Dominant vertices and attractors’ landscape for Boolean networks

The paper’s Theorem 2 proves that the window map h is a semi-conjugacy F∘h = h∘F and is injective on periodic points, via a recursive construction on I^t(U) and dominance propagation; the candidate solution rederives the same recursion and the same dominance-chain propagation (essentially Theorem 1 in the paper) to conclude injectivity on periodic cycles. Aside from minor notational differences (paper reuses F for both systems; candidate writes F_U), the arguments are the same and complete. See Theorem 2 and its proof, including the recursion and the use of Theorem 1 for part (b) .