Corollary: A valid conditional operational bridge

Fix a physical code, complete preparation, unitary deformation, and access partition. Suppose:

1. a residual subsystem or observable is justified as geometric by an independent same-model dictionary;

2. the deformation has a nonzero response witness in that observable, such as the coefficient in Theorem thm:linearresponse;

3. any claimed magic resource is independently defined and certified in the same carrier convention.

Then the certified observable responds to the declared code inputs, the complete complement is nonconstant, and exact whole-code radiation recovery is obstructed.

The magic certificate does not replace the response witness or the geometric dictionary.

Proof. The response witness and the dictionary identify the intended observable variation. Proposition prop:geometrywitness gives nonconstancy and the exact-recovery obstruction.