The case
A30: “Take a classical system with two states, represented by a probability vector p. Consider two stochastic update matrices: A = [[1,1],[0,0]], B = [[0,0],[1,1]]. A resets the system to state 1; B resets it to state 2. Then AB = A, BA = B, so AB ≠ BA. Yet this system is entirely classical.”
What it can show
That order dependence, and noncommuting operations, do not imply nonclassical probability (CLAIM-073, CLAIM-041). The manuscript §9 keeps the conclusion (“Generally AB≠BA even in a finite classical Markov system”) without the example.