Bekenstein bound in the Wolfram model

There have been some questions concerning the expression of the holographic principle in the Wolfram Model. I asked the question in private, and I received the following answer (I will omit names):

We’ve generally believed that the holographic principle is related to
taking spacetime vs. branchtime projections of the multiway causal
graph.

I recall some definitions from the glossary

Branchtime: The analog of spacetime, but for branchial space, and
time. Branchtime is related to the continuum limit of the multiway
graph.

Multiway Causal Graph: A graph giving the causal relationships between
events that generate states in a multiway system from other states.
Edges in the multiway graph can connect both spacelike and branchlike
separated events. In a causal invariant system, the multiway causal
graph factors into many isomorphic spacetime causal graphs.

Any suggestion to prove Bekenstein bound following this approach? A complete proof would be the optimal answer :wink: