  This work has two contributions. The first one is extending the Large
Deviation Principle for uniform hyper-graphons from Lubetzky and Zhao
\cite{lubetzky2015replica} to the multi-relational setting where each
hyper-graphon can have different arities. This extension enables the
formulation of the most typical possible world in Relational Probabilistic
Logic with symmetric relational symbols in terms of entropy maximization
subjected to constraints of quantum sub-hypergraph densities. The second
contribution is to prove the most typical constrained multi-relational
hyper-graphons (the most typical possible worlds) are computable by proving the
solutions of the maximum entropy subjected by quantum sub-hypergraph densities
in the space of multi-relational hyper-graphons are step functions except for
in a zero measure set of combinations of quantum hyper-graphs densities with
multiple relations. This result proves in a very general context the conjecture
formulated by Radin et al.\ \cite{radin2014asymptotics} that states the
constrained graphons with maximum entropy are step functions.
