Fibonacci fusion Hilbert space interpretation. In Section \[sec:unification\] we discuss the coupling of the model with internal $SU(3)$ symmetries and suggest a natural extension to the larger $SU(N)$, $G_2$, and $E_8$, with the same fifth root of unity deformation, and compute some observables. We present our conclusions in Section \[sec:conclusion\].

Spin Foam Code or Sum Over Quantum Computations {#sec:spinfoam}
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Following [@Rovelli-Vidotto-Book], mainly chapters 5 and 6, we consider a discretization of spacetime in terms of a triangulation ($\triangle$) and its dual 2-complex ($\triangle$\*). A three-dimensional triangulation is given by tetrahedrons, triangles, segments and points. For a four-dimensional triangulation, we include the 4-simplex. The dual 2-complex in three-dimensional (3D) bulk is made by associating a tetrahedron with a vertex, a triangle with an edge, and a segment with a face. On the boundary the dual of triangles are nodes and segments are links. In four dimensions (4D), the dual of a 4-simplex is a vertex, the dual of a tetrahedron is an edge and the dual of a triangle is a face. The boundary graph and terminology are equal to 3D. The gauge group of symmetry is $SU(2)$ in 3D, the covering group of the rotation group $SO(3)$, and $SL(2,C)$ 