Assume indistinguishability obfuscation (iO) and one-way functions, both secure against nonuniform polynomial-size adversaries. We show that no randomized polynomial-size pruning procedure isolates a witness with probability at least a/log L, for any constant a > 0, where L is the length of the circuit description. Dell, Kabanets, van Melkebeek, and Watanabe (DKMW) proved without cryptographic assumptions that success 2/3 + 1/poly(L) implies NP ? P/poly. Under iO alone we get the same collapse from success a/log L, and the guarantee only has to hold on nonempty affine-subspace inputs. The isolator is given no affine basis, it may use the circuit description in any way, and the obfuscator may have negligible correctness error.

The reduction hides a known affine subspace inside a larger solution space whose dimension does not depend on the scale being tested. Obfuscation then lets us compare the isolator's output, computationally, with an independent reference output. Along the way we prove an unconditional preprocessing criterion. It characterizes presentation-invariant isolation and, unless NP ? P/poly, gives common and efficiently testable witnesses that a constant-success isolator depends on the presentation. For isolators that see the target only through adaptive membership queries, we determine the optimal tradeoff between queries and success up to absolute constants. Finally, a matching restriction-law construction shows why tests on the planted region stop at the logarithmic scale.