Set q=28*2^44*H^12, n=q²/28. With U=N*B*12^r*(3q)^(7r)*2^(15q)*r!/(7r)!, prove K*U<=(2^88*H^24/r)^r<=28^(-r)<=1/4 for n<=r<q². Intermediate contracts: 4q^8<=2^(10r), q^(10r)<=(28r)^(5r), 2^55*3^11*7^5<=2^88. Never expand the auxiliary matrix at this bound.
Method: native-order. Induction: none. Risk: critical.
This is a human-readable planning contract, not a parsed kernel formula or accepted proof.