  In a previous work [A simplified Parisi Ansatz, Franchini, S., Commun. Theor.
Phys., 73, 055601 (2021)] we introduced a simple method to compute the Random
Overlap Structure of Aizenmann, Simm and Stars and the full-RSB Parisi formula
for the Sherrington-Kirckpatrick Model without using replica theory. The method
consists in partitioning the system into smaller sub-systems that we call
layers, and iterate the Bayes rule. A central ansatz in our derivation was that
these layers could be approximated by Random Energy Models of the Derrida type.
In this paper we analyze the properties of the interface in detail, and show
the equivalence with the Random Energy Model at any temperature.
