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In a previous thread, someone invoked the quotient theorem. However the quotient theorem describes situations like if ## B_{\mu} C^{\mu \nu}## is a tensor whenever ## B_{\mu} ## is a tensor, then ##C^{\mu \nu}## is a tensor. This does not apply to our case, as we only know that ## S A^{\mu} ## is a tensor only when ## S = \Box##; we do not have the universal quantification necessary to invoke the quotient theorem.