Priority restraint ($r\in \mathbb{N}$)

A priority restraint protects finitely many oracle answers by requiring lower-priority enumerations to avoid positions below a numerical bound. Higher-priority action can cancel the priority restraint by initializing its owner. After the last such injury, the protected computation is permanent.

An oracle computation queries only finitely many positions. If the oracle remains unchanged below its use, the same computation has the same output. In a finite-injury priority construction, a successful requirement imposes this bound on lower priorities; the induction that higher priorities stop acting then makes the disagreement permanent.