The min-partition rank method cannot prove superpolynomial mABP lower bounds, as polynomial-size mABPs compute full-rank multilinear polynomials; this follows from proving N(n) = n^{O(1)} for 1-balanced-chain set systems via biased random walks and supermartingales.
Lower bounds for set-multilinear branching programs
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An Unconditional Barrier for Proving Multilinear Algebraic Branching Program Lower Bounds
The min-partition rank method cannot prove superpolynomial mABP lower bounds, as polynomial-size mABPs compute full-rank multilinear polynomials; this follows from proving N(n) = n^{O(1)} for 1-balanced-chain set systems via biased random walks and supermartingales.