Proposition: A transformation can create a conflicting rule when its identity is hidden

Mix equally the original noiseless four-center task and its source-convention $90^{\circ }$ rotation, retain original labels, and withhold the transformation identity. The common observed support has two distinct equally likely labels at every point. The Bayes accuracy of this mixed task is $1/2$, although each separately declared task has Bayes accuracy one.

Proof. The $90^{\circ }$ rotation permutes the four centers with no fixed point. Each point receives its original label in one component and a different label in the rotated component, with equal probabilities.