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Reason about repeat-stable iteration

The learner can use F(F(x)) = F(x) to prove that every positive iterate equals F(x), then combine repeat-stability with a supplied concrete undo or reversibility condition to determine when F must be the identity.

1 published problem

1. The Machine That Repeats Forever — Follow Rook's multiplication machine through any positive number of passes, then use reversibility to determine its hidden whole-number multiplier.