= Sparse injectivity
A <linear map> is injective on the class of <sparse vectors> of order $s$ exactly when its <null space> contains no nonzero <vector> with at most $2s$ nonzero entries. Differences of two sparse <vectors> have at most $2s$ active coordinates. Conversely, splitting the <support of a vector> of a $2s$-sparse null <vector> into two parts constructs two distinct $s$-sparse <vectors> with the same image. The strict <null space property> implies sparse injectivity by applying it to both parts of such a split.
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