Complement proximity is an upper certificate

The information–disturbance theorem of Kretschmann, Schlingemann, and Werner, converted to the half-diamond normalization used here, gives

This is an external mathematical theorem, not a gravitational input KSW. It expresses the fact that a nearly input-independent complete environment permits a nearly reversible accessible channel. It must not be confused with the accessible-output lower bound (eq:featureless-lower). The same directional distinction is retained in En07-B and En07-C CheungEn07B,CheungEn07C.