Compare direct control against two hybrid loops on the same bounded task. The lab separates three effects: pair acquisition, ambiguity removed before control, and the size of the remaining controller.
The direct controller starts here, on all nonempty omission sets at once.
The hybrids first buy pair witnesses. This is the only up-front cost they pay.
All non-singleton omissions are settled before the residual controller even begins.
The remaining controller acts only on singleton residue, either linearly or logarithmically.