A Markov Process Theory for Network Growth Processes of DAG-based Blockchain Systems

The paper’s Theorem 3 gives TH = 2 μ ∑_{k≥1} k (π_k f), where f = (0, 1, C2_3, …, C2_M) and, equivalently, TH = 2 μ ∑_{k≥1}∑_{m=2}^M k C(m,2) π_{k,m}. The proof counts, in each state (k,m), the k internal tips and the C(m,2) boundary-tip pairs, and multiplies by the per-pair approval rate μ, creating two nodes per event; see the theorem statement and proof sketch in the paper and the generator blocks with entries k C(m,2) μ for the (k,m)→(k−1,m−1) transition, which confirm the modeling of rates used in the derivation. The candidate solution derives the same formula via standard CTMC rate-averaging and arrives at the identical expression and interpretation of all factors (2, k, and C(m,2)). The modeling assumptions (Poisson arrivals λ, impatience α, per-pair exponential approval with rate μ, independence) match the paper’s model description, and the stability/positivity assumptions are consistent with the paper’s irreducibility and positive recurrence proof. Therefore, the model solution and the paper agree in substance and method. Citations: theorem and proof outline for TH (Theorem 3) , model description and assumptions , generator block showing k C(m,2) μ rates .