Pairs of rough integers at distance two

Assuming Propositions 4.4 and 5.2 of Pascadi's preprint, I prove that, for all sufficiently large X, at least (c_V/600)X/(log X)^2 integers n <= X satisfy min(P^-(n), P^-(n+2)) > (X/3)40/119, where c_V = 2C_2e⁻ᵍᵃᵐᵐᵃ and C_2 is the twin prime constant. Both members of every counted pair have at most two prime factors, counted with multiplicity, and every fixed roughness exponent c < 40/119 is attained for >> X/(log X)^2 pairs. The least pair of x-rough integers above x has its first member below 3x2.975. The proof sifts a disjoint union of primes and selected semiprime boxes, combines a switched upper sieve with a second Buchstab step, and proves the upper-sieve estimate for the reconstructed weights from published sieve inputs. Interval arithmetic certifies the resulting finite-cell inequality, and a separately implemented checker certifies a second admissible choice from the same analytic formulas. A direct application of Pascadi's Proposition 4.4 and the lower linear sieve gives the benchmark c < 5/16. Ratliff's preprint claims a stronger rough Chen theorem, whose proof is not checked here; I make no priority or best-exponent claim.