An exact rational limit for the canonical homological density of the sphenic dyadic-window complex

For the sphenic dyadic-window complex X(N) (vertices the primes; 2-cells the squarefreeproducts pqr in (N/2, N]; V(N) = pi(N/6)), we prove that the canonical per-vertex densitykappa(N) = (h_1(N) - delta(N)) / V(N) converges to an exact rational:kappa_infinity = K - S_L = 97360699/1078282205 - 824622/30250451 = 300996337/4775249765= 0.0630325850610245. The proof is modular over three previously established inputs (theh_1/V limit K; the rank/homology counting identity; the bulk completer rule with its octetlemma) and reduces both remaining bricks to one elementary fact, the cube-root prime bound:the R-side deficiency density vanishes (delta_R <= 2 pi(N^(1/3))), and the L-side densityconverges by dominated convergence over prime pairs to a telescoping sum evaluated inclosed form (S_L = 824622/30250451, certified by exact rational arithmetic on twoindependent engines). Numerical corroboration includes the R-corner law to N = 10^19 andper-pair limits to 10^9. Prime-side throughout: no zeta-zero data enters any construction,and nothing here bears on or assumes the Riemann Hypothesis. Published record of 10 July 2026.