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I have proposed a\textit{non-Abelian}and stochastic self-organizedcriticality model in which each avalanche contains one stochastic site and allremaining sites in the avalanche are deterministic with a constant threshold$E_{c}^{I}$. Studies of avalanche structures, waves and autocorrelations, sizemoments and probability distribution functions of avalanche size, for thethresholds $4\leq E_{c}^{I}\leq256$, were performed. The shell-like avalanchestructures, correlated waves within avalanches, complex size moments andprobability distribution functions show multifractal scaling like the\textit{Abelian} and deterministic BTW model despite the fact that the model is\textit{non-Abelian}and stochastic with unbalanced relaxation rules at eachstochastic site.

Non-Abelian self-organized criticality model with one stochastic site in any avalanche shows multifractal scaling