A Twin-Prime Propagation Conjecture

I introduce a generative process on consecutive lower twin primes. Let p_n be the n-th lower twin prime and define:C_n = p_n + pₙ₊₁ + 1D_n = p_n + pₙ₊₁ + 3A pair (p_n, pₙ₊₁) is said to propagate if at least one of C_n or D_n is again a lower twin prime.Extensive computation up to 10^13 shows that the success rate declines slowly and regularly. I conjecture that infinitely many such pairs propagate. A conditional argument under the Hardy–Littlewood prime tuples conjecture is also outlined.