can say that spin foam partition functions or transition amplitudes are about the interaction of representations of spacetime symmetry, and so, ultimately, $E_8$ can provide the network of interaction representations incorporating the usual charge symmetries $-$ but here we focus on the first step in 3 dimensions where spacetime symmetry is just $SU(2)$ and internal charge symmetry is $SU(3)$.

Both the LQG and string/M-theory programs lead to the idea of building blocks for all the fields that constitute our classical and quantum worlds, from which the question arises of how to “glue” these fundamental blocks together in an elementary and first-principles way. There have been recent efforts to use the idea of entanglement in both approaches [@EugenioNelson; @Raamsdonk]. Our recent work [@KleeCodetheoreticaxiom; @5throot] pointed out that there is a principle correlated with the physical realization of representations of Lie groups and algebras. This indicates, in accordance with the results of LQG and string theory, that quantization of spacetime must respect a special kind of quantum symmetry, implemented as a code made of a small set of representations of its symmetry group, each with specific fusion rules and syntactical degrees of freedom that express physical “observables” in the form of quantum 