Grammar of admissible mosaics for the two-dimensional spatiotemporal cat

Describe and characterize the admissible symbol mosaics for the two-dimensional spatiotemporal cat lattice field theory defined by (−Δ+μ^2)ϕ_z = n_z with ϕ_z ∈ [0,1), providing a complete grammar analogous to the known one-dimensional case.

Background

Mosaics are symbolic encodings labeling lattice-site intervals that serve to organize and visualize spatiotemporal periodic states. A covering grammar accelerates enumeration by discarding inadmissible mosaics a priori.

While the one-dimensional temporal case has a known grammar, the admissible mosaics for the two-dimensional spatiotemporal cat remain to be established, limiting systematic orbit enumeration.