This note complements the inspiring work on dimensional analysis and market microstructure by Kyle and Obizhaeva \cite{kyle2016dimensional}. Our main theorem shows by a similar argument as usually applied in physics the following remarkable fact. If the market impact of a meta-order only depends on four well-defined and financially meaningful variables, then -- up to a constant -- there is only one possible form of this dependence. In particular, the market impact is proportional to the square root of the size of the meta-order.
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