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) = (h₁ (N) - delta (N) ) / V (N) converges to an exact rational: kappaᵢnfinity = K - SL = 97360699/1078282205 - 824622/30250451 = 300996337/4775249765= 0. 0630325850610245. The proof is modular over three previously established inputs (theh₁/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 (deltaR <= 2 pi (N^ (1/3) ) ), and the L-side densityconverges by dominated convergence over prime pairs to a telescoping sum evaluated inclosed form (SL = 824622/30250451, certified by exact rational arithmetic on twoindependent engines). Numerical corroboration includes the R-corner law to N = 10¹9 andper-pair limits to 10⁹. 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.