StatisticalMechanics / CONCEPT

The Yang-Baxter cellular automata over F_{2^n} have period dividing 2^n

For every finite field F of characteristic 2 and every bijection f of F satisfying f(x) + f(x + f(y)) = f(x + f(y + f(x))), the cellular automaton that runs the R-matrix R(x, y) = (y + f(x + y), x - f(x + y)) along a row of N cells with the helical boundary condition returns to its initial state after |F| steps, for every N. This proves the conjecture of A. Araoka and T. Tokihiro (arXiv:2602.17148), who proved it for |F| = 4 and 8.