies for global
symmetries associated with finite groups. An equivalent statement, based on the
entropic order parameter associated with charged operators in the thermofield
double state, was proven in a previous article by Casini, Huerta, Pontello, and
the present author. Here we describe how the statement about the entropic order
parameter arises, and how it gets transformed into the universal density of
states. The use of the certainty principle, relating the entropic order and
disorder parameters, is crucial for the proof. We remark that although the
immediate application of this result concerns charged states, the origin and
physics of such density can be understood by looking at the vacuum sector only.
We also describe how these arguments lie at the origin of the so-called entropy
equipartition in these type of systems, and how they generalize to QFT's on
non-compact manifolds.
