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We succeed in finding all physical invariants for $A_2$ at levels $\\le 32$, for $G_2$ at levels $\\le 31$, for $C_2$ at levels $\\le 26$, and for $A_1+A_1$ at levels $k_1=k_2\\le 21$. This work thus completes a recent $A_2$ classification proof, where the levels $k=3,5,6,9,12,15,21$ had been left out. 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