The outer boundary sites, marked by triangles, are assigned their ground state spins (+1 in this case). The sites marked by open circles form the inner boundaries of the quadrant; their associated spin sets are labelled {σ 1,...,σ m } and {σ' 1,...,σ' m }, where σ 1 = σ' 1. There are 2 possible configurations for each inner boundary, so we define a 2 ×2 matrix entry-wise by