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Extending a Steenrod-theoretic obstruction of Karpenko, we classify the recursively defined integral Weyl invariants $q_i$ in the Benson--Wood generating set that lie in the Chow characteristic image: the only such invariant is $q_3$ for $\\Spin(10)$. We obtain the analogous classification for the recursive invariants $f_i$ of the special Clifford group $\\Gamma^+(n)$: in their finite generating range, the only such invariant is $f_2$ for $\\Gamma^+(7)$. 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Extending a Steenrod-theoretic obstruction of Karpenko, we classify the recursively defined integral Weyl invariants $q_i$ in the Benson--Wood generating set that lie in the Chow characteristic image: the only such invariant is $q_3$ for $\\Spin(10)$. We obtain the analogous classification for the recursive invariants $f_i$ of the special Clifford group $\\Gamma^+(n)$: in their finite generating range, the only such invariant is $f_2$ for $\\Gamma^+(7)$. 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